Parsimonious neural networks learn interpretable physical laws
This work addresses the need for interpretable machine learning models in the physical sciences, offering a method to uncover fundamental laws from data, though it is incremental in combining existing techniques.
The authors tackled the problem of discovering interpretable physical laws from data by proposing parsimonious neural networks (PNNs) that balance accuracy with simplicity, demonstrating their approach by deriving Newton's second law and outperforming the Lindemann melting law in parsimony-accuracy trade-offs.
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.