Multigrid

Neural Operators: Theory, Architecture, and Applications for PDEs

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B1 L3 R3119

Abstract Neural operator methods provide a novel approach for solving or learning the complex mappings from parameters to solutions arising from intricate physical systems. In this talk, I will cover the foundational aspects of neural operators, encompassing both theoretical frameworks and algorithmic developments, including some well-known neural operator architectures. Additionally, I will share our recent work on applying the neural operator method to multiscale partial differential equations (PDEs). To tackle the challenges of multiscale PDEs, we have developed a neural operator with a

Multigrid Monte Carlo Revisited: Theory and Bayesian Inference

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B1 L3 R3119

Abstract The fast simulation of Gaussian random fields plays a pivotal role in many research areas such as Uncertainty Quantification, data science and spatial statistics. In theory, it is a well understood and solved problem, but in practice the efficiency and performance of traditional sampling procedures degenerates quickly when the random field is discretised on a grid with spatial resolution going to zero. Most existing algorithms, such as Cholesky factorisation samplers, do not scale well on large-scale parallel computers. On the other hand, stationary, iterative approaches such as the

Rolf Krause

Professor Rolf Krause is an experienced researcher and educator specializing in designing and analyzing algorithms to solve complex problems in scientific computing and machine learning.