6 citations · 21 across the 17 of their papers we have counts for
29 papers · 1 filter
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…
Numerical Analysis of Unsupervised Learning Approaches for Parameter Identification in PDEs
Siyu Cen, Bangti Jin, Qimeng Quan +1
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches…
Numerical Approximation and Analysis of the Inverse Robin Problem Using the Kohn-Vogelius Method
Erik Burman, Siyu Cen, Bangti Jin +1
In this work, we numerically investigate the inverse Robin problem of recovering a piecewise constant Robin coefficient in an elliptic or parabolic problem from the Cauchy data on…
Imaging Anisotropic Conductivity from Internal Measurements with Mixed Least-Squares Deep Neural Networks
Siyu Cen, Bangti Jin, Xiyao Li +1
In this work we develop a novel algorithm, termed as mixed least-squares deep neural network (MLS-DNN), to recover an anisotropic conductivity tensor from the internal measurements…
Stochastic Convergence Analysis of Inverse Potential Problem
Bangti Jin, Qimeng Quan, Wenlong Zhang
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling…
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…