{"paper":{"title":"Discovering Physical Directions in Weight Space: Composing Neural PDE Experts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Fine-tuning endpoint experts on a shared neural PDE operator reveals a reusable physical direction in weight space for training-free regime composition.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Dong Ni, Guanyu Chen, Pengkai Wang, Pengwei Liu, Qixin Zhang, Xiaolong Li, Xingyu Ren, Yuanyi Wang, Yuting Kong, Zhongkai Hao","submitted_at":"2026-05-14T08:25:16Z","abstract_excerpt":"Recent advances in neural operators have made partial differential equation (PDE) surrogate modeling increasingly scalable and transferable through large-scale pretraining and in-context adaptation. However, after a shared operator is fine-tuned to multiple regimes within a continuous physical family, it remains unclear whether the resulting weight-space updates merely form isolated regime experts or reveal reusable physical structure. Starting from a shared family anchor, we fine-tune low- and high-regime endpoint experts and show that their updates can be separated into a family-shared adapt"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"endpoint fine-tuning is not arbitrary checkpoint drift, but reveals a calibratable physical direction for training-free transfer across PDE regimes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"that the observed separation of weight updates into family-shared adaptation and a direction aligned with the underlying physical parameter is stable, generalizable, and not an artifact of the specific fine-tuning procedure or chosen regimes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Fine-tuning endpoint experts on a shared neural PDE operator reveals a reusable physical direction in weight space for training-free regime composition.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"70d2524f89757de129312388f2342a1ec6da36dbf1d0f34f069a45211b0cc214"},"source":{"id":"2605.14546","kind":"arxiv","version":1},"verdict":{"id":"79fad18b-0a94-43e0-b49e-3f8421cbcd10","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:59:33.617795Z","strongest_claim":"endpoint fine-tuning is not arbitrary checkpoint drift, but reveals a calibratable physical direction for training-free transfer across PDE regimes.","one_line_summary":"Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"that the observed separation of weight updates into family-shared adaptation and a direction aligned with the underlying physical parameter is stable, generalizable, and not an artifact of the specific fine-tuning procedure or chosen regimes.","pith_extraction_headline":"Fine-tuning endpoint experts on a shared neural PDE operator reveals a reusable physical direction in weight space for training-free regime composition."},"references":{"count":61,"sample":[{"doi":"","year":2010,"title":"Fourier Neural Operator for Parametric Partial Differential Equations","work_id":"cc647655-121e-4055-85f0-fad4530ea964","ref_index":1,"cited_arxiv_id":"2010.08895","is_internal_anchor":true},{"doi":"","year":2024,"title":"Neural operators for accelerating scientific simulations and design","work_id":"3109e4ff-48e4-4cab-ba3f-8be9e47a7450","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Gnot: A general neural operator transformer for operator learning","work_id":"06a918b1-6e2e-4214-94e7-ad376a5a17a6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Laplace neural operator for solving differential equations.Nature Machine Intelligence, 6(6):631–640, 2024","work_id":"aa762c8c-c93a-4842-bcbd-cbcd905ca12d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"Neural Operator: Graph Kernel Network for Partial Differential Equations","work_id":"00a591bc-6cad-477c-be12-26d5623f625d","ref_index":5,"cited_arxiv_id":"2003.03485","is_internal_anchor":true}],"resolved_work":61,"snapshot_sha256":"429b5eac9c2d5f15ac060d5a63da028286993f7a3ece7010df57293576b057c3","internal_anchors":5},"formal_canon":{"evidence_count":2,"snapshot_sha256":"bd556019bbca616847ed6d52f8db497501f2be690eabf490c9982e0cb033418e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}