Machine learning structure preserving brackets for forecasting irreversible processes

Understand

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.