{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:MGE333GALBQLCRQAHW462PRYHH","short_pith_number":"pith:MGE333GA","schema_version":"1.0","canonical_sha256":"6189bdecc05860b146003db9ed3e3839fcdcb4c07160a88baff2509054256dbc","source":{"kind":"arxiv","id":"2109.05237","version":4},"attestation_state":"computed","paper":{"title":"Physics-based Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"B. Holzschuh, F. Trost, G. Kohl, M. Lino, N. Thuerey, P. Holl, P. Schnell, Q. Liu","submitted_at":"2021-09-11T09:38:02Z","abstract_excerpt":"This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up and running quickly. Beyond traditional supervised learning, we dive into physical loss-constraints, differentiable simulations, diffusion-based approaches for probabilistic generative AI, as well as reinforcement learning and advanced neural network architectures. These foundations are paving the way for the next generation of scientific foundation models. We"},"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":"2109.05237","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-11T09:38:02Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"09d129b574a8542286f762ee2e54c226f7ea8f92fff68dbfd272b5a577c86247","abstract_canon_sha256":"4b604d1c2ac56c0bbb9b9bfef6bfae18da8e3a93fd1aea862394565271352963"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:39:44.424649Z","signature_b64":"5RQiq5p8pEwYD/fgt7Zp9SBRrag12EAMhkLhK0GEO0wICDek9tyfXngwDOJ/fJhz6USWqBAu05lq967+HCHNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6189bdecc05860b146003db9ed3e3839fcdcb4c07160a88baff2509054256dbc","last_reissued_at":"2026-07-05T10:39:44.424174Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:39:44.424174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Physics-based Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"B. Holzschuh, F. Trost, G. Kohl, M. Lino, N. Thuerey, P. Holl, P. Schnell, Q. Liu","submitted_at":"2021-09-11T09:38:02Z","abstract_excerpt":"This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up and running quickly. Beyond traditional supervised learning, we dive into physical loss-constraints, differentiable simulations, diffusion-based approaches for probabilistic generative AI, as well as reinforcement learning and advanced neural network architectures. These foundations are paving the way for the next generation of scientific foundation models. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.05237","kind":"arxiv","version":4},"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/2109.05237/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":"2109.05237","created_at":"2026-07-05T10:39:44.424233+00:00"},{"alias_kind":"arxiv_version","alias_value":"2109.05237v4","created_at":"2026-07-05T10:39:44.424233+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.05237","created_at":"2026-07-05T10:39:44.424233+00:00"},{"alias_kind":"pith_short_12","alias_value":"MGE333GALBQL","created_at":"2026-07-05T10:39:44.424233+00:00"},{"alias_kind":"pith_short_16","alias_value":"MGE333GALBQLCRQA","created_at":"2026-07-05T10:39:44.424233+00:00"},{"alias_kind":"pith_short_8","alias_value":"MGE333GA","created_at":"2026-07-05T10:39:44.424233+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.07779","citing_title":"From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier","ref_index":223,"is_internal_anchor":true},{"citing_arxiv_id":"2606.06094","citing_title":"Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2605.31120","citing_title":"SWIM: Single-Instance Whole-Body Imitation for swiMming","ref_index":60,"is_internal_anchor":false},{"citing_arxiv_id":"2604.03321","citing_title":"General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equations","ref_index":38,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07157","citing_title":"Learned Lagrangian Models of PDEs via Euler-Lagrange Residual Minimization","ref_index":20,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH","json":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH.json","graph_json":"https://pith.science/api/pith-number/MGE333GALBQLCRQAHW462PRYHH/graph.json","events_json":"https://pith.science/api/pith-number/MGE333GALBQLCRQAHW462PRYHH/events.json","paper":"https://pith.science/paper/MGE333GA"},"agent_actions":{"view_html":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH","download_json":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH.json","view_paper":"https://pith.science/paper/MGE333GA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2109.05237&json=true","fetch_graph":"https://pith.science/api/pith-number/MGE333GALBQLCRQAHW462PRYHH/graph.json","fetch_events":"https://pith.science/api/pith-number/MGE333GALBQLCRQAHW462PRYHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH/action/storage_attestation","attest_author":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH/action/author_attestation","sign_citation":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH/action/citation_signature","submit_replication":"https://pith.science/pith/MGE333GALBQLCRQAHW462PRYHH/action/replication_record"}},"created_at":"2026-07-05T10:39:44.424233+00:00","updated_at":"2026-07-05T10:39:44.424233+00:00"}