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

Cell-centered extrapolation cascadic multigrid method for solving diffusion equation with discontinuous coeffcients

Xiaoxin Wu, Central South University, China

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https://meeting.tencent.com/dm/bpUiLe2AlgBC

This seminar is an online interview for a postdoctoral position in KAUST.