Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton-Jacobi PDEs (Q2683498)

scientific article; zbMATH DE number 7653180

Language	Label	Description	Also known as
English	Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton-Jacobi PDEs	scientific article; zbMATH DE number 7653180

Statements

instance of

scholarly article

0 references

title

Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton-Jacobi PDEs (English)

0 references

0 references

0 references

0 references

MCSS. Mathematics of Control, Signals, and Systems

0 references

publication date

13 February 2023

0 references

full work available at URL

https://arxiv.org/abs/2105.03336

0 references

zbMATH Keywords

optimal control

0 references

Hamilton-Jacobi partial differential equations

0 references

neural networks

0 references

grid-free numerical methods

0 references

describes a project that uses

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

Neural Networks and Deep Learning

0 references

The Max-Plus Finite Element Method for Solving Deterministic Optimal Control Problems: Basic Properties and Convergence Analysis

0 references

An Efficient DP Algorithm on a Tree-Structure for Finite Horizon Optimal Control Problems

0 references

Error Analysis for POD Approximations of Infinite Horizon Problems via the Dynamic Programming Approach

0 references

Solution of matrix Riccati differential equation for the linear quadratic singular system using neural networks

0 references

Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

0 references

On the Bellman equation for some unbounded control problems

0 references

Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations

0 references

Q3286740

0 references

An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations

0 references

Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

0 references

Global theory of the Riccati equation

0 references

Numerical Methods for Ordinary Differential Equations

0 references

Semiconcave functions, Hamilton-Jacobi equations, and optimal control

0 references

Machine learning for semi linear PDEs

0 references

On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton--Jacobi Equations

0 references

Overcoming the curse of dimensionality for some Hamilton-Jacobi partial differential equations via neural network architectures

0 references

On Decomposition Models in Imaging Sciences and Multi-time Hamilton--Jacobi Partial Differential Equations

0 references

On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton-Jacobi partial differential equations

0 references

Algorithms for overcoming the curse of dimensionality for certain Hamilton-Jacobi equations arising in control theory and elsewhere

0 references

The numerical solution of the matrix Riccati differential equation

0 references

Max-plus representation for the fundamental solution of the time-varying differential Riccati equation

0 references

Neural‐network‐based approximations for solving partial differential equations

0 references

A Max-plus Dual Space Fundamental Solution for a Class of Operator Differential Riccati Equations

0 references

A Max-Plus-Based Algorithm for a Hamilton--Jacobi--Bellman Equation of Nonlinear Filtering

0 references

Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs

0 references

Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids

0 references

On Alternating Direction Methods of Multipliers: A Historical Perspective

0 references

Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations

0 references

Solving high-dimensional partial differential equations using deep learning

0 references

Solving many-electron Schrödinger equation using deep neural networks

0 references

A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations

0 references

Weighted ENO Schemes for Hamilton--Jacobi Equations

0 references

Sympnets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems

0 references

Polynomial Approximation of High-Dimensional Hamilton--Jacobi--Bellman Equations and Applications to Feedback Control of Semilinear Parabolic PDEs

0 references

Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations

0 references

Numerical integration of the differential matrix Riccati equation

0 references

Solving for high-dimensional committor functions using artificial neural networks

0 references

Intelligent optimal control of robotic manipulators using neural networks

0 references

HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems

0 references

Neural algorithm for solving differential equations

0 references

On the Matrix Riccati Equation

0 references

PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network

0 references

Max-plus methods for nonlinear control and estimation.

0 references

A Curse-of-Dimensionality-Free Numerical Method for Solution of Certain HJB PDEs

0 references

A new fundamental solution for differential Riccati equations arising in control

0 references

Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs

0 references

The numerical solution of linear ordinary differential equations by feedforward neural networks

0 references

A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems

0 references

PPINN: parareal physics-informed neural network for time-dependent PDEs

0 references

High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations

0 references

fPINNs: Fractional Physics-Informed Neural Networks

0 references

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

0 references

Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

0 references

Functional multi-layer perceptron: A nonlinear tool for functional data analysis

0 references

DGM: a deep learning algorithm for solving partial differential equations

0 references

Minimax solutions of first-order partial differential equations

0 references

Efficient computation of optimal actions

0 references

A proposal on machine learning via dynamical systems

0 references

Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

0 references

A mean-field optimal control formulation of deep learning

0 references

The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

0 references

An introduction to neural network methods for differential equations

0 references

A deterministic affine-quadratic optimal control problem

0 references

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

0 references

Adversarial uncertainty quantification in physics-informed neural networks

0 references

Perspectives on characteristics based curse-of-dimensionality-free numerical approaches for solving Hamilton-Jacobi equations

0 references

Q4255599

0 references

Turnpike theory of continuous-time linear optimal control problems

0 references

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

0 references

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

0 references

Maximum principle, dynamic programming and their connection in deterministic control

0 references

Identifiers

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

10.1007/S00498-022-00333-2

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:2683498