Neural networks are increasingly used to construct numerical solution methods for partial
differential equations. In this expository review, we introduce and contrast three important …

The recent advancements in security approaches have significantly increased the ability to
identify and mitigate any type of threat or attack in any network infrastructure, such as a …

This paper surveys the extant literature on machine learning, artificial intelligence, and deep
learning mechanisms within the financial sphere using bibliometric methods. We considered …

Computing optimal feedback controls for nonlinear systems generally requires solving
Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state …

This paper develops algorithms for high-dimensional stochastic control problems based on
deep learning and dynamic programming. Unlike classical approximate dynamic …

This chapter presents machine learning techniques and deep reinforcement learning-based
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …

We propose new and original mathematical connections between Hamilton–Jacobi (HJ)
partial differential equations (PDEs) with initial data and neural network architectures …

One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in
many realistic molecular systems, biologically important rare transitions occur on timescales …

Stochastic optimal control and games have a wide range of applications, from finance and
economics to social sciences, robotics, and energy management. Many real-world …

We propose novel connections between several neural network architectures and viscosity
solutions of some Hamilton–Jacobi (HJ) partial differential equations (PDEs) whose …