{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:I5PBLHCISM53LBVGUS5CSQOQBD","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":"7bc5f6994e368c87d7d5131fb94f441ea35873ed905b7481f22811602b775829","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-04T06:37:38Z","title_canon_sha256":"1d220a973c657e8af81c81d5fd504f3a1c2281406a4885737ee3ee7d591b8003"},"schema_version":"1.0","source":{"id":"2402.02366","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.02366","created_at":"2026-05-17T23:38:50Z"},{"alias_kind":"arxiv_version","alias_value":"2402.02366v2","created_at":"2026-05-17T23:38:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.02366","created_at":"2026-05-17T23:38:50Z"},{"alias_kind":"pith_short_12","alias_value":"I5PBLHCISM53","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"I5PBLHCISM53LBVG","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"I5PBLHCI","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:8e659306f4721714ab559ac6f0e36604eb21de684f94732a0aa1d61ab89b7733","target":"graph","created_at":"2026-05-17T23:38:50Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Transolver achieves consistent state-of-the-art with 22% relative gain across six standard benchmarks and also excels in large-scale industrial simulations, including car and airfoil designs."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That mesh points under similar physical states can be reliably and adaptively grouped into a series of learnable slices whose encoded tokens capture the necessary physical correlations without missing critical local interactions."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Transolver learns intrinsic physical states from discretized meshes by adaptively splitting domains into flexible learnable slices and computing attention over physics-aware tokens, achieving state-of-the-art PDE solving on general geometries."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"By grouping mesh points with similar physical states into learnable slices, Transolver lets Transformers solve PDEs on arbitrary geometries in linear time."}],"snapshot_sha256":"340733dc3c2fca53346349ebdddfcf8973164eff6a26d45370eb4fe7393fa51a"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9279b3a01e583a3d2fda6c36ba3669370ed74f26cabc678872ee6c9d1b9ad58e"},"paper":{"abstract_excerpt":"Transformers have empowered many milestones across various fields and have recently been applied to solve partial differential equations (PDEs). However, since PDEs are typically discretized into large-scale meshes with complex geometries, it is challenging for Transformers to capture intricate physical correlations directly from massive individual points. Going beyond superficial and unwieldy meshes, we present Transolver based on a more foundational idea, which is learning intrinsic physical states hidden behind discretized geometries. Specifically, we propose a new Physics-Attention to adap","authors_text":"Haixu Wu, Haowen Wang, Huakun Luo, Jianmin Wang, Mingsheng Long","cross_cats":["cs.NA","math.NA"],"headline":"By grouping mesh points with similar physical states into learnable slices, Transolver lets Transformers solve PDEs on arbitrary geometries in linear time.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-04T06:37:38Z","title":"Transolver: A Fast Transformer Solver for PDEs on General Geometries"},"references":{"count":33,"internal_anchors":4,"resolved_work":33,"sample":[{"cited_arxiv_id":"2303.08774","doi":"","is_internal_anchor":true,"ref_index":1,"title":"GPT-4 Technical Report","work_id":"b928e041-6991-4c08-8c81-0359e4097c7b","year":null},{"cited_arxiv_id":"1512.03012","doi":"","is_internal_anchor":true,"ref_index":2,"title":"ShapeNet: An Information-Rich 3D Model Repository","work_id":"b2ac5b60-daa9-435b-9369-12271e126edd","year":null},{"cited_arxiv_id":"1604.06174","doi":"","is_internal_anchor":true,"ref_index":3,"title":"Training Deep Nets with Sublinear Memory Cost","work_id":"f2c5c287-a500-40e4-a136-e7e3172db1d7","year":null},{"cited_arxiv_id":"2003.03485","doi":"","is_internal_anchor":true,"ref_index":4,"title":"Neural Operator: Graph Kernel Network for Partial Differential Equations","work_id":"00a591bc-6cad-477c-be12-26d5623f625d","year":2003},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Geometry-informed neural operator for large-scale 3d pdes","work_id":"b57f5179-2379-4048-b180-5c84d9a20a8a","year":2003}],"snapshot_sha256":"d12429c3edc1b9404e29e68c2b2eb9802467a2ace0fd478295ad4c00a30f2b0f"},"source":{"id":"2402.02366","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-15T21:37:13.966590Z","id":"cd55237e-63ee-4d4a-acf3-b36c1c8fdbba","model_set":{"reader":"grok-4.3"},"one_line_summary":"Transolver learns intrinsic physical states from discretized meshes by adaptively splitting domains into flexible learnable slices and computing attention over physics-aware tokens, achieving state-of-the-art PDE solving on general geometries.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"By grouping mesh points with similar physical states into learnable slices, Transolver lets Transformers solve PDEs on arbitrary geometries in linear time.","strongest_claim":"Transolver achieves consistent state-of-the-art with 22% relative gain across six standard benchmarks and also excels in large-scale industrial simulations, including car and airfoil designs.","weakest_assumption":"That mesh points under similar physical states can be reliably and adaptively grouped into a series of learnable slices whose encoded tokens capture the necessary physical correlations without missing critical local interactions."}},"verdict_id":"cd55237e-63ee-4d4a-acf3-b36c1c8fdbba"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a91f045978fb410fc73b5f89a70bc0f6e8d2ad1f48c1d5f5ca1e34e33bdb3b63","target":"record","created_at":"2026-05-17T23:38:50Z","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":"7bc5f6994e368c87d7d5131fb94f441ea35873ed905b7481f22811602b775829","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-02-04T06:37:38Z","title_canon_sha256":"1d220a973c657e8af81c81d5fd504f3a1c2281406a4885737ee3ee7d591b8003"},"schema_version":"1.0","source":{"id":"2402.02366","kind":"arxiv","version":2}},"canonical_sha256":"475e159c48933bb586a6a4ba2941d008d3e5607e0a538af8f65035d327d310a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"475e159c48933bb586a6a4ba2941d008d3e5607e0a538af8f65035d327d310a6","first_computed_at":"2026-05-17T23:38:50.065373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:38:50.065373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wq3fI5TvANfDoo8EcDqwwOayLBFVVhaiDrHSXKcE9FFrGs/mC9c/H5MKnUIHvIvajXX9dOgOd6fiYSXwxiJiDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:38:50.065851Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.02366","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a91f045978fb410fc73b5f89a70bc0f6e8d2ad1f48c1d5f5ca1e34e33bdb3b63","sha256:8e659306f4721714ab559ac6f0e36604eb21de684f94732a0aa1d61ab89b7733"],"state_sha256":"4351ce47138d9ba2f68c34c7fadf537707b39caadf3e4ee4cc56193486c4fe34"}