Closing the Sim-to-Real Gap with Physics-Enhanced Neural ODEs

Abstract

A central task in engineering is the modelling of dynamical systems. In addition to first-principle methods, data-driven approaches leverage recent developments in machine learning to infer models from observations. Hybrid models aim to inherit the advantages of both, white- and black-box modelling approaches by combining the two methods in various ways. In this sense, Neural Ordinary Differential Equations (NODEs) proved to be a promising approach that deploys state-of-the-art ODE solvers and offers great modelling flexibility. In this work, an exemplary NODE setup is used to train low-dimensional artificial neural networks with physically meaningful outputs to enhance a dynamical model. The approach maintains the physical integrity of the model and offers the possibility to enforce physical laws during the training. Further, this work outlines how a confidence interval for the learned functions can be inferred based on the deployed training data. The robustness of the approach against noisy data and model uncertainties is investigated and a way to optimize model parameters alongside the neural networks is shown. Finally, the training routine is optimized with mini-batching and sub-sampling, which reduces the training duration in the given example by over 80 %.