Learning dynamics on invariant measures using PDE-constrained optimization
arXiv:2301.05193 · doi:10.1063/5.0149673
Abstract
We extend the methodology in [Yang et al., 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 better stability than direct trajectory simulation in certain situations. We present numerical results for the Van der Pol oscillator and the Lorenz-63 system, together with real-world applications to Hall-effect thruster dynamics and temperature prediction, to demonstrate the effectiveness of the proposed approach.
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 6, June 2023, and may be found at https://doi.org/10.1063/5.0149673
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