Online Seminar: Learning Solution Operators for PDEs with Uncertainty

Join us for an online seminar on Monday, June 10th at 4PM, given by Emilia Magnani, a Ph.D. candidate at the University of Tübingen. She will present her work on “Learning Solution Operators for PDEs with Uncertainty”.

Abstract: We provide a Bayesian formulation of the problem of learning solution operators of PDEs in the formalism of Gaussian processes. We consider neural operators, recent deep architectures that have shown promising results in tackling the task of learning PDE solution operators. The current state of the art for these models lacks explicit uncertainty quantification. Our approach offers a practical and theoretically sound way to apply the linearized Laplace approximation to neural operators to provide uncertainty estimates. Moreover, we introduce a new framework for Bayesian uncertainty quantification in neural operators using function-valued Gaussian processes.

Bio: Emilia Magnani is a Ph.D. candidate at the University of Tübingen under the supervision of Philipp Hennig. She is also part of the ELLIS program and spent part of her Ph.D. in Genoa working with Lorenzo Rosasco. Before that, Emilia obtained her Master’s degree in Mathematics from ETH Zurich. Her research interests span various areas of machine learning such as probabilistic numerics, Gaussian processes, and operator learning.

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