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Solving high-dimensional partial differential equations using deep learning
TLDR
A deep learning-based approach that can handle general high-dimensional parabolic PDEs using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function.
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 a
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 (BSDEs) in high dimension, which is based on an analogy between the
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
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 differential
Deep Learning Approximation for Stochastic Control Problems
TLDR
This work develops a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo sampling and approximate the time-dependent controls as feedforward neural networks and stack these networks together through model dynamics.
A mean-field optimal control formulation of deep learning
TLDR
This paper introduces the mathematical formulation of the population risk minimization problem in deep learning as a mean-field optimal control problem, and state and prove optimality conditions of both the Hamilton–Jacobi–Bellman type and the Pontryagin type.
Convergence of the deep BSDE method for coupled FBSDEs
TLDR
A posteriori error estimation of the solution is provided and it is proved that the error converges to zero given the universal approximation capability of neural networks.
Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning
TLDR
A deep learning-based approach that can handle general high-dimensional parabolic PDEs is presented, reformulated as a control theory problem and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function.
End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems
TLDR
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 is developed.
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