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For an infinite-horizon control problem, the optimal control can be represented by the stable manifold of the characteristic Hamiltonian system of Hamilton-Jacobi-Bellman (HJB) equation in a semiglobal domain. In this paper, we first…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…
Real economies can be modeled as a sequential imperfect-information game with many heterogeneous agents, such as consumers, firms, and governments. Dynamic general equilibrium (DGE) models are often used for macroeconomic analysis in this…
In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is challenging to solve by using conventional methods. We employ…
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…
In this work we apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal…
The approximation of solutions to second order Hamilton--Jacobi--Bellman (HJB) equations by deep neural networks is investigated. It is shown that for HJB equations that arise in the context of the optimal control of certain Markov…
We propose a framework and an algorithm to uncover the unknown parts of nonlinear equations directly from data. The framework is based on eXtended Physics-Informed Neural Networks (X-PINNs), domain decomposition in space-time, but we…
In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…
Non-linear partial differential Kolmogorov equations are successfully used to describe a wide range of time dependent phenomena, in natural sciences, engineering or even finance. For example, in physical systems, the Allen-Cahn equation…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…
Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…
Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing…
We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through…
Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. Deep-learning methods, however, find very challenging learning stiff dynamics. In this paper, we develop DAE-PINN, the…
We propose using deep reinforcement learning to solve dynamic stochastic general equilibrium models. Agents are represented by deep artificial neural networks and learn to solve their dynamic optimisation problem by interacting with the…
This paper develops a novel deep learning approach for solving evolutionary equations, which integrates sequential learning strategies with an enhanced hard constraint strategy featuring trainable parameters, addressing the low…
Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…
Recent research reveals that deep learning is an effective way of solving high dimensional Hamilton-Jacobi-Bellman equations. The resulting feedback control law in the form of a neural network is computationally efficient for real-time…