CCSS Meeting #64: Neural ODEs and stochastic methods for data-driven model closures

Prof. dr. Daan Crommelin (Centrum Wiskunde & Informatica (CWI) and University of Amsterdam) joined us in person to provide the fourth talk within the CCSS lunch meeting theme Neural Differential Equations and the applications in Complex Systems.
Daan Crommelin is a senior researcher in the Scientific Computing research group at CWI (Centrum Wiskunde & Informatica, the national research institute for mathematics and computer science in the Netherlands) and Professor at the Korteweg-de Vries Institute for Mathematics, University of Amsterdam. He works on stochastic and computational methods for multiscale systems, with applications in climate science and energy systems. Key research interests are model uncertainties due to unresolved processes, uncertainty quantification, and rare events. Crommelin is an associate editor of SIAM Multiscale Modeling & Simulation, co-initiated the Dutch national research program on "Mathematics of Planet Earth (MPE). Essential Dynamics and Uncertainty", and was awarded a Vidi grant by NWO.
Lecture Overview
Modeling with differential equations (DEs) is ubiquitous in the physical sciences and beyond. With the advent of machine learning and the deployment of neural networks (NNs) for many different computational tasks, it is a natural step to start incorporating NNs in this framework of DE-based modeling and simulation. Two notable examples where incorporating NNs can be beneficial are (i) cases where physics-based DE models have biases or errors that may be corrected with NNs, and (ii) situations where DE models are too computationally expensive to be solved with more traditional scientific computing methods, so that NNS may be used to accelerate computations. For multiscale systems, these two situations can overlap: it is too expensive to resolve all space/time scales in simulations, whereas simulating only the interesting (typically, macroscopic) part of the system requires a model closure (aka parameterization) to represent left-out (microscopic) degrees of freedom, and this closure can introduce model errors. Augmenting a physics-based DE model with a NN closure is a promising approach that is intensively explored nowadays. It raises fundamental questions regarding the most appropriate way of training the NN, the stability of combined DE-NN model, and its accuracy on longer timescales. Furthermore, including memory and/or stochasticity in the closure poses new challenges, as this goes beyond the setting of (deterministic) neural ODEs. I will discuss these issues as well as some recent work aimed at tackling them.

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Is any papers or references avavilable for the lecture?