Parsimonious neural networks learn interpretable physical laws

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 its use to discover interpretable laws from data. We propose parsimonious neural networks (PNNs) that combine with evolutionary optimization find models balance accuracy parsimony. The power versatility of approach demonstrated by developing for classical mechanics predict melting temperature materials fundamental properties. In first example, resulting PNNs are easily as Newton’s second law, expressed a non-trivial time integrator exhibits time-reversibility conserves energy, where parsimony critical extract underlying symmetries case, not only celebrated Lindemann but also new relationships outperform it pareto sense vs. accuracy.