Latent Space Prediction of Dynamical Systems

We consider a data-driven framework for prediction tasks in which the dynamics are learnt in a low-dimensional latent space. We rely on dimensionality reduction techniques --- linear principal component analysis and nonlinear autoencoders and their variants --- to then learn dynamical evolution  in the corresponding latent space using disparate methodologies --- linear inverse modeling, dictionary-based sparse regression, reservoir computing, neural differential equations, attention-based transformers, etc. In this setting, we seek to better understand the interplay between the spatial and temporal representations of variability and how they affect prediction skill.

Balu Nadiga, Los Alamos National Laboratory and Kaushik Srinivasan, University of California Los Angeles