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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…
Kernel Limit for a Class of Recurrent Neural Networks Trained on Ergodic Data Sequences
Samuel Chun-Hei Lam, Justin Sirignano, Konstantinos Spiliopoulos
Mathematical methods are developed to characterize the asymptotics of recurrent neural networks (RNN) as the number of hidden units, data samples in the sequence, hidden state upda…
PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence
Justin Sirignano, Jonathan MacArt, Konstantinos Spiliopoulos
Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural ne…
DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)
Jonathan B. Freund, Jonathan F. MacArt, Justin Sirignano
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training o…
Asymptotics of Reinforcement Learning with Neural Networks
Justin Sirignano, Konstantinos Spiliopoulos
We prove that a single-layer neural network trained with the Q-learning algorithm converges in distribution to a random ordinary differential equation as the size of the model and…