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Interpretable neural equation learning for high-dimensional materials data
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First announced by arXiv: 2026-10-30 · Indexed by Pub-AI: 2026-10-30 UTC
Interpretable neural equation learning for high-dimensional materials data
First announced by arXiv: 2026-10-30 · Original record ↗
- arxiv
- 2610.37880
Explicit source versions (1)
- v1 · Date not supplied
- Preprint available
Source date: 2026-10-30 · First detected: 2026-10-30 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · RSS guid=oai:arXiv.org:2610.37880v1; arxiv:announce_type=new; item pubDate (official metadata)
Abstract · arxiv
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.