2.3k citations · 2.3k across the 9 of their papers we have counts for
19 papers
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…
Online Adjoint Methods for Optimization of PDEs
Justin Sirignano, Konstantinos Spiliopoulos
We present and mathematically analyze an online adjoint algorithm for the optimization of partial differential equations (PDEs). Traditional adjoint algorithms would typically solv…
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…
Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum
Justin Sirignano, Konstantinos Spiliopoulos
We analyze single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent tr…
Mean Field Analysis of Deep Neural Networks
Justin Sirignano, Konstantinos Spiliopoulos
We analyze multi-layer neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations.…
Mean Field Analysis of Neural Networks: A Central Limit Theorem
Justin Sirignano, Konstantinos Spiliopoulos
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A)…
Mean Field Analysis of Neural Networks: A Law of Large Numbers
Justin Sirignano, Konstantinos Spiliopoulos
Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in…
Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem
Justin Sirignano, Konstantinos Spiliopoulos
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in…
DGM: A deep learning algorithm for solving partial differential equations
Justin Sirignano, Konstantinos Spiliopoulos
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is…
Stochastic Gradient Descent in Continuous Time
Justin Sirignano, Konstantinos Spiliopoulos
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in…
Deep Learning for Mortgage Risk
Justin Sirignano, Apaar Sadhwani, Kay Giesecke
We develop a deep learning model of multi-period mortgage risk and use it to analyze an unprecedented dataset of origination and monthly performance records for over 120 million mo…
Deep Learning for Limit Order Books
Justin Sirignano
This paper develops a new neural network architecture for modeling spatial distributions (i.e., distributions on R^d) which is computationally efficient and specifically designed t…
Fluctuation Analysis for the Loss From Default
Konstantinos Spiliopoulos, Justin A. Sirignano, Kay Giesecke
We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak co…
Large Portfolio Asymptotics for Loss From Default
Kay Giesecke, Konstantinos Spiliopoulos, Richard B. Sowers +1
We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The…