AI Poincaré 2.0: Machine Learning Conservation Laws from Differential Equations

03/23/2022

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by   Ziming Liu, et al.

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We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the 3-body problem, the KdV equation and nonlinear Schrödinger equation.