A physics-informed graph neural network conserving linear and angular momentum for dynamical systems.

Area of Science:

• Physics
• Computer Science
• Engineering

Background:

• Accurate modeling of multi-body dynamical systems is crucial for prediction and inference.
• Traditional physics-based models struggle with scalability and computational cost.
• Data-driven Graph Neural Networks (GNNs) often lack physical consistency and interpretability.

Purpose of the Study:

• To propose DYNAMI-CAL GRAPHNET, a Physics-Informed Graph Neural Network.
• To integrate GNN learning with physics-based inductive biases for improved modeling.
• To address limitations of traditional and purely data-driven approaches in dynamical systems.

Main Methods:

• Developed DYNAMI-CAL GRAPHNET, a novel Physics-Informed Graph Neural Network.
• Enforced pairwise conservation of linear and angular momentum using equivariant edge-local reference frames.
• Designed for rotational equivariance, translational invariance, and permutation equivariance.

Main Results:

• Achieved physically consistent predictions of node dynamics.
• Provided interpretable, edge-wise linear and angular impulses.
• Demonstrated stable error accumulation, effective extrapolation, and robust handling of heterogeneous interactions and external forces on a 3D granular system.

Conclusions:

• DYNAMI-CAL GRAPHNET offers accurate, interpretable, and real-time modeling of complex multi-body dynamical systems.
• Enables inference of forces and moments while efficiently handling complex interactions.
• Valuable for robotics, aerospace engineering, materials science, control systems, and mechanical process optimization.