8 papers
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…
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…
Optimizing Coarse Propagators in Parareal Algorithms
Bangti Jin, Qingle Lin, Zhi Zhou
The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective sp…
Point Source Identification in Subdiffusion from A Posteriori Internal Measurement
Kuang Huang, Bangti Jin, Yavar Kian +2
In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion mo…