Latent-space Dynamics for Reduced Deformable Simulation

We propose the first reduced model simulation framework for deformable solid dynamics using autoencoder neural networks. We provide a data-driven approach to generating nonlinear reduced spaces for deformation dynamics. In contrast to previous methods using machine learning which accelerate simulation by approximating the time-stepping function, we solve the true equations of motion in the latent-space using a variational formulation of implicit integration. Our approach produces drastically smaller reduced spaces than conventional linear model reduction, improving performance and robustness. Furthermore, our method works well with existing force-approximation cubature methods.