{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:DFKMG3HQDRKZ6W7MHTA7CFRL3L","short_pith_number":"pith:DFKMG3HQ","canonical_record":{"source":{"id":"2109.13076","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-27T14:25:10Z","cross_cats_sorted":["physics.plasm-ph"],"title_canon_sha256":"1b4ec1adeefb3548cdab0a366d9d324a3f69d0744ee2bfc2741d8e8dcbfb4fa1","abstract_canon_sha256":"bdf233706eccc420d4bd8ec9d056e9aefc2b9e46f461af8e8b71324dc246532b"},"schema_version":"1.0"},"canonical_sha256":"1954c36cf01c559f5bec3cc1f1162bdaec81e5e6174bc5d16229cd694cd7ead6","source":{"kind":"arxiv","id":"2109.13076","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.13076","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"2109.13076v3","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.13076","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"DFKMG3HQDRKZ","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"pith_short_16","alias_value":"DFKMG3HQDRKZ6W7M","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"pith_short_8","alias_value":"DFKMG3HQ","created_at":"2026-07-05T03:32:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:DFKMG3HQDRKZ6W7MHTA7CFRL3L","target":"record","payload":{"canonical_record":{"source":{"id":"2109.13076","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-27T14:25:10Z","cross_cats_sorted":["physics.plasm-ph"],"title_canon_sha256":"1b4ec1adeefb3548cdab0a366d9d324a3f69d0744ee2bfc2741d8e8dcbfb4fa1","abstract_canon_sha256":"bdf233706eccc420d4bd8ec9d056e9aefc2b9e46f461af8e8b71324dc246532b"},"schema_version":"1.0"},"canonical_sha256":"1954c36cf01c559f5bec3cc1f1162bdaec81e5e6174bc5d16229cd694cd7ead6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:32:54.752384Z","signature_b64":"Ti8bzKN3drlmTRxJCRjBveO/hSjyduDxbDe5wUrbPHppI7fzUYJwydKXfixIY3Kpyzc/beB+Df1OK5I85FxsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1954c36cf01c559f5bec3cc1f1162bdaec81e5e6174bc5d16229cd694cd7ead6","last_reissued_at":"2026-07-05T03:32:54.751900Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:32:54.751900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.13076","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JbTiY4JsuwZvApoFw8RKb0ojC6K7iUFSxtDJ2waXFHxZ30ldKr2a55jm072TvDl5XOvtrY+xmNSDaPIT4SvkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:45:34.517026Z"},"content_sha256":"2395706ccf3175109ea2a1300b00124432bd65e2a85e1f8bcda57422158375bd","schema_version":"1.0","event_id":"sha256:2395706ccf3175109ea2a1300b00124432bd65e2a85e1f8bcda57422158375bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:DFKMG3HQDRKZ6W7MHTA7CFRL3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Using neural networks to solve the 2D Poisson equation for electric field computation in plasma fluid simulations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["physics.plasm-ph"],"primary_cat":"cs.LG","authors_text":"Benedicte Cuenot, Ekhi Ajuria Illarramendi, Guillaume Bogopolsky, Lionel Cheng, Michael Bauerheim","submitted_at":"2021-09-27T14:25:10Z","abstract_excerpt":"The Poisson equation is critical to get a self-consistent solution in plasma fluid simulations used for Hall effect thrusters and streamer discharges, since the Poisson solution appears as a source term of the unsteady nonlinear flow equations. As a first step, solving the 2D Poisson equation with zero Dirichlet boundary conditions using a deep neural network is investigated using multiple-scale architectures, defined in terms of number of branches, depth and receptive field. One key objective is to better understand how neural networks learn the Poisson solutions and provide guidelines to ach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.13076","kind":"arxiv","version":3},"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/2109.13076/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":"2026-07-05T03:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tdk1U8sPhNfUXN1x4RDQro7aXTTY40AONoTmsdOstyN4JYAQ/I3iggxLmTsINRqHWWEnbVb/Y+kE924R3POGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:45:34.517423Z"},"content_sha256":"7325d8b20e384676f1d5e53f78ba4de20e61430a8a0d438ab787a3b2026de95a","schema_version":"1.0","event_id":"sha256:7325d8b20e384676f1d5e53f78ba4de20e61430a8a0d438ab787a3b2026de95a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFKMG3HQDRKZ6W7MHTA7CFRL3L/bundle.json","state_url":"https://pith.science/pith/DFKMG3HQDRKZ6W7MHTA7CFRL3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFKMG3HQDRKZ6W7MHTA7CFRL3L/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":"2026-07-06T18:45:34Z","links":{"resolver":"https://pith.science/pith/DFKMG3HQDRKZ6W7MHTA7CFRL3L","bundle":"https://pith.science/pith/DFKMG3HQDRKZ6W7MHTA7CFRL3L/bundle.json","state":"https://pith.science/pith/DFKMG3HQDRKZ6W7MHTA7CFRL3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFKMG3HQDRKZ6W7MHTA7CFRL3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DFKMG3HQDRKZ6W7MHTA7CFRL3L","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":"bdf233706eccc420d4bd8ec9d056e9aefc2b9e46f461af8e8b71324dc246532b","cross_cats_sorted":["physics.plasm-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-27T14:25:10Z","title_canon_sha256":"1b4ec1adeefb3548cdab0a366d9d324a3f69d0744ee2bfc2741d8e8dcbfb4fa1"},"schema_version":"1.0","source":{"id":"2109.13076","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.13076","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"2109.13076v3","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.13076","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"DFKMG3HQDRKZ","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"pith_short_16","alias_value":"DFKMG3HQDRKZ6W7M","created_at":"2026-07-05T03:32:54Z"},{"alias_kind":"pith_short_8","alias_value":"DFKMG3HQ","created_at":"2026-07-05T03:32:54Z"}],"graph_snapshots":[{"event_id":"sha256:7325d8b20e384676f1d5e53f78ba4de20e61430a8a0d438ab787a3b2026de95a","target":"graph","created_at":"2026-07-05T03:32:54Z","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/2109.13076/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Poisson equation is critical to get a self-consistent solution in plasma fluid simulations used for Hall effect thrusters and streamer discharges, since the Poisson solution appears as a source term of the unsteady nonlinear flow equations. As a first step, solving the 2D Poisson equation with zero Dirichlet boundary conditions using a deep neural network is investigated using multiple-scale architectures, defined in terms of number of branches, depth and receptive field. One key objective is to better understand how neural networks learn the Poisson solutions and provide guidelines to ach","authors_text":"Benedicte Cuenot, Ekhi Ajuria Illarramendi, Guillaume Bogopolsky, Lionel Cheng, Michael Bauerheim","cross_cats":["physics.plasm-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-27T14:25:10Z","title":"Using neural networks to solve the 2D Poisson equation for electric field computation in plasma fluid simulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.13076","kind":"arxiv","version":3},"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":"sha256:2395706ccf3175109ea2a1300b00124432bd65e2a85e1f8bcda57422158375bd","target":"record","created_at":"2026-07-05T03:32:54Z","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":"bdf233706eccc420d4bd8ec9d056e9aefc2b9e46f461af8e8b71324dc246532b","cross_cats_sorted":["physics.plasm-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2021-09-27T14:25:10Z","title_canon_sha256":"1b4ec1adeefb3548cdab0a366d9d324a3f69d0744ee2bfc2741d8e8dcbfb4fa1"},"schema_version":"1.0","source":{"id":"2109.13076","kind":"arxiv","version":3}},"canonical_sha256":"1954c36cf01c559f5bec3cc1f1162bdaec81e5e6174bc5d16229cd694cd7ead6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1954c36cf01c559f5bec3cc1f1162bdaec81e5e6174bc5d16229cd694cd7ead6","first_computed_at":"2026-07-05T03:32:54.751900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:32:54.751900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ti8bzKN3drlmTRxJCRjBveO/hSjyduDxbDe5wUrbPHppI7fzUYJwydKXfixIY3Kpyzc/beB+Df1OK5I85FxsDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:32:54.752384Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.13076","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2395706ccf3175109ea2a1300b00124432bd65e2a85e1f8bcda57422158375bd","sha256:7325d8b20e384676f1d5e53f78ba4de20e61430a8a0d438ab787a3b2026de95a"],"state_sha256":"9257bd2e50bde75490b07ad8a8d5c145972bf8f9fd08e191a396b1a39bed9c3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1nkcNch0MKbwmO9akfCpjjAiBqtaITLj9o7/ZBC8iLrBNl60y/1U2EMLQLDYnSb6AgoOvmoR4YN1XHIZShaRCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:45:34.519504Z","bundle_sha256":"ba10981ac0c3f3b8011412ae9d0bce3d4a1d75f1857800dcb5eca15585bd459a"}}