Sebastian Kaltenbach: Physics-aware reduced order modelling for forecasting the dynamics of high dimensional systems

Abstract

 Reliable predictions of critical phenomena, such as weather, turbulence, and epidemics, often rely on models described by Partial Differential Equations (PDEs). However, simulations of the full high-dimensional systems described by such PDEs are often prohibitively expensive due to the small spatio-temporal scales that need to be resolved. To address this, reduced-order simulations are usually deployed that adopt various heuristics and/or data-driven closure terms. In the first part of this talk, we will discuss our latest advances in accelerating simulations of high-dimensional systems through learning and evolving their effective dynamics. We introduce the Generative Learning of Effective Dynamics (G-LED) framework, which leverages a Bayesian diffusion model and integrates physical information through virtual observables. Additionally, we will present the interpretable iLED framework, which is based on Koopman Operator theory and the Mori-Zwanzig formalism. The second part of the talk will focus on a systematic approach for identifying closures in under-resolved PDEs using grid-based Reinforcement Learning. Our method incorporates inductive bias and exploits locality through a central policy efficiently represented by a Fully Convolutional Network.