1 citations · 1 across the 13 of their papers we have counts for
14 papers
A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problems
Tianhao Hu, Bangti Jin, Fengru Wang +1
In this work, we propose a hybrid iterative deep Ritz method (H-IDRM) for a class of interface problems for second-order elliptic operators. It is based on a new mixed formulation…
On the extreme eigenvalues of the Gram Matrix in Physics-Informed Neural Networks for the Poisson Equation
Bangti Jin, Longjun Wu
The smallest and largest eigenvalues of the Gram matrix induced by the differential neural tangent kernel (DNTK) play a pivotal role in the analysis of over-parameterized PINNs tra…
Stability of Electrical Impedance Tomography with Anisotropies and its Application to the Deep Caldeón Method
Tianhao Hu, Bangti Jin, Yiran Wang
In this work, we establish new conditional Lipschitz stability results for electrical impedance tomography (EIT) with anisotropies, of recovering the conductivity in a conformal cl…
The Differential Neural Tangent Kernel and Its Positivity
Bangti Jin, Longjun Wu
The Neural Tangent Kernel (NTK) is one powerful tool for analyzing the training dynamics of neural networks in the over-parameterized regime. Recently, the theoretical framework ha…
An Iterative Direct Sampling Method for Reconstructing Moving Inhomogeneities in Parabolic Problems
Bangti Jin, Fengru Wang, Jun Zou
We propose in this work a novel iterative direct sampling method for imaging moving inhomogeneities in parabolic problems using boundary measurements. It can efficiently identify t…
A Stable Iterative Direct Sampling Method for Elliptic Inverse Problems with Partial Cauchy Data
Bangti Jin, Fengru Wang, Jun Zou
We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a da…
Shallow neural network yields regularization for ill-posed inverse problems
Lan Wang, Qiao Zhu, Bangti Jin +1
In this paper, we develop regularization theory for neural network approximations of general ill-posed operator equations with noisy data. Within the framework of iterative regular…
A Warm-basis Method for Bridging Learning and Iteration: a Case Study in Fluorescence Molecular Tomography
Ruchi Guo, Jiahua Jiang, Bangti Jin +2
Fluorescence Molecular Tomography (FMT) is a widely used non-invasive optical imaging technology in biomedical research. It usually faces significant accuracy challenges in depth r…
On the convergence of stochastic variance reduced gradient for linear inverse problems
Bangti Jin, Zehui Zhou
Stochastic variance reduced gradient (SVRG) is an accelerated version of stochastic gradient descent based on variance reduction, and is promising for solving large-scale inverse p…
Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation
Bangti Jin, Longjun Wu
Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient des…
Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations
Qiao Zhu, Dmitrii Chaikovskii, Bangti Jin +1
Physics-informed neural network (PINN) has shown great potential in solving partial differential equations. However, it faces challenges when dealing with problems involving steep…
Iterative Direct Sampling Method for Elliptic Inverse Problems with Limited Cauchy Data
Kazufumi Ito, Bangti Jin, Fengru Wang +1
In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the o…
An Iterative Deep Ritz Method for Monotone Elliptic Problems
Tianhao Hu, Bangti Jin, Fengru Wang
In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the lo…
Lagrange optimality system for a class of nonsmooth convex optimization
Bangti Jin, Tomoya Takeuchi
In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associ…