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Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fields — arXiv:2608.27475

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.27475
License (as archived): CC0-1.0
Archived: 2026-10-17T10:47:01.464Z
SHA-256 of the archived text: 30d77a17a9b8e31fd5a9bd9234066ca6ddbf23ec061e1013b0a48613f371aca2
Stable URL of this page: https://metraipolis.com/documento/dc_49558ecb4abd

How to cite

Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fields — arXiv:2608.27475 — arXiv (en), https://arxiv.org/abs/2608.27475 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_49558ecb4abd (Metraipolis archive dc_49558ecb4abd, sha256 30d77a17a9b8e31fd5a9bd9234066ca6ddbf23ec061e1013b0a48613f371aca2)

BibTeX

@misc{dc49558ecb4abd,
  title = {Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fields — arXiv:2608.27475},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.27475},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_49558ecb4abd; sha256 30d77a17a9b8e31fd5a9bd9234066ca6ddbf23ec061e1013b0a48613f371aca2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.27475. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Discovering PDEs in heterogeneous media requires jointly identifying the governing operator and the unknown spatial fields that parameterize it. These tasks are coupled: changing field placement changes the differential law, while a sufficiently flexible field can conceal structural error on a single trajectory. We present Hypothesize, Evaluate, Refine for PDE Discovery (HER-PDE), a scientific-agent framework that discovers compositional PDE structure together with nonparametric, time-invariant coefficient fields. The Agent analyzes two noisy trajectories generated by different excitations, proposes complete expression-tree hypotheses, and combines creative structural exploration with local candidate refinement. Its Hypothesis Evaluation Interface (HEI) estimates only the fields explicitly declared in each hypothesis, never adds missing terms, and scores structures by bidirectional cross-excitation transfer. The selected law is subsequently audited on a sealed temporal interval. Across five controlled two-dimensional systems observed with 5 percent relative Gaussian state noise, the Agent recovers the generating operator in all five cases, including equivalent signed-field and product-rule parameterizations. Across nine unknown coefficient fields, the recovered fields attain a median Pearson correlation of approximately 0.85 and a median relative L2 error of approximately 0.28. These results show that agent-guided hypothesis refinement can recover heterogeneous governing laws without prescribing a parametric form for their spatial coefficients.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-31 in cs.AI).
Categorie arXiv: Artificial Intelligence (cs.AI) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2608.27475 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T10:33:42.324Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-08-31?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).