Learning Reduced Order Dynamics via Geometric Representations

Abstract

Geometric Representation Learning is a cornerstone of (unsupervised) learning and as such has been widely applied across domains. In this work, we consider the problem of data-driven discovery of system dynamics from spatial-temporal data. We propose to encode similarity structure in such data via a temporal proximity graph, to which we apply a range of manifold learning and deep-learning based approaches. We perform a systematic analysis of the learnt representation, focusing on their ability to capture local and global structural geometric features, which are crucial for recovering the system's dynamics. Geometric Representation Learning is a cornerstone of (unsupervised) learning and as such has been widely applied across domains. In this work, we consider the problem of data-driven discovery of system dynamics from spatial-temporal data. We propose to encode similarity structure in such data via a spatial-temporal proximity graph; we then apply a range of manifold learning and deep-learning based approaches to recover reduced order dynamics. We perform a systematic analysis of the learned representations, comparing the different approaches’ ability to capture local and global geometric features of the system dynamics.