293 citations · 1.8k across the 110 of their papers we have counts for
14 papers · 1 filter
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…
On the Convergence of Stochastic Gradient Descent for Linear Inverse Problems in Banach Spaces
Z. Kereta, B. Jin
In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most succe…
Image Reconstruction via Deep Image Prior Subspaces
Riccardo Barbano, Javier Antorán, Johannes Leuschner +3
Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised l…