Machine learning structure preserving brackets for forecasting irreversible processes
This work addresses forecasting irreversible time-series data for applications requiring thermodynamic consistency, representing a novel method for a known bottleneck rather than an incremental improvement.
The paper tackles forecasting irreversible processes by developing a novel parameterization of dissipative brackets from metriplectic dynamical systems, which learns generalized Casimirs for energy and entropy with guaranteed conservation and nondecrease. The result shows that the learned dynamics are more robust and generalize better than black-box or penalty-based approaches in benchmarks for dissipative systems.
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.