Variational integrator graph networks for learning energy-conserving dynamical systems.

Area of Science:

• Computational Physics
• Machine Learning
• Dynamical Systems

Background:

• Physics-informed neural networks (PINNs) improve predictions of complex physical systems.
• Optimal combination of physics priors in PINNs remains understudied.
• Existing methods represent a subset of potential inductive bias combinations.

Purpose of the Study:

• To systematically investigate combinations of inductive biases for improved predictive performance.
• To introduce a novel unifying framework for physics-informed neural networks.
• To enhance data-efficient learning and predictive accuracy in dynamical systems.

Main Methods:

• Unpacking and generalizing innovations into individual inductive bias segments.
• Systematically investigating all possible combinations of inductive biases.
• Introducing variational integrator graph networks (VIGNs) combining energy constraints, high-order symplectic variational integrators, and graph neural networks.

Main Results:

• The proposed VIGN framework outperforms existing methods in data-efficient learning and predictive accuracy.
• Demonstrated superior performance across both single- and many-body problems.
• Empirically showed that high-order variational integrators and energy constraints enable coupled learning of position and momentum updates.

Conclusions:

• The unifying framework of VIGNs effectively integrates diverse physics priors.
• VIGNs offer significant improvements in learning and predicting complex physical dynamics.
• The partitioned Runge-Kutta method formalizes the coupled learning mechanism in VIGNs.