Disentangling ODE parameters from dynamics in VAEs

Deep networks have become increasingly of interest in dynamical system prediction, but generalization remains elusive. In this work, we consider the physical parameters of ODEs as factors of variation of the data generating process. By leveraging ideas from supervised disentanglement in VAEs, we aim to separate the ODE parameters from the dynamics in the latent space. Experiments show that supervised disentanglement allows VAEs to capture the variability in the dynamics and extrapolate better to ODE parameter spaces that were not present in the training data.

Simulating Surface Wave Dynamics with Convolutional Networks

We investigate the performance of fully convolutional networks to simulate the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net architecture and analyse how well it generalises to geometric configurations not seen during training. We demonstrate that a modified U-Net architecture is capable of accurately predicting the height distribution of waves on a liquid surface within curved and multi-faceted open and closed geometries, when only simple box and right-angled corner geometries were seen during training. We also consider a separate and independent 3D CNN for performing time-interpolation on the predictions produced by our U-Net. This allows generating simulations with a smaller time-step size than the one the U-Net has been trained for.