{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:BMXGGRZIC5RYZLERWQT2A4VLA2","short_pith_number":"pith:BMXGGRZI","canonical_record":{"source":{"id":"2012.03448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-07T05:00:22Z","cross_cats_sorted":["cs.AI","cs.SY","eess.SY","math.DG","math.DS"],"title_canon_sha256":"d5a41e40a198615f0c1af27f37cc26f3910fa24315c00eb31ca23f3275267edf","abstract_canon_sha256":"259834804fbe7ff14022d135a9b5578d589b43802b82f50943d0a2413eca96de"},"schema_version":"1.0"},"canonical_sha256":"0b2e63472817638cac91b427a072ab06aff1f56fad6cc554c0f0e9f04c09fef1","source":{"kind":"arxiv","id":"2012.03448","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.03448","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"2012.03448v2","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.03448","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"BMXGGRZIC5RY","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"pith_short_16","alias_value":"BMXGGRZIC5RYZLER","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"pith_short_8","alias_value":"BMXGGRZI","created_at":"2026-07-05T02:23:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:BMXGGRZIC5RYZLERWQT2A4VLA2","target":"record","payload":{"canonical_record":{"source":{"id":"2012.03448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-07T05:00:22Z","cross_cats_sorted":["cs.AI","cs.SY","eess.SY","math.DG","math.DS"],"title_canon_sha256":"d5a41e40a198615f0c1af27f37cc26f3910fa24315c00eb31ca23f3275267edf","abstract_canon_sha256":"259834804fbe7ff14022d135a9b5578d589b43802b82f50943d0a2413eca96de"},"schema_version":"1.0"},"canonical_sha256":"0b2e63472817638cac91b427a072ab06aff1f56fad6cc554c0f0e9f04c09fef1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:23:21.181838Z","signature_b64":"plhGp6zAAPJvsltc/4RSbK3Xiu2eVxQ1UkotbL7g19LW5+2hFTEjJHLTaOEzW22MSzpYOWy+OgwogSH+i87kAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b2e63472817638cac91b427a072ab06aff1f56fad6cc554c0f0e9f04c09fef1","last_reissued_at":"2026-07-05T02:23:21.181284Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:23:21.181284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.03448","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TFoJXEIWzkJTvAUtA8qiYSUy67KibXs/y/tVWw0LuRCiFB4ApjVIWNmRJAday45+pgbt+eZxXjqFy3ygAv7NAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:14:06.447715Z"},"content_sha256":"f5e7d5f2c7dfba52c76ccfec1f7c83e10fd4bd1b1c18d3c09929aab9aae0add8","schema_version":"1.0","event_id":"sha256:f5e7d5f2c7dfba52c76ccfec1f7c83e10fd4bd1b1c18d3c09929aab9aae0add8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:BMXGGRZIC5RYZLERWQT2A4VLA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.SY","eess.SY","math.DG","math.DS"],"primary_cat":"cs.LG","authors_text":"Paul J. Atzberger, Ryan Lopez","submitted_at":"2020-12-07T05:00:22Z","abstract_excerpt":"We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03448","kind":"arxiv","version":2},"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/2012.03448/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":"2026-07-05T02:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+/AcQkf8akR/pv4IdqgZPs99c134SdIfoYIHw5CxYEzHFSIaZFMIIkx9SRAQKioRofgdxNuLkinHpNhwwcohBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T05:14:06.448782Z"},"content_sha256":"3adb0bd463867d1f28419aff4d97d631a2eaf4e5c617a9653bc205b4c72f0d25","schema_version":"1.0","event_id":"sha256:3adb0bd463867d1f28419aff4d97d631a2eaf4e5c617a9653bc205b4c72f0d25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BMXGGRZIC5RYZLERWQT2A4VLA2/bundle.json","state_url":"https://pith.science/pith/BMXGGRZIC5RYZLERWQT2A4VLA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BMXGGRZIC5RYZLERWQT2A4VLA2/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":"2026-08-09T05:14:06Z","links":{"resolver":"https://pith.science/pith/BMXGGRZIC5RYZLERWQT2A4VLA2","bundle":"https://pith.science/pith/BMXGGRZIC5RYZLERWQT2A4VLA2/bundle.json","state":"https://pith.science/pith/BMXGGRZIC5RYZLERWQT2A4VLA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BMXGGRZIC5RYZLERWQT2A4VLA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:BMXGGRZIC5RYZLERWQT2A4VLA2","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":"259834804fbe7ff14022d135a9b5578d589b43802b82f50943d0a2413eca96de","cross_cats_sorted":["cs.AI","cs.SY","eess.SY","math.DG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-07T05:00:22Z","title_canon_sha256":"d5a41e40a198615f0c1af27f37cc26f3910fa24315c00eb31ca23f3275267edf"},"schema_version":"1.0","source":{"id":"2012.03448","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.03448","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"2012.03448v2","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.03448","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"BMXGGRZIC5RY","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"pith_short_16","alias_value":"BMXGGRZIC5RYZLER","created_at":"2026-07-05T02:23:21Z"},{"alias_kind":"pith_short_8","alias_value":"BMXGGRZI","created_at":"2026-07-05T02:23:21Z"}],"graph_snapshots":[{"event_id":"sha256:3adb0bd463867d1f28419aff4d97d631a2eaf4e5c617a9653bc205b4c72f0d25","target":"graph","created_at":"2026-07-05T02:23:21Z","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/2012.03448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.","authors_text":"Paul J. Atzberger, Ryan Lopez","cross_cats":["cs.AI","cs.SY","eess.SY","math.DG","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-07T05:00:22Z","title":"Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03448","kind":"arxiv","version":2},"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:f5e7d5f2c7dfba52c76ccfec1f7c83e10fd4bd1b1c18d3c09929aab9aae0add8","target":"record","created_at":"2026-07-05T02:23:21Z","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":"259834804fbe7ff14022d135a9b5578d589b43802b82f50943d0a2413eca96de","cross_cats_sorted":["cs.AI","cs.SY","eess.SY","math.DG","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-07T05:00:22Z","title_canon_sha256":"d5a41e40a198615f0c1af27f37cc26f3910fa24315c00eb31ca23f3275267edf"},"schema_version":"1.0","source":{"id":"2012.03448","kind":"arxiv","version":2}},"canonical_sha256":"0b2e63472817638cac91b427a072ab06aff1f56fad6cc554c0f0e9f04c09fef1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b2e63472817638cac91b427a072ab06aff1f56fad6cc554c0f0e9f04c09fef1","first_computed_at":"2026-07-05T02:23:21.181284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:23:21.181284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"plhGp6zAAPJvsltc/4RSbK3Xiu2eVxQ1UkotbL7g19LW5+2hFTEjJHLTaOEzW22MSzpYOWy+OgwogSH+i87kAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:23:21.181838Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.03448","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5e7d5f2c7dfba52c76ccfec1f7c83e10fd4bd1b1c18d3c09929aab9aae0add8","sha256:3adb0bd463867d1f28419aff4d97d631a2eaf4e5c617a9653bc205b4c72f0d25"],"state_sha256":"d27fc25568cb61f878a336cd70faa77f17330a589fe71319dcbe886385730fdf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+U35pdkFIkRA8IVyqKYpIiU6hUdNWWdwHqznG6Cpr6NxBBJ59el1MLi/6RjWYN8bm7UQ/W4jMbP2q1/GOtMXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T05:14:06.455079Z","bundle_sha256":"b299b28861db19544228b551652a00969b5cd1661b4f28748c051285b36846e8"}}