Three ways to solve partial differential equations with neural networks—A review
J Blechschmidt, OG Ernst - GAMM‐Mitteilungen, 2021 - Wiley Online Library
Neural networks are increasingly used to construct numerical solution methods for partial
differential equations. In this expository review, we introduce and contrast three important …
differential equations. In this expository review, we introduce and contrast three important …
Machine learning techniques to detect a DDoS attack in SDN: A systematic review
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 …
identify and mitigate any type of threat or attack in any network infrastructure, such as a …
Examining the research taxonomy of artificial intelligence, deep learning & machine learning in the financial sphere—a bibliometric analysis
This paper surveys the extant literature on machine learning, artificial intelligence, and deep
learning mechanisms within the financial sphere using bibliometric methods. We considered …
learning mechanisms within the financial sphere using bibliometric methods. We considered …
Adaptive deep learning for high-dimensional Hamilton--Jacobi--Bellman equations
Computing optimal feedback controls for nonlinear systems generally requires solving
Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state …
Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state …
Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis
This paper develops algorithms for high-dimensional stochastic control problems based on
deep learning and dynamic programming. Unlike classical approximate dynamic …
deep learning and dynamic programming. Unlike classical approximate dynamic …
Neural networks-based algorithms for stochastic control and PDEs in finance
This chapter presents machine learning techniques and deep reinforcement learning-based
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …
algorithms for the efficient resolution of nonlinear partial differential equations and dynamic …
Overcoming the curse of dimensionality for some Hamilton–Jacobi partial differential equations via neural network architectures
We propose new and original mathematical connections between Hamilton–Jacobi (HJ)
partial differential equations (PDEs) with initial data and neural network architectures …
partial differential equations (PDEs) with initial data and neural network architectures …
Overcoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learning
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 …
many realistic molecular systems, biologically important rare transitions occur on timescales …
Recent developments in machine learning methods for stochastic control and games
R Hu, M Lauriere - arXiv preprint arXiv:2303.10257, 2023 - arxiv.org
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 …
economics to social sciences, robotics, and energy management. Many real-world …
On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations
We propose novel connections between several neural network architectures and viscosity
solutions of some Hamilton–Jacobi (HJ) partial differential equations (PDEs) whose …
solutions of some Hamilton–Jacobi (HJ) partial differential equations (PDEs) whose …