Interpretable neural equation learning for high-dimensional materials data
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.
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BibTeX
@misc{jacobson2026interpretable,
title = {{Interpretable neural equation learning for high-dimensional materials data}},
author = {Philip Jacobson and Prasad Iyer and Remi Dingreville and Saaketh Desai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37880},
eprint = {2610.37880},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37880},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Interpretable neural equation learning for high-dimensional materials data
AU - Philip Jacobson
AU - Prasad Iyer
AU - Remi Dingreville
AU - Saaketh Desai
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37880
UR - https://arxiv.org/abs/2610.37880
AB - 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.
ER -