Physics-enhanced Neural Networks in the Small Data Regime
This work addresses the challenge of accurate dynamics prediction in physics-informed machine learning for scenarios with small datasets, representing an incremental improvement over existing methods.
The paper tackles the problem of learning physical system dynamics with limited data by incorporating energy-level regularization into Hamiltonian-based neural networks, resulting in significant gains in predictive accuracy for pendulum systems under unseen conditions.
Identifying the dynamics of physical systems requires a machine learning model that can assimilate observational data, but also incorporate the laws of physics. Neural Networks based on physical principles such as the Hamiltonian or Lagrangian NNs have recently shown promising results in generating extrapolative predictions and accurately representing the system's dynamics. We show that by additionally considering the actual energy level as a regularization term during training and thus using physical information as inductive bias, the results can be further improved. Especially in the case where only small amounts of data are available, these improvements can significantly enhance the predictive capability. We apply the proposed regularization term to a Hamiltonian Neural Network (HNN) and Constrained Hamiltonian Neural Network (CHHN) for a single and double pendulum, generate predictions under unseen initial conditions and report significant gains in predictive accuracy.