most citedGaussian Process Regression for Uncertainty Quantification: An Introductory Tutorial

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math.NA2025

Nemytskii neural operator: a nonlinear model reduction method for parametrized partial differential equations

Jingye Li, Alex Bespalov, Jinglai Li

We introduce a Nemytskii neural operator framework for nonlinear model reduction of parametrized steady-state partial differential equations. The method generalizes reduced basis a…

math.NA2025

Stochastic gradient descent based variational inference for infinite-dimensional inverse problems

Jiaming Sui, Junxiong Jia, Jinglai Li

This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed…