Neural network finds simple math equations from complex materials data
Interpretable neural equation learning for high-dimensional materials data
Machine Learning
Summary
Finding simple and understandable equations that explain complex data is hard, especially when there are many variables involved. The authors created nn-EQL, a special method that uses neural networks to discover these equations by training, pruning, and retraining with user-chosen functions. They also score these equations to balance how accurate and simple they are and check how important each term is. They tested it on standard problems and on complicated materials data from experiments and simulations, showing it can explain the results in clear equations.
What this means in practice
- •For materials engineers: Generate interpretable equations from high-dimensional simulations to better understand material behaviors.
- •For experimental process teams: Use interpretable equations derived from high-throughput experimental data to improve thin-film deposition processes.
Authors
Philip Jacobson, Prasad Iyer, Remi Dingreville, Saaketh Desai
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.