1 citations · 2 across the 10 of their papers we have counts for
12 papers
Recovery of a Measure-valued Source in the Heat Equation from Sparse Boundary Measurements
Ulysse Dalmasso, Siyu Cen, Yavar Kian
This article is devoted to the inverse source problem of uniquely determining a measure-valued source from sparse boundary measurements. The measurements considered consist of flux…
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…
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…
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…
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…
Inverse Coefficient Problem for One-Dimensional Subdiffusion with Data on Disjoint Sets in Time
Siyu Cen, Bangti Jin, Yavar Kian +3
In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is…
Numerical Reconstruction of Diffusion and Potential Coefficients from Two Observations: Decoupled Recovery and Error Estimates
Siyu Cen, Zhi Zhou
The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measu…
Recovery of Multiple Parameters in Subdiffusion from One Lateral Boundary Measurement
Siyu Cen, Bangti Jin, Yikan Liu +1
This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while…
Electrical Impedance Tomography with Deep Calderón Method
Siyu Cen, Bangti Jin, Kwancheol Shin +1
Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calderón's method…
Hybrid Neural-Network FEM Approximation of Diffusion Coefficient in Elliptic and Parabolic Problems
Siyu Cen, Bangti Jin, Qimeng Quan +1
In this work we investigate the numerical identification of the diffusion coefficient in elliptic and parabolic problems using neural networks. The numerical scheme is based on the…