{"as_of":"2026-08-08T21:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8dcb9de427a66caa026774d021276cb2a3083195e0213c7b5059d27babad352e","coverage":[{"denominator":71,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":71,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T00:44:05.545752Z","state":"measured"},{"denominator":71,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":71,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.14944/citation-record","integrity":"/paper/2607.14944/integrity","json":"/paper/2607.14944/citation-record.json","paper":"/paper/2607.14944"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.318853Z","title":"On the formulation of rheological equations of state","venue":null,"work_id":null,"year":1950},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.318853Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:2e392c85bebddd101b5d4d29825ecc2b4136929db0fd7cc6dbb27c18ab77ae42","observation_id":"20efb9df-d6df-40a4-a24a-ad9f9868c289","resolution":{"observed_at":"2026-08-02T00:44:05.318853Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.323400Z","title":"A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.323400Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:975d8b24e65c6fd91cef40caef639b65fe80027f0becc1448ac34f851a790285","observation_id":"875a065e-58ad-4478-b6ac-9e64aeda5117","resolution":{"observed_at":"2026-08-02T00:44:05.323400Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.327386Z","title":"A new constitutive equation derived from network theory","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.327386Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:b6413fcd9a259e2e794d73c2ec39646149ca731287eb2278a5750aab37106ff6","observation_id":"fd30e293-9031-435c-93ff-c7abbab91d47","resolution":{"observed_at":"2026-08-02T00:44:05.327386Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.331291Z","title":"Generalized viscoelastic models: their fractional equa- tions with solutions","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.331291Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:1f99d62074bdff0f5f6ea756f1e3c62afb0f1a484d20ce989fefd54f0c211e28","observation_id":"d3ba9bd2-4f17-45a3-b139-c0ad0d7efac2","resolution":{"observed_at":"2026-08-02T00:44:05.331291Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.335854Z","title":"Numerical simulation of non-linear elastic flows with a general collocated finite-volume method","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.335854Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:2e2adc8123e5bf198b713cf33067a4f2ae7bc7ab84a8b687151c91b2cd515012","observation_id":"ceebd949-6967-450a-b84f-b71ee4dcc8e0","resolution":{"observed_at":"2026-08-02T00:44:05.335854Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.339233Z","title":"Stabilization of an open-source finite-volume solver for viscoelastic fluid flows","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.339233Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:e0fc180bb573ef85039ec9a285c2ce9b255d7e67095dd73529698e15345005d3","observation_id":"1d17ae38-ae4f-478b-a64f-cd7df936fae3","resolution":{"observed_at":"2026-08-02T00:44:05.339233Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.342387Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.342387Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:c40078395be7636ecd5752026b3f01702fa404481dab330dd58c3c3c4013ee97","observation_id":"8baced88-494e-49ee-a6a5-c7cec248e044","resolution":{"observed_at":"2026-08-02T00:44:05.342387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.345146Z","title":"Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.345146Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:5ff0d2f6e8a13b6f9a8091f4989583405db372996204f669f495a03e6178ff65","observation_id":"9e7e4289-b971-4017-b646-34f0337121af","resolution":{"observed_at":"2026-08-02T00:44:05.345146Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.347779Z","title":"nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.347779Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:d7aca8003559d0e8c2233e378e180a7460a3c6b511ea5823e421af3efb7a905c","observation_id":"12837eb1-b0ae-4986-8d73-d9c621b0c6a3","resolution":{"observed_at":"2026-08-02T00:44:05.347779Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.350675Z","title":"RheologyNet: A physics-informed neural network solution to evaluate the thixotropic properties of cementitious materials","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.350675Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:d80bbf05b5a9cd44d8b2169c51a9067b0403ec6cc2bdbf2735321f2903fda01e","observation_id":"835c8507-380a-4679-8f09-cbd0a800d67d","resolution":{"observed_at":"2026-08-02T00:44:05.350675Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.353360Z","title":"ViscoelasticNet: A physics informed neural network framework for stress discovery and model selection","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.353360Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:5d9a754e3aec5ceaf5aecb25aefa6b14dc806228d10eba0e8644920126af1f15","observation_id":"42b39c86-476c-4e6d-bddc-25b5c6d503be","resolution":{"observed_at":"2026-08-02T00:44:05.353360Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.356474Z","title":"Data-driven selection of constitutive models via rheology- informed neural networks (RhINNs)","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.356474Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:bb1efc143f46780986e687ad098f87a3a5eb396e885e753b7cd6d63d3c5643dc","observation_id":"63892244-d7f6-4bcf-9b9b-d571e3c36c1a","resolution":{"observed_at":"2026-08-02T00:44:05.356474Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.359069Z","title":"Data-driven constitutive model of complex fluids using recurrent neural networks","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.359069Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:c49e96a7fd8e83b436466bdde92c07edbbc52e0f0501dca87c82b5e11bb73839","observation_id":"1f9d83f7-de90-42d0-81aa-5d1f09c8684a","resolution":{"observed_at":"2026-08-02T00:44:05.359069Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.363143Z","title":"Recurrent neural networks (RNNs) learn the constitutive law of viscoelasticity","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.363143Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:7776a33365377b7fd56760bc44997a142e2f5faad722a4201e351e3b93dd3ed6","observation_id":"6018f25f-15ff-44c9-a2ea-ea8fc5536899","resolution":{"observed_at":"2026-08-02T00:44:05.363143Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.366211Z","title":"One test to predict them all: Rheological characterization of complex fluids via artificial neural network","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.366211Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:8fb99d68ab706818f41c6cfff79c4d53acedd0df7cc624d21271512bca555262","observation_id":"3eb5af35-6000-4452-a70d-ad5787c03f6b","resolution":{"observed_at":"2026-08-02T00:44:05.366211Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.368822Z","title":"RheOFormer: A generative transformer model for simulation of complex fluids and flows","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.368822Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:341c365d5e63bcd7e7b1815ffd429eee223edb27f9da54e55bcc495200271d28","observation_id":"dd8c2bc6-6ed7-4451-b605-b971aab74541","resolution":{"observed_at":"2026-08-02T00:44:05.368822Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.372336Z","title":"Rheo-SINDy: Finding a constitutive model from rheological data for complex fluids using sparse identification for nonlinear dynamics","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.372336Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:5a5a2b3d55150d4d35382d918db46ac485f2d685572d6f5933f7d040c32a6217","observation_id":"01a8bfe0-c780-4f09-afd6-ac8aa744f6ac","resolution":{"observed_at":"2026-08-02T00:44:05.372336Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.375540Z","title":"Sparse regression for discovery of constitutive models from oscillatory shear mea- surements","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.375540Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:5982281f17649e4f6de35f4c074dc19a1a4e2a1238c92668dcbd96d717675dc5","observation_id":"109b6db4-7d28-492f-b2ea-9ea213c8b024","resolution":{"observed_at":"2026-08-02T00:44:05.375540Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.378166Z","title":"Hammering at the entropy: a GENERIC- guided approach to learning polymeric rheological constitutive equations using PINNs","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.378166Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:d5620a8bbbc58e950381a23bbc74aac02acc695b4b73b634ee9e5426f541093b","observation_id":"105ca4cd-5140-4628-87ab-afa9fae3d09b","resolution":{"observed_at":"2026-08-02T00:44:05.378166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.380839Z","title":"Cfd-Nn Coupling for the Simulation of Complex Fluids","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.380839Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:604005634570300d8920dafa126a852f183234c60f564e5b42b6e6f06ec07c14","observation_id":"ab4e2935-3930-4ae0-bfee-5ded36109f7f","resolution":{"observed_at":"2026-08-02T00:44:05.380839Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.383356Z","title":"Scientific machine learning for modeling and simulating complex fluids","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.383356Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:51a4012e0b83dffc3faec254f812732f596d3a3ac879968d91e333a970012086","observation_id":"a0c4cd9f-56f9-4b24-8132-0d743409960c","resolution":{"observed_at":"2026-08-02T00:44:05.383356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.386319Z","title":"Learning constitutive models and rheology from partial flow measurements","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.386319Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:ca89dc67941bb5931c49ed980c879402214bc78220c397a06026c94a536067a5","observation_id":"05aa3326-73fb-4a9c-b7c6-2f8b1e67efbc","resolution":{"observed_at":"2026-08-02T00:44:05.386319Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.388880Z","title":"Unbiased construction of constitutive relations for soft materials from experiments via rheology-informed neural networks","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.388880Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:df2b3bcf32b218eb98dadca62572473edc4faef42ee358eebd369d9e94aaf33e","observation_id":"eeca90c3-661d-48c2-a338-8da949f63cd2","resolution":{"observed_at":"2026-08-02T00:44:05.388880Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.391922Z","title":"Learning a family of rheological constitutive models using neural operators","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.391922Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:a965a5a135109a306ad0334e7a4a83c01da8f41f6c1230c188d36ac45c0464cc","observation_id":"e4e9a1af-428e-4c9d-9eec-b375e8b151a9","resolution":{"observed_at":"2026-08-02T00:44:05.391922Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.394757Z","title":"Data- driven physics-informed constitutive metamodeling of complex fluids: A multifidelity neural network (MFNN) framework","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.394757Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:c6334fbac0d8a72ba41352fe6322e32cca127f3ed1a0fbc0df62c011a6ea68fb","observation_id":"1d92369a-0162-4790-94b1-2b950f703a24","resolution":{"observed_at":"2026-08-02T00:44:05.394757Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.398204Z","title":"Machine learning for viscoelastic constitutive model identification and parameterisation using large amplitude oscillatory shear","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.398204Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:6d9ae7dc173e471272e62210ef9a49ea33635fe245d36cc511d5936c4080e078","observation_id":"13a904c0-24dd-4ab1-a9a1-4379980758c7","resolution":{"observed_at":"2026-08-02T00:44:05.398204Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.402020Z","title":"Digital rheometer twins: Learning the hidden rheology of complex fluids through rheology-informed graph neural networks","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.402020Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:3b5f248fc2a27e5433df2875cad0498a7b7021548b90fa3f710d952a1db31c92","observation_id":"8f5a4270-af5a-4244-a095-4e417f9cf294","resolution":{"observed_at":"2026-08-02T00:44:05.402020Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11833","last_updated":"2024-05-07T14:04:16Z","snapshot_observed_at":"2026-07-06T15:57:08.701922Z","submitted_at":"2023-07-21T18:06:27Z","title":"PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.11833","snapshot_observed_at":"2026-08-02T00:44:05.405259Z","title":"Pinnsformer: A transformer-based framework for physics-informed neural networks","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.405259Z"},"links":{"cited_paper":"/paper/2307.11833","citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:c770635996ca0f27df7254726bd717215d032c9f2799b1c45ce0c09f1c1f2fd8","observation_id":"6183cf8b-4dc3-4209-8b53-ee911760b0db","resolution":{"observed_at":"2026-08-02T00:44:05.405259Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.409348Z","title":"Attention is all you need","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.409348Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:c9b2be9823f828a9b40536810982f1b4e98e4d714f158e9a275e351c748af63b","observation_id":"19f6c6c1-6621-4d3b-9e04-43a22dad2281","resolution":{"observed_at":"2026-08-02T00:44:05.409348Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.08895","last_updated":"2021-05-17T03:12:33Z","snapshot_observed_at":"2026-07-06T10:05:26.653366Z","submitted_at":"2020-10-18T00:34:21Z","title":"Fourier Neural Operator for Parametric Partial Differential Equations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.08895","snapshot_observed_at":"2026-08-02T00:44:05.412334Z","title":"Fourier neural operator for parametric partial differential equations","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.412334Z"},"links":{"cited_paper":"/paper/2010.08895","citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:ca1dbc94195730b13b136abb9312c9d9b5fe102a7d0b3dd591d5ab5857e5c878","observation_id":"e0f15e43-e5c1-49a4-ae64-124533f5a712","resolution":{"observed_at":"2026-08-02T00:44:05.412334Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.416211Z","title":"A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.416211Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:041ccdda7cb9f38da0b88791e26fdb14a56e6b709e9bc9a69564e188176c673a","observation_id":"a3a6b7af-eea7-4319-8590-9738a80f90fa","resolution":{"observed_at":"2026-08-02T00:44:05.416211Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.419006Z","title":"Multiscale simulations for viscoelastic fluids with approximate constitutive models derived by a sparse identification method","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.419006Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:73759efc01cc530503a58e7f3141f9478e5e33311f944b7c7f195cad48c55498","observation_id":"bb0abb20-a9ab-499d-8c9a-56a28d26263b","resolution":{"observed_at":"2026-08-02T00:44:05.419006Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.421939Z","title":"A survey on the application of machine learning in turbulent flow simulations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.421939Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:c769f89c041d0bc199d3e3629d353265173f70959bc6af3092ffaf5a67b1d255","observation_id":"b559cd14-d59b-49c4-9b7c-5fd40b63453d","resolution":{"observed_at":"2026-08-02T00:44:05.421939Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.424499Z","title":"Reynolds averaged turbulence modelling using deep neural networks with embedded invariance","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.424499Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:6d78d829b771dd48498cf78312a532277d86f40f31bbd252d2db2cf990792abe","observation_id":"0c10bd89-0d1c-470d-ab3e-aad5db05de01","resolution":{"observed_at":"2026-08-02T00:44:05.424499Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.427619Z","title":"Finding the underlying viscoelastic constitutive equation via universal differential equations and differentiable physics","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.427619Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:64835a2cfc009401edbd1150e1f2c186ab298d73115b861e44b12146e9d2cc89","observation_id":"d416314f-bda1-4de2-846e-c91d216ad6c2","resolution":{"observed_at":"2026-08-02T00:44:05.427619Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.431150Z","title":"Discovering governing equations from data by sparse identification of nonlinear dynamical systems","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.431150Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:ee9afa76fc6da324b542228a146f7c960ca31098f8dedeedd2359f7460412a55","observation_id":"a9abe52f-5065-401e-97c6-55855e53e533","resolution":{"observed_at":"2026-08-02T00:44:05.431150Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.434060Z","title":"On the high Weissenberg number problem","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.434060Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:829bde34af9144b6abde7d6509e5d61baece879987a8429510a5a990b80bbab3","observation_id":"23a07fdc-4f84-4704-bf69-36817256dd1f","resolution":{"observed_at":"2026-08-02T00:44:05.434060Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.437011Z","title":"The log-conformation tensor approach in the finite-volume method framework","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.437011Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:1fdc6d483027ccc4e6636cac85074981fcc00096ae8b0578a6f45ecae3aef994","observation_id":"bf279cdc-64fd-40f1-94ed-b802f1a54256","resolution":{"observed_at":"2026-08-02T00:44:05.437011Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.439691Z","title":"Numerical methods for viscoelastic fluid flows","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.439691Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:9c9724d3b36e1a38cc12e03a1cca4514d73ba71ac81e46e16e968ac2a4b0eaa7","observation_id":"bdd866aa-1054-493f-bb28-5c060a86b7a7","resolution":{"observed_at":"2026-08-02T00:44:05.439691Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2001.04385","last_updated":"2021-11-02T12:06:44Z","snapshot_observed_at":"2026-08-08T03:57:24.280922Z","submitted_at":"2020-01-13T16:40:35Z","title":"Universal Differential Equations for Scientific Machine Learning","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2001.04385","snapshot_observed_at":"2026-08-02T00:44:05.442356Z","title":"Universal differential equations for scientific machine learning","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.442356Z"},"links":{"cited_paper":"/paper/2001.04385","citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:09b0a5bb62e52988b23679b50927942fbd9b0c89ecba042a3333e14966c1c06a","observation_id":"96da49e5-1880-4857-95de-78b552fad42d","resolution":{"observed_at":"2026-08-02T00:44:05.442356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.445417Z","title":"Neural ordinary differential equations","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.445417Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:0d3b17a9e6978858845887f3201fa14e6ef8715351ef31b1873f7b935e578cda","observation_id":"8b96fe7f-6530-4c98-b42b-d7ccfc7ee84e","resolution":{"observed_at":"2026-08-02T00:44:05.445417Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.448387Z","title":"Multilayer feedforward networks are universal approximators","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.448387Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:c404a3ea2d7ae641c75d81bacea457dfd5e9d89b22da9979e8fb63558d715a25","observation_id":"9051699f-fe08-4e6d-9f6a-3c78e1a15ca7","resolution":{"observed_at":"2026-08-02T00:44:05.448387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.451982Z","title":"The theory of matrix polynomials and its application to the mechanics of isotropic continua","venue":null,"work_id":null,"year":1958},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.451982Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:0beec1e4e6d1460dba0309c1d7cc8f1145c4b7c8e3d5f3795a147454a3644349","observation_id":"5d252c2e-6ce5-4ff4-b86b-e3244197a6f2","resolution":{"observed_at":"2026-08-02T00:44:05.451982Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.455354Z","title":"On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.455354Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:c2a990ba1b22f8a7ab948bbd7119add78e2ed546e699d014efb449cd0a73cc14","observation_id":"2a93b5bc-c596-4488-a48e-8e490f0f9804","resolution":{"observed_at":"2026-08-02T00:44:05.455354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.458325Z","title":"Clarifying the representation of isotropic symmetric tensor-valued functions of two symmetric tensors","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.458325Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:7886536b0aef4a476ed0eb92e7ede64de6ff56cfccf57e926c8ba3aa962b9e50","observation_id":"46dd57d3-4050-4990-adf5-64ac397b51c1","resolution":{"observed_at":"2026-08-02T00:44:05.458325Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.461622Z","title":"Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.461622Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:be97b7739319c67da2df39d3172758298b2c6fb3c6119bdcbbe3a01680245324","observation_id":"967e102b-e164-479a-b3e5-b89955c6d286","resolution":{"observed_at":"2026-08-02T00:44:05.461622Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.465164Z","title":"F.The theory of Polymer Dynamics","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.465164Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:8e0aab1cd57907f4e13be6fa30bd993d35b77c0f9314d6fe7b8b49ff70f76767","observation_id":"80ce558c-6f7f-4ad5-af0f-1088e9008813","resolution":{"observed_at":"2026-08-02T00:44:05.465164Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.468488Z","title":"Pytorch: An imperative style, high-performance deep learning library","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.468488Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:5a095f7d8c3804825cbf6138ea45f6e201573b5288783eb60e84bf063a4f1482","observation_id":"ab529c94-c237-42ff-9573-d832a224fc09","resolution":{"observed_at":"2026-08-02T00:44:05.468488Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.471451Z","title":"Compiling machine learning programs via high-level tracing","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.471451Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:4f3760de997c0e253376847ca22fa1bb2d45369db4af62809ad4a1f1f01a0661","observation_id":"cfad0046-3644-4dff-8b42-37da9666f502","resolution":{"observed_at":"2026-08-02T00:44:05.471451Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.474687Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.474687Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:9e23e8fb679685264bf8b5bb01dd922b507059461df381e0699fb3ea39ab71aa","observation_id":"710b44b7-cf48-49ca-a846-f5313c4ecb12","resolution":{"observed_at":"2026-08-02T00:44:05.474687Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.477581Z","title":"A general approach for running Python codes in OpenFOAM using an embedded Pybind11 Python interpreter","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.477581Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:b51036706d2bf40adc8c33e8407f149698ac01eb4df697a3ce156260b6e7917b","observation_id":"193f371c-aa41-499d-a77c-e8f3f732d92e","resolution":{"observed_at":"2026-08-02T00:44:05.477581Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.480462Z","title":"Understanding the difficulty of training deep feedforward neural networks","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.480462Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:ce4e4283f64b056c45062de014bf2bd47cd507c61f55b9a8e5f9ada9704c130d","observation_id":"ed1c51c8-2624-426f-9384-d84f1e8e71ab","resolution":{"observed_at":"2026-08-02T00:44:05.480462Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.483670Z","title":"Batch normalization: Accelerating deep network training by reducing internal covariate shift","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.483670Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:97d93fb3b6cffb1325369e75392eb8402919860e5585e1c1c9d0356877197a0d","observation_id":"4c9d44ba-c230-43b0-b11d-8409c82fd140","resolution":{"observed_at":"2026-08-02T00:44:05.483670Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.486708Z","title":"A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.486708Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:f93c816de7d0b046ce1726421aea3c611b21827c760ea6a8b7413193fb11628d","observation_id":"6e1ac535-9533-4308-8d94-8b3d63611d16","resolution":{"observed_at":"2026-08-02T00:44:05.486708Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.489923Z","title":"Self-consistent Fourier–Tschebyshev rep- resentations of the first normal stress difference in large amplitude oscillatory shear","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.489923Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:1ef697ed8416c8e228cc41419d2771b42d99a064d79b931967860892cd021868","observation_id":"d3b8aeb9-040b-4f44-8abd-73e8f3d30aac","resolution":{"observed_at":"2026-08-02T00:44:05.489923Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.493419Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.493419Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:4eccf276060500d7b06f47decabea57e02908147d087246dec7ed673449d8db1","observation_id":"057e456e-e3cc-431f-8213-f6b8588b08dd","resolution":{"observed_at":"2026-08-02T00:44:05.493419Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.496827Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.496827Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:cdfa86f9d2c10f609181e7c2fd666247c0bff02a716cc4dacf393e09cc6aa0bb","observation_id":"8310bb60-603e-4386-8b80-8a51cc8d4c7a","resolution":{"observed_at":"2026-08-02T00:44:05.496827Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-02T00:44:05.499779Z","title":"Adam: A method for stochastic optimization","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.499779Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:8839813f3dd5494d2d9d261979b910942d57b865a444440c29e8881da41c9aa1","observation_id":"51a983bb-02b7-4a0b-b19a-3f656aee4875","resolution":{"observed_at":"2026-08-02T00:44:05.499779Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.503715Z","title":"On the limited memory BFGS method for large scale optimization","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.503715Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:f1089b268749dd0459c5722b7649cada2a59c2e6171e7fd980c7a21b2d84c8db","observation_id":"885cc115-105b-414f-9848-0f44231b2cfe","resolution":{"observed_at":"2026-08-02T00:44:05.503715Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.507315Z","title":"An overview of overfitting and its solutions","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.507315Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:f8256e142f180fb9d3056ad9b794b5731a1e9b333d2af39803ed1aec44c0bb5d","observation_id":"b2a08dfc-d406-45f9-8780-3e0ca08caaa4","resolution":{"observed_at":"2026-08-02T00:44:05.507315Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.510679Z","title":"A nonlinear network viscoelastic model","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.510679Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:688f6810a7fbc430f38e53d98cecf41cd5adade62c929619f4facc6133be14ac","observation_id":"81128fac-9fc3-4a23-adf0-21e69ae75c3c","resolution":{"observed_at":"2026-08-02T00:44:05.510679Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.513766Z","title":"Working group on numerical techniques","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.513766Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:ee160a7ea4b72b635041e23bd328fd771fe399bb1559e2dc2dcfeb56f85abdc7","observation_id":"204778f6-6648-458d-bf9b-515cc772966d","resolution":{"observed_at":"2026-08-02T00:44:05.513766Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.517331Z","title":"Dynamics of high-Deborah-number entry flows: a numerical study","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.517331Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:e99eb6aea345c8c7c8159afb918c2d8cfd02b0671dc228b10026a369a2be2450","observation_id":"2321e99e-900a-4940-a328-f43251af29c0","resolution":{"observed_at":"2026-08-02T00:44:05.517331Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.520614Z","title":"Numerical simulation of the planar contraction flow of a Giesekus fluid","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.520614Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:2bb22b679aff2a52ffbe723cf022c6e7c0c5cf8f48e23a8d047777ac9c0f83db","observation_id":"fce0328e-8ab1-45fd-904a-b4243bffc79c","resolution":{"observed_at":"2026-08-02T00:44:05.520614Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.524269Z","title":"Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square–square contractions","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.524269Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:2d6fca46f5e9edfb474d19d2e821a0d6a0cd2138ea90f659187e339b40e047c2","observation_id":"b0a8305d-e26f-4092-b98e-e8c8811d8a2c","resolution":{"observed_at":"2026-08-02T00:44:05.524269Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.527746Z","title":"Extrapolation limitations of multilayer feedforward neural networks","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.527746Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:cb7026f721594c12873a974e0fe58aae348809d3038680d92a376886675f5f03","observation_id":"9492e4d1-87df-4563-a8e7-52cd94929258","resolution":{"observed_at":"2026-08-02T00:44:05.527746Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.531360Z","title":"Large amplitude oscilla- tory extension (LAOE) of dilute polymer solutions","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.531360Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:78bd9f799125aede8c2b2f9ba20d0d746caee0036bc255833bec9fa61bddf346","observation_id":"7095e6ac-23a6-49e2-b14f-8119b7d019df","resolution":{"observed_at":"2026-08-02T00:44:05.531360Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.535017Z","title":"Optimized cross-slot flow geometry for microfluidic extensional rheometry","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.535017Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:0566e0723b36dfee8e43aa613f17c7dba61123402cd9534c4fe60c26ea1d243a","observation_id":"54f8836b-f37f-4115-9bf7-d5882a58468b","resolution":{"observed_at":"2026-08-02T00:44:05.535017Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.538402Z","title":"Purely elastic flow asymmetries","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.538402Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:d932592d5c2dfae0ce83ca49f0d9d42106ffb4de77f2e72432869738d5478796","observation_id":"9b456d5e-3291-4a02-8218-96ca05c5f17a","resolution":{"observed_at":"2026-08-02T00:44:05.538402Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.542302Z","title":"A new viscoelastic benchmark flow: Stationary bifurcation in a cross-slot","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.542302Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:a186aeb18c394b81c50c0da587083db53d6eaae66be70fc240e61d0fa53a3baa","observation_id":"acc5a5e5-44bf-4f8b-9028-fde29f603a48","resolution":{"observed_at":"2026-08-02T00:44:05.542302Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:44:05.545752Z","title":"On extensibility effects in the cross-slot flow bifurcation","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-02T00:44:05.545752Z"},"links":{"citing_paper":"/paper/2607.14944"},"observation_digest":"sha256:d6563e3d32d85cb738f8ddb3b09a144a016273ee93667aa1052f15c1225e6c2d","observation_id":"0e2f0abb-fcb8-4ec6-ba03-8851dff246ae","resolution":{"observed_at":"2026-08-02T00:44:05.545752Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.14944","last_updated":"2026-07-16T12:53:06Z","latest_version":1,"primary_category":"physics.flu-dyn","snapshot_observed_at":"2026-08-07T06:42:17.928195Z","submitted_at":"2026-07-16T12:53:06Z","title":"Harnessing Machine Learning for Hybrid Constitutive Modelling of Viscoelastic Fluid Flows in Computational Rheology"},"reference_resolution":{"displayed":71,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":71,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":71},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 71 of 71 outbound references and 0 inbound Pith citation observations for arXiv:2607.14944."}