{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:O4X2TWJUSLUTDL2M2AHYF7UJHD","short_pith_number":"pith:O4X2TWJU","schema_version":"1.0","canonical_sha256":"772fa9d93492e931af4cd00f82fe8938f19a259df02059d2eb4fd0d559687f20","source":{"kind":"arxiv","id":"2601.11259","version":1},"attestation_state":"computed","paper":{"title":"Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Federico Pichi, Gianluigi Rozza, Lorenzo Tomada","submitted_at":"2026-01-16T13:10:00Z","abstract_excerpt":"Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric inductive biases with interpretable latent behavior, overlooking dynamics-driven features or disregarding spatial information. In this work, we address this gap by introducing Latent Dynamics Graph Convolutional Network (LD-GCN), a purely data-driven, encoder-free architecture that learns a global, low-dimensional representation of dynamical systems conditioned o"},"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":"2601.11259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-01-16T13:10:00Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"74bb17070f48f46762c40d15ef1187e62cff98ff2a8c26753b1baaec8f3e1f9f","abstract_canon_sha256":"e4c43056ced5b6188f1948b2a2d482e820fb0e2b5137fdab0dae6d1d3c9ef959"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:13:53.346844Z","signature_b64":"4M1AdtXXRl4XsGa3HR1c7bsYJhGD/jeEPzff5FmlSjgwYxBSWgxq1vj9kKeN1Fd+XQAC3rSX4x99GDsTf64jCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"772fa9d93492e931af4cd00f82fe8938f19a259df02059d2eb4fd0d559687f20","last_reissued_at":"2026-06-23T03:13:53.346383Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:13:53.346383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Federico Pichi, Gianluigi Rozza, Lorenzo Tomada","submitted_at":"2026-01-16T13:10:00Z","abstract_excerpt":"Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric inductive biases with interpretable latent behavior, overlooking dynamics-driven features or disregarding spatial information. In this work, we address this gap by introducing Latent Dynamics Graph Convolutional Network (LD-GCN), a purely data-driven, encoder-free architecture that learns a global, low-dimensional representation of dynamical systems conditioned o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.11259","kind":"arxiv","version":1},"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/2601.11259/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":"2601.11259","created_at":"2026-06-23T03:13:53.346441+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.11259v1","created_at":"2026-06-23T03:13:53.346441+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.11259","created_at":"2026-06-23T03:13:53.346441+00:00"},{"alias_kind":"pith_short_12","alias_value":"O4X2TWJUSLUT","created_at":"2026-06-23T03:13:53.346441+00:00"},{"alias_kind":"pith_short_16","alias_value":"O4X2TWJUSLUTDL2M","created_at":"2026-06-23T03:13:53.346441+00:00"},{"alias_kind":"pith_short_8","alias_value":"O4X2TWJU","created_at":"2026-06-23T03:13:53.346441+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD","json":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD.json","graph_json":"https://pith.science/api/pith-number/O4X2TWJUSLUTDL2M2AHYF7UJHD/graph.json","events_json":"https://pith.science/api/pith-number/O4X2TWJUSLUTDL2M2AHYF7UJHD/events.json","paper":"https://pith.science/paper/O4X2TWJU"},"agent_actions":{"view_html":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD","download_json":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD.json","view_paper":"https://pith.science/paper/O4X2TWJU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.11259&json=true","fetch_graph":"https://pith.science/api/pith-number/O4X2TWJUSLUTDL2M2AHYF7UJHD/graph.json","fetch_events":"https://pith.science/api/pith-number/O4X2TWJUSLUTDL2M2AHYF7UJHD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD/action/storage_attestation","attest_author":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD/action/author_attestation","sign_citation":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD/action/citation_signature","submit_replication":"https://pith.science/pith/O4X2TWJUSLUTDL2M2AHYF7UJHD/action/replication_record"}},"created_at":"2026-06-23T03:13:53.346441+00:00","updated_at":"2026-06-23T03:13:53.346441+00:00"}