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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…