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04/28/2023
Improving Gradient Computation for Differentiable Physics Simulation with Contacts
Differentiable simulation enables gradients to be back-propagated throug...
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02/20/2023
Reinforcement Learning with Function Approximation: From Linear to Nonlinear
Function approximation has been an indispensable component in modern rei...
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12/16/2022
A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem
We consider the inverse acoustic obstacle problem for sound-soft star-sh...
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08/18/2022
Pandemic Control, Game Theory and Machine Learning
Game theory has been an effective tool in the control of disease spread ...
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07/08/2022
Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?
In recent years, an increasing amount of work has focused on differentia...
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04/25/2022
Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence
One of the core problems in mean-field control and mean-field games is t...
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12/29/2021
DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks
We propose an efficient, reliable, and interpretable global solution met...
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12/28/2021
Frame invariance and scalability of neural operators for partial differential equations
Partial differential equations (PDEs) play a dominant role in the mathem...
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11/05/2021
Perturbational Complexity by Distribution Mismatch: A Systematic Analysis of Reinforcement Learning in Reproducing Kernel Hilbert Space
Most existing theoretical analysis of reinforcement learning (RL) is lim...
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04/24/2021
A Class of Dimensionality-free Metrics for the Convergence of Empirical Measures
This paper concerns the convergence of empirical measures in high dimens...
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04/15/2021
An L^2 Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation
Reinforcement learning (RL) algorithms based on high-dimensional functio...
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03/11/2021
Frame-independent vector-cloud neural network for nonlocal constitutive modelling on arbitrary grids
Constitutive models are widely used for modelling complex systems in sci...
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02/22/2021
Actor-Critic Method for High Dimensional Static Hamilton–Jacobi–Bellman Partial Differential Equations based on Neural Networks
We propose a novel numerical method for high dimensional Hamilton–Jacobi...
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01/05/2021
Recurrent Neural Networks for Stochastic Control Problems with Delay
Stochastic control problems with delay are challenging due to the path-d...
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12/12/2020
Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm
Game theory has been an effective tool in the control of disease spread ...
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09/16/2020
On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis
We study the approximation properties and optimization dynamics of recur...
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08/31/2020
Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning
In recent years, tremendous progress has been made on numerical algorith...
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08/16/2020
Global Convergence of Policy Gradient for Linear-Quadratic Mean-Field Control/Game in Continuous Time
Reinforcement learning is a powerful tool to learn the optimal policy of...
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08/12/2020
Convergence of Deep Fictitious Play for Stochastic Differential Games
Stochastic differential games have been used extensively to model agents...
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06/04/2020
Integrating Machine Learning with Physics-Based Modeling
Machine learning is poised as a very powerful tool that can drastically ...
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05/09/2020
Perturbed gradient descent with occupation time
This paper develops further the idea of perturbed gradient descent, by a...
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02/07/2020
Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach
We propose a new method to solve eigenvalue problems for linear and semi...
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12/04/2019
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games
We propose a deep neural network-based algorithm to identify the Markovi...
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12/04/2019
Universal approximation of symmetric and anti-symmetric functions
We consider universal approximations of symmetric and anti-symmetric fun...
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11/03/2018
Convergence of the Deep BSDE Method for Coupled FBSDEs
The recently proposed numerical algorithm, deep BSDE method, has shown r...
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07/03/2018
A Mean-Field Optimal Control Formulation of Deep Learning
Recent work linking deep neural networks and dynamical systems opened up...
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12/11/2017
DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
Recent developments in many-body potential energy representation via dee...
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06/15/2017
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
We propose a new algorithm for solving parabolic partial differential eq...
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11/02/2016