{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XF66MFZTE2UO2VOXF4UIP3FWTM","short_pith_number":"pith:XF66MFZT","canonical_record":{"source":{"id":"2105.14410","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-05-30T02:10:59Z","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph"],"title_canon_sha256":"b133055d5c51c7587c985ac76b8a669484268825abf60980d5374064595da9cf","abstract_canon_sha256":"1688b59328849d434ded89ebca2f1c457ac7f132bd5775817486a6dfeb6d409e"},"schema_version":"1.0"},"canonical_sha256":"b97de6173326a8ed55d72f2887ecb69b1ba8c949cfe13dd32a9c2e1f54ed714b","source":{"kind":"arxiv","id":"2105.14410","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.14410","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"2105.14410v1","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.14410","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"XF66MFZTE2UO","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"pith_short_16","alias_value":"XF66MFZTE2UO2VOX","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"pith_short_8","alias_value":"XF66MFZT","created_at":"2026-07-05T02:44:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XF66MFZTE2UO2VOXF4UIP3FWTM","target":"record","payload":{"canonical_record":{"source":{"id":"2105.14410","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-05-30T02:10:59Z","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph"],"title_canon_sha256":"b133055d5c51c7587c985ac76b8a669484268825abf60980d5374064595da9cf","abstract_canon_sha256":"1688b59328849d434ded89ebca2f1c457ac7f132bd5775817486a6dfeb6d409e"},"schema_version":"1.0"},"canonical_sha256":"b97de6173326a8ed55d72f2887ecb69b1ba8c949cfe13dd32a9c2e1f54ed714b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:44:23.618023Z","signature_b64":"9kjbDSiqY/gmRNBAXmufcClKjvuPly29SlxAZQWAcoBEnxFs1vT/IJeBeXt2a45d6eNEXPG0kr/QDKZRNQqSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b97de6173326a8ed55d72f2887ecb69b1ba8c949cfe13dd32a9c2e1f54ed714b","last_reissued_at":"2026-07-05T02:44:23.617529Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:44:23.617529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.14410","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":"2026-07-05T02:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofGthmGoQLh2GOXRzmihGW1gdv7667LXWRCuRMskTgjG5FVxVGjRHq4UvtL6RettjmbdU1mGI5rxIj5TzolSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T06:43:54.359612Z"},"content_sha256":"1f709ac759225a39ac5032c5a6a610abadedc192ca0a761636bd15e7ccc333bb","schema_version":"1.0","event_id":"sha256:1f709ac759225a39ac5032c5a6a610abadedc192ca0a761636bd15e7ccc333bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XF66MFZTE2UO2VOXF4UIP3FWTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Andrew J. Christlieb, Juntao Huang, Luke F. Roberts, Wen-an Yong, Yingda Cheng","submitted_at":"2021-05-30T02:10:59Z","abstract_excerpt":"This is the second paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \\cite{huang2021gradient}, we proposed an approach to directly learn the gradient of the unclosed high order moment, which performs much better than learning the moment itself and the conventional $P_N$ closure. However, the ML moment closure model in \\cite{huang2021gradient} is not able to guarantee hyperbolicity and long time stability. We propose in this paper a method to enforce the global hyperbolicity of the ML closure model. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.14410","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/2105.14410/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":"2026-07-05T02:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aOY+1eFlQ2cC4lNVFVRS9ckPfVrxbr++8mu+ic1oJtOy5CnfWX2j1utOrW+O9X4k0LyNPdxC9gxYc+dZMEydDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T06:43:54.359993Z"},"content_sha256":"45294d5e71edb6371a79fecf409c9ee12de6685f6ef499e11c0b387e16f1a85d","schema_version":"1.0","event_id":"sha256:45294d5e71edb6371a79fecf409c9ee12de6685f6ef499e11c0b387e16f1a85d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XF66MFZTE2UO2VOXF4UIP3FWTM/bundle.json","state_url":"https://pith.science/pith/XF66MFZTE2UO2VOXF4UIP3FWTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XF66MFZTE2UO2VOXF4UIP3FWTM/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":"2026-07-22T06:43:54Z","links":{"resolver":"https://pith.science/pith/XF66MFZTE2UO2VOXF4UIP3FWTM","bundle":"https://pith.science/pith/XF66MFZTE2UO2VOXF4UIP3FWTM/bundle.json","state":"https://pith.science/pith/XF66MFZTE2UO2VOXF4UIP3FWTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XF66MFZTE2UO2VOXF4UIP3FWTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XF66MFZTE2UO2VOXF4UIP3FWTM","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":"1688b59328849d434ded89ebca2f1c457ac7f132bd5775817486a6dfeb6d409e","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-05-30T02:10:59Z","title_canon_sha256":"b133055d5c51c7587c985ac76b8a669484268825abf60980d5374064595da9cf"},"schema_version":"1.0","source":{"id":"2105.14410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.14410","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"2105.14410v1","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.14410","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"XF66MFZTE2UO","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"pith_short_16","alias_value":"XF66MFZTE2UO2VOX","created_at":"2026-07-05T02:44:23Z"},{"alias_kind":"pith_short_8","alias_value":"XF66MFZT","created_at":"2026-07-05T02:44:23Z"}],"graph_snapshots":[{"event_id":"sha256:45294d5e71edb6371a79fecf409c9ee12de6685f6ef499e11c0b387e16f1a85d","target":"graph","created_at":"2026-07-05T02:44:23Z","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/2105.14410/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is the second paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \\cite{huang2021gradient}, we proposed an approach to directly learn the gradient of the unclosed high order moment, which performs much better than learning the moment itself and the conventional $P_N$ closure. However, the ML moment closure model in \\cite{huang2021gradient} is not able to guarantee hyperbolicity and long time stability. We propose in this paper a method to enforce the global hyperbolicity of the ML closure model. ","authors_text":"Andrew J. Christlieb, Juntao Huang, Luke F. Roberts, Wen-an Yong, Yingda Cheng","cross_cats":["cs.LG","cs.NA","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-05-30T02:10:59Z","title":"Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.14410","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":"sha256:1f709ac759225a39ac5032c5a6a610abadedc192ca0a761636bd15e7ccc333bb","target":"record","created_at":"2026-07-05T02:44:23Z","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":"1688b59328849d434ded89ebca2f1c457ac7f132bd5775817486a6dfeb6d409e","cross_cats_sorted":["cs.LG","cs.NA","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2021-05-30T02:10:59Z","title_canon_sha256":"b133055d5c51c7587c985ac76b8a669484268825abf60980d5374064595da9cf"},"schema_version":"1.0","source":{"id":"2105.14410","kind":"arxiv","version":1}},"canonical_sha256":"b97de6173326a8ed55d72f2887ecb69b1ba8c949cfe13dd32a9c2e1f54ed714b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b97de6173326a8ed55d72f2887ecb69b1ba8c949cfe13dd32a9c2e1f54ed714b","first_computed_at":"2026-07-05T02:44:23.617529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:44:23.617529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9kjbDSiqY/gmRNBAXmufcClKjvuPly29SlxAZQWAcoBEnxFs1vT/IJeBeXt2a45d6eNEXPG0kr/QDKZRNQqSCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:44:23.618023Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.14410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f709ac759225a39ac5032c5a6a610abadedc192ca0a761636bd15e7ccc333bb","sha256:45294d5e71edb6371a79fecf409c9ee12de6685f6ef499e11c0b387e16f1a85d"],"state_sha256":"e361c7ab24f243fc724b09af6254a1e0b38c02557e903f1f44117246d705cdaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5odrhtxVNEdk65XJowJuHLh5PBEH678fw77vEf3vhr3DwqRCZ5EFc6Imi4M80iTVGAtawyAO62mhZBjHnTaMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-22T06:43:54.362031Z","bundle_sha256":"9c4892806a7fec5d99608715ca28760674e08cbc3458f293b6a56def5da6bffc"}}