{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YICJO7Z2QCATZQTQ2J5TW4OZ3T","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":"df3f936bbe91a5c6df6bff23173469c01040b391b5872d6cf8ed6b847a78d512","cross_cats_sorted":["cs.NA","cs.NE","math.NA","physics.comp-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-08T03:24:50Z","title_canon_sha256":"70a9828e3c6888d2f4b8b9a9ef48c6d0b47189a0ec6a26cec9e1fe6003026b6b"},"schema_version":"1.0","source":{"id":"1806.02957","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02957","created_at":"2026-06-04T19:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02957v2","created_at":"2026-06-04T19:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02957","created_at":"2026-06-04T19:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"YICJO7Z2QCAT","created_at":"2026-06-04T19:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"YICJO7Z2QCATZQTQ","created_at":"2026-06-04T19:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"YICJO7Z2","created_at":"2026-06-04T19:11:57Z"}],"graph_snapshots":[{"event_id":"sha256:7829544972785c19cafda354a66ed94e8be8058faaf94d04c7eeea6e3195c3c6","target":"graph","created_at":"2026-06-04T19:11:57Z","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/1806.02957/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for these problems based on a deep learning approach. Specifically, the random PDE is approximated by a feed-forward fully-connected deep residual network, with either strong or weak enforcement of initial and boundary constraints. The framework is mesh-free, and can handle irregular computational domains. Parameters of the approximating deep neural network are d","authors_text":"Hadi Meidani, Mohammad Amin Nabian","cross_cats":["cs.NA","cs.NE","math.NA","physics.comp-ph","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-08T03:24:50Z","title":"A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02957","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":"sha256:64bb9d75b2c5e7f0f0d9ccf42c065bba02774aac49ad29337fc48aa056bdbc09","target":"record","created_at":"2026-06-04T19:11:57Z","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":"df3f936bbe91a5c6df6bff23173469c01040b391b5872d6cf8ed6b847a78d512","cross_cats_sorted":["cs.NA","cs.NE","math.NA","physics.comp-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-08T03:24:50Z","title_canon_sha256":"70a9828e3c6888d2f4b8b9a9ef48c6d0b47189a0ec6a26cec9e1fe6003026b6b"},"schema_version":"1.0","source":{"id":"1806.02957","kind":"arxiv","version":2}},"canonical_sha256":"c204977f3a80813cc270d27b3b71d9dcfd8e6399bc319b72956bdd06eac56aff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c204977f3a80813cc270d27b3b71d9dcfd8e6399bc319b72956bdd06eac56aff","first_computed_at":"2026-06-04T19:11:57.476961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:11:57.476961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FhFYe2M1WCgjFzOvaZAxOr2fkUJtYuF35QU7M+CK/XcHqU/8h4iyy4iyoXM81lM4VB9vg9oNkOmbW7Y3Ub8MAg==","signature_status":"signed_v1","signed_at":"2026-06-04T19:11:57.477584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02957","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64bb9d75b2c5e7f0f0d9ccf42c065bba02774aac49ad29337fc48aa056bdbc09","sha256:7829544972785c19cafda354a66ed94e8be8058faaf94d04c7eeea6e3195c3c6"],"state_sha256":"283e210b7694dd66a74934726aa387d014df64ff636456372c34d3818cf6d63d"}