Figure: bouncing ball.
Newton’s cradle. As an additional baseline, we employ a vanilla residual network (ResNet) as well as a residual network with additional contact inputs (ResNet contact). The CD-Lagrange network exhibits the best approximation behaviour and learn both the potential and contact events more accurately than the residual networks.
State-of-the-art physics-inspired neural networks generally struggle to learn contact dynamics. Central-Difference-Lagrange networks are a class of networks that not only exhibit strong conservation properties, comparable to other physically structured neural networks, but also allow accurate learning of contact dynamics from observed data. In this regime, the information available to the network when making predictions has a significant effect on performance: the addition of touch feedback sensor data ensures that noise and contact events are correctly differentiated. We hope these contributions enable neural network models to be used in wider settings.
S. Sæmundsson, A. Terenin, K. Hofmann, M. P. Deisenroth. Variational Integrator Networks for Physically Structured Embeddings. AISTATS, 2020. ↩
F.-E. Fekak, M. Brun, A. Gravouil, and B. Depale. A new heterogeneous asynchronous explicit–implicit time integrator for nonsmooth dynamics. Computational Mechanics, 60(1):1–21, 2017. ↩