Unifying physical systems' inductive biases in neural ODE using dynamics constraints
This work addresses a problem for researchers in physics-informed machine learning by offering an incremental improvement that simplifies the integration of physical inductive biases into neural networks.
The authors tackled the lack of a unifying method for predicting trajectories in dynamical systems while adhering to physical laws like conservation of energy, by proposing a simple regularization-based approach that applies to both energy-conserving and dissipative systems without architectural changes.
Conservation of energy is at the core of many physical phenomena and dynamical systems. There have been a significant number of works in the past few years aimed at predicting the trajectory of motion of dynamical systems using neural networks while adhering to the law of conservation of energy. Most of these works are inspired by classical mechanics such as Hamiltonian and Lagrangian mechanics as well as Neural Ordinary Differential Equations. While these works have been shown to work well in specific domains respectively, there is a lack of a unifying method that is more generally applicable without requiring significant changes to the neural network architectures. In this work, we aim to address this issue by providing a simple method that could be applied to not just energy-conserving systems, but also dissipative systems, by including a different inductive bias in different cases in the form of a regularisation term in the loss function. The proposed method does not require changing the neural network architecture and could form the basis to validate a novel idea, therefore showing promises to accelerate research in this direction.