Modular Neural Ordinary Differential Equations
This work addresses the problem of learning physics-based differential equations from data for researchers in machine learning and physics, offering an incremental improvement over prior methods.
The paper tackles the limitations of existing Neural ODE architectures, such as inability to represent general equations of motion or lack of interpretability, by proposing Modular Neural ODEs that learn force components with separate modules, resulting in better performance, increased interpretability, and added flexibility.
The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned from a dataset. These have been applied to classical dynamics simulations in the form of Lagrangian Neural Net-works (LNNs) and Second Order Neural Differential Equations (SONODEs). However, they either cannot represent the most general equations of motion or lack interpretability. In this paper, we propose Modular Neural ODEs, where each force component is learned with separate modules. We show how physical priors can be easily incorporated into these models. Through a number of experiments, we demonstrate these result in better performance, are more interpretable, and add flexibility due to their modularity.