Parsimonious neural networks learn interpretable physical laws

TL;DR

This paper introduces parsimonious neural networks that combine neural networks with evolutionary optimization to discover interpretable physical laws from data, demonstrating their effectiveness in classical mechanics and materials science.

Contribution

The paper presents a novel approach that balances accuracy and simplicity in neural network models to uncover interpretable physical laws from data.

Findings

PNNs can recover Newton's second law with energy conservation and time-reversibility.

PNNs discover the Lindemann melting law and propose new, more accurate relationships.

The approach effectively balances model parsimony and predictive accuracy.

Abstract

Machine learning is playing an increasing role in the physical sciences and significant progress has been made towards embedding domain knowledge into models. Less explored is its use to discover interpretable physical laws from data. We propose parsimonious neural networks (PNNs) that combine neural networks with evolutionary optimization to find models that balance accuracy with parsimony. The power and versatility of the approach is demonstrated by developing models for classical mechanics and to predict the melting temperature of materials from fundamental properties. In the first example, the resulting PNNs are easily interpretable as Newton's second law, expressed as a non-trivial time integrator that exhibits time-reversibility and conserves energy, where the parsimony is critical to extract underlying symmetries from the data. In the second case, the PNNs not only find the celebrated Lindemann melting law, but also new relationships that outperform it in the pareto sense of parsimony vs. accuracy.