{
  "abstract": "Equation learning seeks to discover compact, interpretable equations from data using various machine-learning techniques. However, few workflows discover and interpret learned equations in sparse, high-dimensional materials datasets. We present nn-EQL, an equation-learning framework that generates candidate equations through iterative training, pruning, and retraining of a neural network with customizable, user-specified neuron-level activation functions. Candidate equations are ranked using a minimum description length (MDL)-inspired score, balancing error and sparsity, and diagnosed to assess term-wise contributions, input-scaled sensitivities, and uncertainties. We demonstrate nn-EQL on standard AI-Feynman benchmarks as well as multiscale high-dimensional materials datasets such as finite-element simulations of heterogeneous materials, and high-throughput experimental thin-film deposition data. nn-EQL integrates with tabular data and high-dimensional data via standard encoder models, learning equations and providing insight into learned terms. Looking forward, integrating physically interpretable representations, multimodal and multi-fidelity data, and adaptive data acquisition could enable equation learning to formulate and test mechanistic hypotheses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37880",
  "author_total": 4,
  "authors": [
    {
      "name": "Philip Jacobson"
    },
    {
      "name": "Prasad Iyer"
    },
    {
      "name": "Remi Dingreville"
    },
    {
      "name": "Saaketh Desai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bysmpft30yek.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37880",
  "fulltext_url": null,
  "id": "7bysmpft30yek",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37880",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cs.LG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37880",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bysmpft30yek.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.37880",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37880"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Interpretable neural equation learning for high-dimensional materials data",
  "title_text": "Interpretable neural equation learning for high-dimensional materials data",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/7bysmpft30yek",
  "venue": "arXiv",
  "versions": []
}