arXiv Open Access 2023

Learning dynamics on invariant measures using PDE-constrained optimization

Jonah Botvinick-Greenhouse Robert Martin Yunan Yang

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Abstrak

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.

Topik & Kata Kunci

math.DS math.NA

Penulis (3)

Jonah Botvinick-Greenhouse

Robert Martin

Yunan Yang

Format Sitasi

APA MLA BibTeX

Botvinick-Greenhouse, J., Martin, R., Yang, Y. (2023). Learning dynamics on invariant measures using PDE-constrained optimization. https://arxiv.org/abs/2301.05193

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓