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Solving high-dimensional partial differential equations using deep learning
This paper introduces a practical algorithm for solving nonlinear PDEs in very high (hundreds and potentially thousands of) dimensions, in terms of both accuracy and speed. Expand
Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach
We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to aExpand
Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss function given by the error between the prescribed terminal condition and the solution of BSDE. Expand
Heterogeneous Agent Models in Continuous Time
We study a class of continuous time heterogeneous agent models with idiosyncratic shocks and incomplete markets. This class can be boiled down to a system of two coupled partial differentialExpand
Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. Expand
Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning
We extend the power of deep neural networks to another dimension by developing a deep learning-based approach that can handle general high-dimensional parabolic PDEs. Expand
Deep Learning Approximation for Stochastic Control Problems
We develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo sampling. Expand
A mean-field optimal control formulation of deep learning
This paper introduces the mathematical formulation of the population risk minimization problem in deep learning as a mean-field optimal control problem. Expand
From Microscopic Theory to Macroscopic Theory: a Systematic Study on Modeling for Liquid Crystals
In this paper, we propose a systematic way of liquid crystal modeling to build connections between microscopic theory and macroscopic theory. In the first part, we propose a new Q-tensor model basedExpand
End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems
We develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES for a wide variety of systems with the accuracy of ab initio quantum mechanics models. Expand