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08/28/2023
Kernel Limit of Recurrent Neural Networks Trained on Ergodic Data Sequences
Mathematical methods are developed to characterize the asymptotics of re...
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05/10/2023
Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations
Numerically solving high-dimensional partial differential equations (PDE...
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03/04/2023
Dynamic Deep Learning LES Closures: Online Optimization With Embedded DNS
Deep learning (DL) has recently emerged as a candidate for closure model...
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08/06/2022
Deep Learning Closure Models for Large-Eddy Simulation of Flows around Bluff Bodies
A deep learning (DL) closure model for large-eddy simulation (LES) is de...
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07/10/2022
A Forward Propagation Algorithm for Online Optimization of Nonlinear Stochastic Differential Equations
Optimizing over the stationary distribution of stochastic differential e...
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03/31/2022
Neural Q-learning for solving elliptic PDEs
Solving high-dimensional partial differential equations (PDEs) is a majo...
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02/14/2022
Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations
We develop a new continuous-time stochastic gradient descent method for ...
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08/19/2021
Global Convergence of the ODE Limit for Online Actor-Critic Algorithms in Reinforcement Learning
Actor-critic algorithms are widely used in reinforcement learning, but a...
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05/18/2021
PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence
Recent research has used deep learning to develop partial differential e...
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05/03/2021
Embedded training of neural-network sub-grid-scale turbulence models
The weights of a deep neural network model are optimized in conjunction ...
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11/20/2019
DPM: A deep learning PDE augmentation method (with application to large-eddy simulation)
Machine learning for scientific applications faces the challenge of limi...
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11/13/2019
Asymptotics of Reinforcement Learning with Neural Networks
We prove that a single-layer neural network trained with the Q-learning ...
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07/09/2019
Scaling Limit of Neural Networks with the Xavier Initialization and Convergence to a Global Minimum
We analyze single-layer neural networks with the Xavier initialization i...
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03/11/2019
Mean Field Analysis of Deep Neural Networks
We analyze multi-layer neural networks in the asymptotic regime of simul...
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08/28/2018
Mean Field Analysis of Neural Networks: A Central Limit Theorem
Machine learning has revolutionized fields such as image, text, and spee...
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03/19/2018
Universal features of price formation in financial markets: perspectives from Deep Learning
Using a large-scale Deep Learning approach applied to a high-frequency d...
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10/11/2017
Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem
Stochastic gradient descent in continuous time (SGDCT) provides a comput...
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08/24/2017
DGM: A deep learning algorithm for solving partial differential equations
High-dimensional PDEs have been a longstanding computational challenge. ...
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11/17/2016
