Machine learning structure preserving brackets for forecasting irreversible processesDownload PDF

21 May 2021, 20:51 (modified: 26 Oct 2021, 16:25)NeurIPS 2021 PosterReaders: Everyone
Keywords: structure preserving machine learning, neural odes, forecasting, dissipative systems
TL;DR: We design an architecture for learning dissipative ODEs preserving algebraic structure guaranteeing compatibility with 1st and 2nd law of thermodynamics.
Abstract: Forecasting of time-series data requires imposition of inductive biases to obtain predictive extrapolation, and recent works have imposed Hamiltonian/Lagrangian form to preserve structure for systems with \emph{reversible} dynamics. In this work we present a novel parameterization of dissipative brackets from metriplectic dynamical systems appropriate for learning \emph{irreversible} dynamics with unknown a priori model form. The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing, respectively. Furthermore, for the case of added thermal noise, we guarantee exact preservation of a fluctuation-dissipation theorem, ensuring thermodynamic consistency. We provide benchmarks for dissipative systems demonstrating learned dynamics are more robust and generalize better than either "black-box" or penalty-based approaches.
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