293 citations · 1.8k across the 110 of their papers we have counts for
113 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…
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…
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…
On an Inverse Problem of the Generalized Bathtub Model of Network Trip Flows
Kuang Huang, Bangti Jin, Zhi Zhou
In this work, we investigate the generalized bathtub model, a nonlocal transport equation for describing network trip flows served by privately operated vehicles inside a road netw…
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…
Regularity Analysis and High-Order Time Stepping Scheme for Quasilinear Subdiffusion
Bangti Jin, Qimeng Quan, Barbara Wohlmuth +1
In this work, we investigate a quasilinear subdiffusion model which involves a fractional derivative of order in time and a nonlinear diffusion coefficient. First, usi…
Identification of a Spatially-Dependent Variable Order in One-Dimensional Subdiffusion
Jiho Hong, Bangti Jin, Yavar Kian
In this work we investigate an inverse problem of identifying a spatially variable order in the one-dimensional subdiffusion model from the boundary flux measurement. The model inv…
Numerical Recovery of the Diffusion Coefficient in Diffusion Equations from Terminal Measurement
Bangti Jin, Xiliang Lu, Qimeng Quan +1
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigo…
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 Recovery of a Time-Dependent Potential in Subdiffusion
Bangti Jin, Kwancheol Shin, Zhi Zhou
In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the dom…
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…
On the Approximation of Bi-Lipschitz Maps by Invertible Neural Networks
Bangti Jin, Zehui Zhou, Jun Zou
Invertible neural networks (INNs) represent an important class of deep neural network architectures that have been widely used in several applications. The universal approximation…
Solving Poisson Problems in Polygonal Domains with Singularity Enriched Physics Informed Neural Networks
Tianhao Hu, Bangti Jin, Zhi Zhou
Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications a…
Score-Based Generative Models for PET Image Reconstruction
Imraj RD Singh, Alexander Denker, Riccardo Barbano +5
Score-based generative models have demonstrated highly promising results for medical image reconstruction tasks in magnetic resonance imaging or computed tomography. However, their…
Solving Elliptic Optimal Control Problems via Neural Networks and Optimality System
Yongcheng Dai, Bangti Jin, Ramesh Sau +1
In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It…
An Adaptive Phase-Field Method for Structural Topology Optimization
Bangti Jin, Jing Li, Yifeng Xu +1
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase fiel…
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…
Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks
Bangti Jin, Xiyao Li, Qimeng Quan +1
In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the…
SVD-DIP: Overcoming the Overfitting Problem in DIP-based CT Reconstruction
Marco Nittscher, Michael Lameter, Riccardo Barbano +3
The deep image prior (DIP) is a well-established unsupervised deep learning method for image reconstruction; yet it is far from being flawless. The DIP overfits to noise if not ear…
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…