Parsimonious neural networks learn classical mechanics, its underlying symmetries, and an accurate time integrator
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Machine learning is playing an increasing role in the physical sciences and significant progress has been made towards embedding physics into domain-agnostic models. Less explored is the potential of machine learning in the discovery of physical laws from observational data through interpretable models. We combine neural networks with evolutionary optimization to find the simplest models that describe the time evolution of a point particle under a highly nonlinear potential. The resulting parsimonious neural networks are easily interpretable as Newton's second law expressed as a non-trivial time integrator that exhibits time-reversibility and conserves energy. By extracting the underlying physics, the model significantly outperforms a generic feed-forward neural network. Furthermore, the models discovered belong to the widely used family of Verlet algorithms which are not only reversible but symplectic.
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