8 papers
Numerical Analysis of Space-Time Dependent Source Identification in Subdiffusion Equations
Siyu Cen, Bangti Jin, Yavar Kian +1
In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The…
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…
Finite element approximation for quantitative photoacoustic tomography in a diffusive regime
Giovanni S. Alberti, Siyu Cen, Zhi Zhou
In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption…
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…
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…
Determining a Time-Varying Potential in Time-Fractional Diffusion from Observation at a Single Point
Siyu Cen, Kwancheol Shin, Zhi Zhou
We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a…
Galerkin FEM for fractional order parabolic equations with initial data in
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous…