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A spectral-subspace-augmented POD-Galerkin method for parametrized PDEs with limited snapshot data
Tianhao Hu, Zecheng Gan
Parametrized partial differential equations (PDEs) arise in many-query simulation, optimization, control, and uncertainty quantification, where repeated full-order solves restrict…
Dual Variational Neural Network for the -Laplace Problem
Tianhao Hu, Guanglian Li, Fengru Wang +2
The reliable and accurate numerical approximation of the -Laplacian is particularly challenging in the extreme regimes and , where the operator becomes ei…
Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates
Tianhao Hu, Xinchi Huang, Bangti Jin +2
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We estab…
An Iterative Deep Ritz Method for Monotone Elliptic Problems
Tianhao Hu, Bangti Jin, Fengru Wang
In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the lo…
Point Source Identification Using Singularity Enriched Neural Networks
Tianhao Hu, Bangti Jin, Zhi Zhou
The inverse problem of recovering point sources represents an important class of applied inverse problems. However, there is still a lack of neural network-based methods for point…