Learning dynamics from partial observations with structured neural ODEs

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. We propose a flexible framework to incorporate a broad spectrum of physical insight into neural ODE-based system identification, giving physical interpretability to the resulting latent space. This insight is either enforced through hard constraints in the optimization problem or added in its cost function. In order to link the partial and possibly noisy observations to the latent state, we rely on tools from nonlinear observer theory to build a recognition model. We demonstrate the performance of the proposed approach on numerical simulations and on an experimental dataset from a robotic exoskeleton.