{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OQCKHCUXT4VEVXP42GV3XLXFIK","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":"f31bd1290b1bd5e1553e3137162042faf5a0deb2f260dc3ec4e77ac3432812a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-11T13:32:45Z","title_canon_sha256":"8d54a3d8f1d82ec922d09f4bb3669398633691576df2ef6b5698220fdae3485a"},"schema_version":"1.0","source":{"id":"1812.04387","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04387","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04387v4","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04387","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"pith_short_12","alias_value":"OQCKHCUXT4VE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OQCKHCUXT4VEVXP4","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OQCKHCUX","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:fa4dc7ebf46396f61325b4d5ea6d253ddb8075d1e6b813797371ccd26448374d","target":"graph","created_at":"2026-05-17T23:54:02Z","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"},"paper":{"abstract_excerpt":"This work proposes a systematic model reduction approach based on rank adaptive tensor recovery for partial differential equation (PDE) models with high-dimensional random parameters. Since the standard outputs of interest of these models are discrete solutions on given physical grids which are high-dimensional, we use kernel principal component analysis to construct stochastic collocation approximations in reduced dimensional spaces of the outputs. To address the issue of high-dimensional random inputs, we develop a new efficient rank adaptive tensor recovery approach to compute the collocati","authors_text":"Kejun Tang, Qifeng Liao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-11T13:32:45Z","title":"Rank adaptive tensor recovery based model reduction for partial differential equations with high-dimensional random inputs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04387","kind":"arxiv","version":4},"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:d86d372e928e91be672fad26ad5797d1ea2838035301832aa0c70ff12c703570","target":"record","created_at":"2026-05-17T23:54:02Z","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":"f31bd1290b1bd5e1553e3137162042faf5a0deb2f260dc3ec4e77ac3432812a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-11T13:32:45Z","title_canon_sha256":"8d54a3d8f1d82ec922d09f4bb3669398633691576df2ef6b5698220fdae3485a"},"schema_version":"1.0","source":{"id":"1812.04387","kind":"arxiv","version":4}},"canonical_sha256":"7404a38a979f2a4addfcd1abbbaee54299a787b6964f9cab26fd0ad7c5326c44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7404a38a979f2a4addfcd1abbbaee54299a787b6964f9cab26fd0ad7c5326c44","first_computed_at":"2026-05-17T23:54:02.269449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:02.269449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8gjtI6kxSqUrvAt7t16ZxbKzXR/NdGVEDr/hxYy1qxMXrK/W8MqnIrrCTVNqjPr43oEjETpnjjxZAyylC13sDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:02.269912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04387","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d86d372e928e91be672fad26ad5797d1ea2838035301832aa0c70ff12c703570","sha256:fa4dc7ebf46396f61325b4d5ea6d253ddb8075d1e6b813797371ccd26448374d"],"state_sha256":"f50fdf96f9d3f29576e01e761065d9b2a5471a7e4a0d999a3e4af92939c073c8"}