A Forward-backward Algorithm for Stochastic Control Problems - Using the Stochastic Maximum Principle as an Alternative to Dynamic Programming. - Stephan E. Ludwig; Justin A. Sirignano; Ruojun Huang; George Papanicolaou (ICORES, 2012)

Large-Scale Loan Portfolio Selection. - Justin A. Sirignano; Gerry Tsoukalas; Kay Giesecke (Oper. Res., 2016)

Stochastic Gradient Descent in Continuous Time. - Justin A. Sirignano; Konstantinos Spiliopoulos (SIAM J. Financial Math., 2017)

DGM: A deep learning algorithm for solving partial differential equations. - Justin A. Sirignano; Konstantinos Spiliopoulos (J. Comput. Phys., 2018)

Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum. - Justin A. Sirignano; Konstantinos Spiliopoulos (CoRR, 2019)

Asymptotics of Reinforcement Learning with Neural Networks. - Justin A. Sirignano; Konstantinos Spiliopoulos (CoRR, 2019)

Risk Analysis for Large Pools of Loans. - Justin A. Sirignano; Kay Giesecke (Manag. Sci., 2019)

DPM: A deep learning PDE augmentation method with application to large-eddy simulation. - Justin A. Sirignano; Jonathan F. MacArt; Jonathan B. Freund (J. Comput. Phys., 2020)

Mean Field Analysis of Neural Networks: A Law of Large Numbers. - Justin A. Sirignano; Konstantinos Spiliopoulos (SIAM J. Appl. Math., 2020)

Embedded training of neural-network sub-grid-scale turbulence models. - Jonathan F. MacArt; Justin A. Sirignano; Jonathan B. Freund (CoRR, 2021)

Global Convergence of the ODE Limit for Online Actor-Critic Algorithms in Reinforcement Learning. - Ziheng Wang; Justin A. Sirignano (CoRR, 2021)

Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations. - Ziheng Wang; Justin A. Sirignano (CoRR, 2022)

Neural Q-learning for solving elliptic PDEs. - Samuel N. Cohen; Deqing Jiang; Justin A. Sirignano (CoRR, 2022)

A Forward Propagation Algorithm for Online Optimization of Nonlinear Stochastic Differential Equations. - Ziheng Wang; Justin A. Sirignano (CoRR, 2022)

Deep Learning Closure Models for Large-Eddy Simulation of Flows around Bluff Bodies. - Justin A. Sirignano; Jonathan F. MacArt (CoRR, 2022)

Mean Field Analysis of Deep Neural Networks. - Justin A. Sirignano; Konstantinos Spiliopoulos (Math. Oper. Res., 2022)

Dynamic Deep Learning LES Closures: Online Optimization With Embedded DNS. - Justin A. Sirignano; Jonathan F. MacArt (CoRR, 2023)

Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations. - Deqing Jiang; Justin A. Sirignano; Samuel N. Cohen (CoRR, 2023)

Kernel Limit of Recurrent Neural Networks Trained on Ergodic Data Sequences. - Samuel Chun-Hei Lam; Justin A. Sirignano; Konstantinos Spiliopoulos (CoRR, 2023)

Neural Q-learning for solving PDEs. - Samuel N. Cohen; Deqing Jiang; Justin A. Sirignano (J. Mach. Learn. Res., 2023)

PDE-constrained models with neural network terms: Optimization and global convergence. - Justin A. Sirignano; Jonathan F. MacArt; Konstantinos Spiliopoulos (J. Comput. Phys., 2023)

Weak Convergence Analysis of Online Neural Actor-Critic Algorithms. - Samuel Chun-Hei Lam; Justin A. Sirignano; Ziheng Wang (CoRR, 2024)

Convergence Analysis of Real-time Recurrent Learning (RTRL) for a class of Recurrent Neural Networks. - Samuel Chun-Hei Lam; Justin A. Sirignano; Konstantinos Spiliopoulos (CoRR, 2025)

Global Convergence of Adjoint-Optimized Neural PDEs. - Konstantin Riedl; Justin A. Sirignano; Konstantinos Spiliopoulos (CoRR, 2025)

OGF: An Online Gradient Flow Method for Optimizing the Statistical Steady-State Time Averages of Unsteady Turbulent Flows. - Tom Hickling; Jonathan F. MacArt; Justin A. Sirignano; Den Waidmann (CoRR, 2025)

Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studies. - Samuel N. Cohen; Jackson Hebner; Deqing Jiang; Justin A. Sirignano (CoRR, 2025)

Physics-Based Machine Learning Closures and Wall Models for Hypersonic Transition-Continuum Boundary Layer Predictions. - Ashish S. Nair; Narendra Singh; Marco Panesi; Justin A. Sirignano; Jonathan F. MacArt (CoRR, 2025)