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We propose the GENERIC formalism informed neural networks (GFINNs) that obeythe symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprisetwo modules, each of which contains two components. We model each componentusing a neural network whose architecture is designed to satisfy the requiredconditions. The component-wise architecture design provides flexible ways ofleveraging available physics information into neural networks. We provetheoretically that GFINNs are sufficiently expressive to learn the underlyingequations, hence establishing the universal approximation theorem. Wedemonstrate the performance of GFINNs in three simulation problems: gascontainers exchanging heat and volume, thermoelastic double pendulum and theLangevin dynamics. In all the examples, GFINNs outperform existing methods,hence demonstrating good accuracy in predictions for both deterministic andstochastic systems.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems