2023
DOI: 10.1063/5.0149673
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Learning dynamics on invariant measures using PDE-constrained optimization

Abstract: We extend the methodology in Yang et al. [SIAM J. Appl. Dyn. Syst. 22, 269–310 (2023)] to learn autonomous continuous-time dynamical systems from invariant measures. The highlight of our approach is to reformulate the inverse problem of learning ODEs or SDEs from data as a PDE-constrained optimization problem. This shift in perspective allows us to learn from slowly sampled inference trajectories and perform uncertainty quantification for the forecasted dynamics. Our approach also yields a forward model with b… Show more

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