Author

Justin A. Sirignano

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#machine learning May 2026

Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit

A convergence analysis is developed for the regularized Newton method for training neural networks (NNs) in the overparameterized limit and it is proved that the NN converges exponentially fast to the target data (i.e., a global minimizer with zero loss).

Konstantin Riedl, Konstantinos Spiliopoulos, Justin A. Sirignano · arXiv.org · 0 citations

#machine learning Jul 2026

Global Convergence of DGM and PINN Algorithms for Solving Nonlinear PDEs

It is proved that neural networks trained with gradient descent to minimize the PDE residual objective function will converge to the PDE solution as the network width and training time $\rightarrow \infty$.

Justin A. Sirignano, Konstantinos Spiliopoulos, Samuel N. Cohen · arXiv.org · 0 citations