Exact conservation laws for neural network integrators of dynamical systems. (arXiv:2209.11661v1 [math.DS])

The solution of time dependent differential equations with neural networks
has attracted a lot of attention recently. The central idea is to learn the
laws that govern the evolution of the solution from data, which might be
polluted with random noise. However, in contrast to other machine learning
applications, usually a lot is known about the system at hand. For example, for
many dynamical systems physical quantities such as energy or (angular) momentum
are exactly conserved. Hence, the neural network …

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