3 papers
math.NA2026
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…
cs.LG2026
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…
cs.LG2025
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…