3 papers
math.NA2025
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…
math.NA2025
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…
math.NA2024
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…