PDE-Driven Spatiotemporal Disentanglement

A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose in this article a novel and general paradigm for this task based on a resolution method for partial differential equations: the separation of variables. This inspiration allows us to introduce a dynamical interpretation of spatiotemporal disentanglement. It induces a principled model based on learning disentangled spatial and temporal representations of a phenomenon to accurately predict future observations. We experimentally demonstrate the performance and broad applicability of our method against prior state-of-the-art models on physical and synthetic video datasets. The interest of the machine learning community in physical phenomena has substantially grown for the last few years (Shi et al., 2015; Long et al., 2018; Greydanus et al., 2019). In particular, an increasing amount of works studies the challenging problem of modeling the evolution of dynamical systems, with applications in sensible domains like climate or health science, making the understanding of physical phenomena a key challenge in machine learning. To this end, the community has successfully leveraged the formalism of dynamical systems and their associated differential formulation as powerful tools to specifically design efficient prediction models. In this work, we aim at studying this prediction problem with a principled and general approach, through the prism of Partial Differential Equations (PDEs), with a focus on learning spatiotemporal disentangled representations. Prediction via spatiotemporal disentanglement was first studied in video prediction works, in order to separate static and dynamic information (Denton & Birodkar, 2017) for prediction and interpretability purposes. Existing models are particularly complex, involving either adversarial losses or variational inference.