{"paper":{"title":"SPDEBench: An Extensive Benchmark for Learning Stochastic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"SPDEBench supplies the first unified collection of ready-to-use datasets for machine learning models that approximate solutions to stochastic partial differential equations, including singular cases.","cross_cats":["math.AP","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Bingguang Chen, Dai Shi, Hao Ni, Jose Miguel Lara Rangel, Luke Thompson, Oliver Nash, Qi Meng, Rongchan Zhu, Siran Li, Yuantu Zhu, Zheyan Li","submitted_at":"2025-05-24T05:15:45Z","abstract_excerpt":"Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although machine learning (ML)-based surrogate models have shown promise for efficiently approximating such dynamics, progress remains limited by the lack of a unified benchmark with controlled data generation and comprehensive evaluation. This gap is particularly significant for singular SPDEs, for which benchmark datasets are largely unavailable and reliable simulation "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"SPDEBench is the first unified benchmark for ML-based SPDE learning that provides ready-to-use datasets for regular and singular SPDEs; numerical results show that SPDE-aware architectures generally achieve stronger performance than generic operator-learning baselines on accuracy, robustness, and out-of-distribution generalization.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The data-generation procedures (noise approximation, basis choice, renormalization for singular SPDEs) produce representative datasets that enable unbiased model comparisons without hidden numerical artifacts or selection effects that would favor certain architectures.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"SPDEBench is the first unified benchmark providing ready-to-use datasets for regular and singular SPDEs, ML operator-learning baselines, and evaluations showing SPDE-aware models outperform generic ones on accuracy, robustness, and OOD generalization.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"SPDEBench supplies the first unified collection of ready-to-use datasets for machine learning models that approximate solutions to stochastic partial differential equations, including singular cases.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"04f17de20af6d7faf8a29e0a1cec7becdbcf2d8fd7235e2f70ec69a8946b5a9e"},"source":{"id":"2505.18511","kind":"arxiv","version":3},"verdict":{"id":"8ce8ccdf-f774-46a0-bb23-75e9ee7c08eb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T13:47:53.512721Z","strongest_claim":"SPDEBench is the first unified benchmark for ML-based SPDE learning that provides ready-to-use datasets for regular and singular SPDEs; numerical results show that SPDE-aware architectures generally achieve stronger performance than generic operator-learning baselines on accuracy, robustness, and out-of-distribution generalization.","one_line_summary":"SPDEBench is the first unified benchmark providing ready-to-use datasets for regular and singular SPDEs, ML operator-learning baselines, and evaluations showing SPDE-aware models outperform generic ones on accuracy, robustness, and OOD generalization.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The data-generation procedures (noise approximation, basis choice, renormalization for singular SPDEs) produce representative datasets that enable unbiased model comparisons without hidden numerical artifacts or selection effects that would favor certain architectures.","pith_extraction_headline":"SPDEBench supplies the first unified collection of ready-to-use datasets for machine learning models that approximate solutions to stochastic partial differential equations, including singular cases."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.18511/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":2,"snapshot_sha256":"77b12e0132ce43dd707ddd44fdc2b8dacedadd3c344ae7c1ac5b0c435575ddde"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}