11 papers
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…
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…
Shallow neural network yields regularization for ill-posed inverse problems
Lan Wang, Qiao Zhu, Bangti Jin +1
In this paper, we develop a regularization theory for neural network approximations of general ill-posed operator equations with noisy data. Within the framework of iterative regul…
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…
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…