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 selection and diagnosis
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.
- Ranking: MDL-inspired score balancing error and sparsity
- Diagnosis:
- term-wise contributions
- input-scaled sensitivities
- uncertainties
Demonstrations
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.