Learning dynamics on invariant measures using PDE-constrained optimization
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.
Cite
@article{arxiv.2301.05193,
title = {Learning dynamics on invariant measures using PDE-constrained optimization},
author = {Jonah Botvinick-Greenhouse and Robert Martin and Yunan Yang},
journal= {arXiv preprint arXiv:2301.05193},
year = {2023}
}
Comments
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