{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:A4T5ZDIXHRT5Y32IIOSW6PV5PY","short_pith_number":"pith:A4T5ZDIX","schema_version":"1.0","canonical_sha256":"0727dc8d173c67dc6f4843a56f3ebd7e2e065803aa90bbfb36577f17bbe73c9e","source":{"kind":"arxiv","id":"2204.11127","version":3},"attestation_state":"computed","paper":{"title":"U-NO: U-shaped Neural Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kamyar Azizzadenesheli, Md Ashiqur Rahman, Zachary E. Ross","submitted_at":"2022-04-23T19:18:44Z","abstract_excerpt":"Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented success in learning solution operators of partial differential equations. Due to their close proximity to fully connected architectures, these models mainly suffer from high memory usage and are generally limited to shallow deep learning models. In this paper, we propose U-shaped Neural Operator (U-NO), a U-shaped memory enhanced architecture that allows for "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2204.11127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-04-23T19:18:44Z","cross_cats_sorted":[],"title_canon_sha256":"52dccf3782d4be1a759ab39f10a47b1da75ffa69c34e24383f79f39b8f81fdec","abstract_canon_sha256":"79eb8c9d0081bec3bca77fdfbaec90d4d1254d85f5d6620629fd07929003e036"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:07:08.403519Z","signature_b64":"b672vKG10Swa/Ytt7/eIjz4VGuUxrd7cLxMICZB0emBG90BGrxVMxo5WBDrquhwetlDLBaw6cPGlaUe3jjxJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0727dc8d173c67dc6f4843a56f3ebd7e2e065803aa90bbfb36577f17bbe73c9e","last_reissued_at":"2026-07-05T06:07:08.403114Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:07:08.403114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"U-NO: U-shaped Neural Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kamyar Azizzadenesheli, Md Ashiqur Rahman, Zachary E. Ross","submitted_at":"2022-04-23T19:18:44Z","abstract_excerpt":"Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented success in learning solution operators of partial differential equations. Due to their close proximity to fully connected architectures, these models mainly suffer from high memory usage and are generally limited to shallow deep learning models. In this paper, we propose U-shaped Neural Operator (U-NO), a U-shaped memory enhanced architecture that allows for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.11127","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.11127/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2204.11127","created_at":"2026-07-05T06:07:08.403171+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.11127v3","created_at":"2026-07-05T06:07:08.403171+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.11127","created_at":"2026-07-05T06:07:08.403171+00:00"},{"alias_kind":"pith_short_12","alias_value":"A4T5ZDIXHRT5","created_at":"2026-07-05T06:07:08.403171+00:00"},{"alias_kind":"pith_short_16","alias_value":"A4T5ZDIXHRT5Y32I","created_at":"2026-07-05T06:07:08.403171+00:00"},{"alias_kind":"pith_short_8","alias_value":"A4T5ZDIX","created_at":"2026-07-05T06:07:08.403171+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":26,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.25952","citing_title":"Principal-Part Decomposition for Neural Operator Learning of Dirichlet-to-Neumann Maps","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30495","citing_title":"McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2606.11963","citing_title":"HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2607.01128","citing_title":"GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2606.06164","citing_title":"On the training of physics-informed neural operators for solving parametric partial differential equations","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2606.28122","citing_title":"Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs","ref_index":37,"is_internal_anchor":false},{"citing_arxiv_id":"2606.31574","citing_title":"Temperature Field Reconstruction of Tungsten Monoblock Divertor on EAST using Physics-aware Neural Operator Transformer","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30495","citing_title":"McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2605.25413","citing_title":"Autoregression-Free Neural Operators for Time-Dependent PDEs","ref_index":57,"is_internal_anchor":false},{"citing_arxiv_id":"2505.13919","citing_title":"Generative Adaptation of Dynamics to Environmental Shifts via Weight-space Diffusion","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.22182","citing_title":"IKNO: Infinite-order Kernel Neural Operators","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2601.03613","citing_title":"A Simple but Efficient Transformer-Based Physics-Informed Neural Network for Incompressible Navier--Stokes Equations","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03548","citing_title":"PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2505.18288","citing_title":"Operator Learning for Schr\\\"{o}dinger Equation: Unitarity, Error Bounds, and Time Generalization","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2510.00233","citing_title":"Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling","ref_index":42,"is_internal_anchor":false},{"citing_arxiv_id":"2602.01486","citing_title":"Multi-Scale Wavelet Transformers for Operator Learning of Dynamical Systems","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12965","citing_title":"U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09523","citing_title":"HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations","ref_index":35,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09523","citing_title":"HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2605.08915","citing_title":"Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow","ref_index":69,"is_internal_anchor":false},{"citing_arxiv_id":"2605.10154","citing_title":"Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09016","citing_title":"CATO: Charted Attention for Neural PDE Operators","ref_index":23,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03548","citing_title":"PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04198","citing_title":"Deep Wave Network for Modeling Multi-Scale Physical Dynamics","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2604.07421","citing_title":"SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY","json":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY.json","graph_json":"https://pith.science/api/pith-number/A4T5ZDIXHRT5Y32IIOSW6PV5PY/graph.json","events_json":"https://pith.science/api/pith-number/A4T5ZDIXHRT5Y32IIOSW6PV5PY/events.json","paper":"https://pith.science/paper/A4T5ZDIX"},"agent_actions":{"view_html":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY","download_json":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY.json","view_paper":"https://pith.science/paper/A4T5ZDIX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.11127&json=true","fetch_graph":"https://pith.science/api/pith-number/A4T5ZDIXHRT5Y32IIOSW6PV5PY/graph.json","fetch_events":"https://pith.science/api/pith-number/A4T5ZDIXHRT5Y32IIOSW6PV5PY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY/action/storage_attestation","attest_author":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY/action/author_attestation","sign_citation":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY/action/citation_signature","submit_replication":"https://pith.science/pith/A4T5ZDIXHRT5Y32IIOSW6PV5PY/action/replication_record"}},"created_at":"2026-07-05T06:07:08.403171+00:00","updated_at":"2026-07-05T06:07:08.403171+00:00"}