GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems

Area of Science:

• Physics
• Machine Learning
• Dynamical Systems

Background:

• Dynamical systems modeling often requires complex equations.
• Integrating physics principles into machine learning is crucial for accurate predictions.
• Existing data-driven methods may struggle with complex physical constraints.

Purpose of the Study:

• To propose a novel neural network architecture, GENERIC formalism informed neural networks (GFINNs).
• To ensure GFINNs satisfy the symmetric degeneracy conditions of the GENERIC formalism.
• To demonstrate the effectiveness of GFINNs in predicting dynamical systems.

Main Methods:

• Developing GFINNs with a modular architecture of two components each.
• Designing neural network components to inherently satisfy physics-based conditions.
• Theoretically proving the universal approximation theorem for GFINNs.
• Testing GFINNs on simulations of gas containers, a thermoelastic double pendulum, and Langevin dynamics.

Main Results:

• GFINNs successfully learn underlying equations and satisfy physics constraints.
• GFINNs demonstrate superior accuracy compared to existing methods in all tested simulations.
• The architecture allows flexible integration of physics information into neural networks.
• Accurate predictions were achieved for both deterministic and stochastic systems.

Conclusions:

• GFINNs offer a powerful, physics-informed approach for data-driven prediction in dynamical systems.
• The proposed architecture provides a robust framework for incorporating physical laws into machine learning models.
• GFINNs represent a significant advancement in accurately modeling complex physical phenomena.