5 papers · 1 filter
Global Convergence of DGM and PINN Algorithms for Solving Nonlinear PDEs
Justin Sirignano, Konstantinos Spiliopoulos, Samuel Cohen
The Deep Galerkin Method (DGM) and Physics Informed Neural Networks (PINNs) have become widely-used methods for solving partial differential equations (PDEs) in the rapidly growing…
Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit
Konstantin Riedl, Konstantinos Spiliopoulos, Justin Sirignano
A convergence analysis is developed for the regularized Newton method for training neural networks (NNs) in the overparameterized limit. As the number of hidden units tends to infi…
Scaling Effects and Uncertainty Quantification in Neural Actor Critic Algorithms
Nikos Georgoudios, Konstantinos Spiliopoulos, Justin Sirignano
We investigate the neural Actor Critic algorithm using shallow neural networks for both the Actor and Critic models. The focus of this work is twofold: first, to compare the conver…
Global Convergence of Adjoint-Optimized Neural PDEs
Konstantin Riedl, Justin Sirignano, Konstantinos Spiliopoulos
Many engineering and scientific fields have recently become interested in modeling terms in partial differential equations (PDEs) with neural networks, which requires solving the i…
Convergence Analysis of Real-time Recurrent Learning (RTRL) for a class of Recurrent Neural Networks
Samuel Chun-Hei Lam, Justin Sirignano, Konstantinos Spiliopoulos
Recurrent neural networks (RNNs) are commonly trained with the truncated backpropagation-through-time (TBPTT) algorithm. For the purposes of computational tractability, the TBPTT a…