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

Tid: On 2024-06-12 kl 13.30 - 14.30

Plats: Digital Futures Hub, Osquars Backe 5, floor 2

Medverkande: Sebastian Kaltenbach (Harvard University)

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 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.