{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YXE6YLMSHSV5WHXCH7HDYONLQ5","short_pith_number":"pith:YXE6YLMS","canonical_record":{"source":{"id":"2403.00599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2024-03-01T15:23:01Z","cross_cats_sorted":["astro-ph.SR","math-ph","math.MP"],"title_canon_sha256":"d7c1f0e57d24a8830e1718f67d99e2fa32c4ab354c5e08269dd1f7233048d36a","abstract_canon_sha256":"564a4e1d8eda5a7d003a01b0c80ff4f556d1ade9bc18bd4e944c36a6fcd3b807"},"schema_version":"1.0"},"canonical_sha256":"c5c9ec2d923cabdb1ee23fce3c39ab87657429c8ce0510d1eab717477f0df72c","source":{"kind":"arxiv","id":"2403.00599","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.00599","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"2403.00599v1","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.00599","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"YXE6YLMSHSV5","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"pith_short_16","alias_value":"YXE6YLMSHSV5WHXC","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"pith_short_8","alias_value":"YXE6YLMS","created_at":"2026-07-05T07:51:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YXE6YLMSHSV5WHXCH7HDYONLQ5","target":"record","payload":{"canonical_record":{"source":{"id":"2403.00599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2024-03-01T15:23:01Z","cross_cats_sorted":["astro-ph.SR","math-ph","math.MP"],"title_canon_sha256":"d7c1f0e57d24a8830e1718f67d99e2fa32c4ab354c5e08269dd1f7233048d36a","abstract_canon_sha256":"564a4e1d8eda5a7d003a01b0c80ff4f556d1ade9bc18bd4e944c36a6fcd3b807"},"schema_version":"1.0"},"canonical_sha256":"c5c9ec2d923cabdb1ee23fce3c39ab87657429c8ce0510d1eab717477f0df72c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:51:06.255145Z","signature_b64":"ty6dvufLNlHvxU8diNRGgxBHD1H7d2qAB4fOjoHSQzI1z26rew12Zink/Alk5ikATZ/YCyyfAgRbybroxZ7qDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5c9ec2d923cabdb1ee23fce3c39ab87657429c8ce0510d1eab717477f0df72c","last_reissued_at":"2026-07-05T07:51:06.254748Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:51:06.254748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.00599","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:51:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"frOjpm5lHhHfikK8y0HanYSMRPu1E6bbfYLJz3OogC5wWQyJe9vm/3Eq30x/M67O+HkKhz6hwRfvgzmT6SnzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:51:39.808532Z"},"content_sha256":"bd00036ea3a11cf427f71eaa2c606b8aad94cf02d81d88823ec688c2adf26c77","schema_version":"1.0","event_id":"sha256:bd00036ea3a11cf427f71eaa2c606b8aad94cf02d81d88823ec688c2adf26c77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YXE6YLMSHSV5WHXCH7HDYONLQ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A hands-on introduction to Physics-Informed Neural Networks for solving partial differential equations with benchmark tests taken from astrophysics and plasma physics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.SR","math-ph","math.MP"],"primary_cat":"physics.comp-ph","authors_text":"Hubert Baty","submitted_at":"2024-03-01T15:23:01Z","abstract_excerpt":"I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the equation evaluated at various points within the domain. Boundary conditions are incorporated either by introducing soft constraints with corresponding boundary data values in the minimization process or by strictly enforcing the solution with hard constraints. PINNs are tested on diverse PDEs extracted from two-dimensional physical/astrophysical problems. Spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.00599","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/2403.00599/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:51:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rpWrr4NJJzCX7USF8yUxGIcNN8zcjI3rGGW+knxi0Eod9cLek1qifue9Qo6+D5x8B5bHinq43k3WDF0rXN5uCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:51:39.809036Z"},"content_sha256":"bd002fe1db50ebbb8b62a1c5f47f01a27dd0f5ed3023b8d120f30a2656fc2d62","schema_version":"1.0","event_id":"sha256:bd002fe1db50ebbb8b62a1c5f47f01a27dd0f5ed3023b8d120f30a2656fc2d62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXE6YLMSHSV5WHXCH7HDYONLQ5/bundle.json","state_url":"https://pith.science/pith/YXE6YLMSHSV5WHXCH7HDYONLQ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXE6YLMSHSV5WHXCH7HDYONLQ5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T07:51:39Z","links":{"resolver":"https://pith.science/pith/YXE6YLMSHSV5WHXCH7HDYONLQ5","bundle":"https://pith.science/pith/YXE6YLMSHSV5WHXCH7HDYONLQ5/bundle.json","state":"https://pith.science/pith/YXE6YLMSHSV5WHXCH7HDYONLQ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXE6YLMSHSV5WHXCH7HDYONLQ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YXE6YLMSHSV5WHXCH7HDYONLQ5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"564a4e1d8eda5a7d003a01b0c80ff4f556d1ade9bc18bd4e944c36a6fcd3b807","cross_cats_sorted":["astro-ph.SR","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2024-03-01T15:23:01Z","title_canon_sha256":"d7c1f0e57d24a8830e1718f67d99e2fa32c4ab354c5e08269dd1f7233048d36a"},"schema_version":"1.0","source":{"id":"2403.00599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.00599","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"arxiv_version","alias_value":"2403.00599v1","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.00599","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"pith_short_12","alias_value":"YXE6YLMSHSV5","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"pith_short_16","alias_value":"YXE6YLMSHSV5WHXC","created_at":"2026-07-05T07:51:06Z"},{"alias_kind":"pith_short_8","alias_value":"YXE6YLMS","created_at":"2026-07-05T07:51:06Z"}],"graph_snapshots":[{"event_id":"sha256:bd002fe1db50ebbb8b62a1c5f47f01a27dd0f5ed3023b8d120f30a2656fc2d62","target":"graph","created_at":"2026-07-05T07:51:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.00599/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the equation evaluated at various points within the domain. Boundary conditions are incorporated either by introducing soft constraints with corresponding boundary data values in the minimization process or by strictly enforcing the solution with hard constraints. PINNs are tested on diverse PDEs extracted from two-dimensional physical/astrophysical problems. Spec","authors_text":"Hubert Baty","cross_cats":["astro-ph.SR","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2024-03-01T15:23:01Z","title":"A hands-on introduction to Physics-Informed Neural Networks for solving partial differential equations with benchmark tests taken from astrophysics and plasma physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.00599","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bd00036ea3a11cf427f71eaa2c606b8aad94cf02d81d88823ec688c2adf26c77","target":"record","created_at":"2026-07-05T07:51:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"564a4e1d8eda5a7d003a01b0c80ff4f556d1ade9bc18bd4e944c36a6fcd3b807","cross_cats_sorted":["astro-ph.SR","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2024-03-01T15:23:01Z","title_canon_sha256":"d7c1f0e57d24a8830e1718f67d99e2fa32c4ab354c5e08269dd1f7233048d36a"},"schema_version":"1.0","source":{"id":"2403.00599","kind":"arxiv","version":1}},"canonical_sha256":"c5c9ec2d923cabdb1ee23fce3c39ab87657429c8ce0510d1eab717477f0df72c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5c9ec2d923cabdb1ee23fce3c39ab87657429c8ce0510d1eab717477f0df72c","first_computed_at":"2026-07-05T07:51:06.254748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:51:06.254748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ty6dvufLNlHvxU8diNRGgxBHD1H7d2qAB4fOjoHSQzI1z26rew12Zink/Alk5ikATZ/YCyyfAgRbybroxZ7qDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:51:06.255145Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.00599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd00036ea3a11cf427f71eaa2c606b8aad94cf02d81d88823ec688c2adf26c77","sha256:bd002fe1db50ebbb8b62a1c5f47f01a27dd0f5ed3023b8d120f30a2656fc2d62"],"state_sha256":"f3432c893f71875020617c9b7d9e4dcd904f8a1e1bf9dab50fc9f5022ed627df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OwneoCJSHwvm8YskaxcL814uZfE2QWFo2kEwjCZMPlMpKvlphtzUsvCWvsv3gGymTs4sY55huuc7PIc+3t/IAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:51:39.813552Z","bundle_sha256":"2c0e8a3afe7b30ae6ddc78f6f9fe88189b1957b6ae9edc77357e1c7aa3588f35"}}