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

Abstract

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.

References in corpus (4)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Reversible Architectures for Arbitrarily Deep Residual Neural Networks
• Machine learning structure preserving brackets for forecasting irreversible processes
• Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Kriging-Based Optimization

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