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Date
2023-01-12Type
- Working Paper
ETH Bibliography
yes
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Abstract
We extend the methodology in [Yang et al., 2021] to learn autonomous continuous-time dynamical systems from invariant measures. We assume that our data accurately describes the dynamics' asymptotic statistics but that the available time history of observations is insufficient for approximating the Lagrangian velocity. Therefore, invariant measures are treated as the inference data and velocity learning is reformulated as a data-fitting, PDE-constrained optimization problem in which the stationary distributional solution to the Fokker--Planck equation is used as a differentiable surrogate forward model. We consider velocity parameterizations based upon global polynomials, piecewise polynomials, and fully connected neural networks, as well as various objective functions to compare synthetic and reference invariant measures. We utilize the adjoint-state method together with the backpropagation technique to efficiently perform gradient-based parameter identification. Numerical results for the Van der Pol oscillator and Lorenz-63 system, together with real-world applications to Hall-effect thruster dynamics and temperature prediction, are presented to demonstrate the effectiveness of the proposed approach. Show more
Publication status
publishedJournal / series
arXivPages / Article No.
Publisher
Cornell UniversityEdition / version
v1Subject
Dynamical systems; Invariant measures; Inverse Frobenius–Perron problem; Parameter identification; Fokker–Planck equation; Neural networks; Time-delay embedding; · Computational ergodic theoryOrganisational unit
02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies
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