Machine learning structure preserving brackets for forecasting irreversible processes

• URL: http://arxiv.org/abs/2106.12619v1
• Date: Wed, 23 Jun 2021 18:27:59 GMT
• Title: Machine learning structure preserving brackets for forecasting irreversible processes
• Authors: Kookjin Lee and Nathaniel A. Trask and Panos Stinis
• Abstract summary: We present a novel parameterization of dissipative brackets from metriplectic dynamical systems. The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing. We provide benchmarks for dissipative systems demonstrating learned dynamics are more robust and generalize better than either "black-box" or penalty-based approaches.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 reversible dynamics. In this work we present a novel parameterization of dissipative brackets from metriplectic dynamical systems appropriate for learning 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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