{"paper":{"title":"Stochastic Dimension-Free Zeroth-Order Estimator for High-Dimensional and High-Order PINNs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A stochastic zeroth-order estimator trains physics-informed neural networks with up to 10 million dimensions using memory and computation costs that stay independent of dimension and derivative order.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Huanhuan Gao, Zhangyong Liang","submitted_at":"2026-03-25T07:02:34Z","abstract_excerpt":"Physics-Informed Neural Networks (PINNs) for high-dimensional and high-order partial differential equations (PDEs) are primarily constrained by the $\\mathcal{O}(d^k)$ spatial derivative complexity and the $\\mathcal{O}(P)$ memory overhead of backpropagation (BP). While randomized spatial estimators successfully reduce the spatial complexity to $\\mathcal{O}(1)$, their reliance on first-order optimization still leads to prohibitive memory consumption at scale. Zeroth-order (ZO) optimization offers a BP-free alternative; however, naively combining randomized spatial operators with ZO perturbations"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"SDZE achieves dimension-independent complexity in both space and memory, enabling the training of 10-million-dimensional PINNs on a single NVIDIA A100 GPU.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That Common Random Numbers Synchronization algebraically cancels the O(1/ε²) variance explosion while preserving unbiasedness and convergence of the zeroth-order estimator for the specific randomized spatial operators used in high-order PINNs.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"SDZE uses common random number synchronization and implicit subspace projection to enable training of 10-million-dimensional PINNs on a single GPU with O(1) space and memory complexity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A stochastic zeroth-order estimator trains physics-informed neural networks with up to 10 million dimensions using memory and computation costs that stay independent of dimension and derivative order.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cce95cab2d91f82cd1c16740df7a1672831a3402336bde2b90944e77972c6a64"},"source":{"id":"2603.24002","kind":"arxiv","version":2},"verdict":{"id":"cc46fed2-606d-433d-991f-557445800809","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T00:43:08.698061Z","strongest_claim":"SDZE achieves dimension-independent complexity in both space and memory, enabling the training of 10-million-dimensional PINNs on a single NVIDIA A100 GPU.","one_line_summary":"SDZE uses common random number synchronization and implicit subspace projection to enable training of 10-million-dimensional PINNs on a single GPU with O(1) space and memory complexity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That Common Random Numbers Synchronization algebraically cancels the O(1/ε²) variance explosion while preserving unbiasedness and convergence of the zeroth-order estimator for the specific randomized spatial operators used in high-order PINNs.","pith_extraction_headline":"A stochastic zeroth-order estimator trains physics-informed neural networks with up to 10 million dimensions using memory and computation costs that stay independent of dimension and derivative order."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"36f8abfc8b0367cd9c9bc65e108737ae6faffc71705ece9f31118bc8b40f6f9a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}