Abstract:  Numerical integration of a given dynamic system can be viewed as a forward problem with the learning of unknown dynamics from available state observations as an inverse problem. The latter has been around in various settings such as model reductions of multiscale processes. It has received particular attention recently in the data-driven modeling via deep/machine learning. The solution of both forward and inverse problems forms the loop of informative and intelligent scientific computing. A naturally related question is whether a good numerical integrator for discretizing prescribed dynamics is also good for discovering unknown dynamics. This lecture presents a study in the context of linear multistep methods.

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