GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems
This work addresses the challenge of modeling complex physical systems with neural networks, offering a domain-specific improvement for computational physics and engineering applications.
The authors tackled the problem of learning deterministic and stochastic dynamical systems by proposing GFINNs, which incorporate the GENERIC formalism to enforce physical constraints, and demonstrated that GFINNs outperform existing methods in accuracy across three simulation examples.
We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of which contains two components. We model each component using a neural network whose architecture is designed to satisfy the required conditions. The component-wise architecture design provides flexible ways of leveraging available physics information into neural networks. We prove theoretically that GFINNs are sufficiently expressive to learn the underlying equations, hence establishing the universal approximation theorem. We demonstrate the performance of GFINNs in three simulation problems: gas containers exchanging heat and volume, thermoelastic double pendulum and the Langevin dynamics. In all the examples, GFINNs outperform existing methods, hence demonstrating good accuracy in predictions for both deterministic and stochastic systems.