Data-Driven Tensor Train Gradient Cross Approximation for Hamilton–Jacobi–Bellman Equations (Q6054276)

scientific article; zbMATH DE number 7742960

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English	Data-Driven Tensor Train Gradient Cross Approximation for Hamilton–Jacobi–Bellman Equations	scientific article; zbMATH DE number 7742960

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instance of

scholarly article

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title

Data-Driven Tensor Train Gradient Cross Approximation for Hamilton–Jacobi–Bellman Equations (English)

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SIAM Journal on Scientific Computing

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publication date

27 September 2023

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full work available at URL

https://arxiv.org/abs/2205.05109

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zbMATH Keywords

dynamic programming

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optimal feedback control

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Hamilton-Jacobi-Bellman equations

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tensor decomposition

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high-dimensional approximation

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MaRDI profile type

MaRDI publication profile

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cites work

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

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A tree structure algorithm for optimal control problems with state constraints

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State-dependent Riccati equation feedback stabilization for nonlinear PDEs

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Q4998939

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Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach

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Range-Separated Tensor Format for Many-Particle Modeling

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Spectral Tensor-Train Decomposition

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

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

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Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations

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Computation of extreme eigenvalues in higher dimensions using block tensor train format

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Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions

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Variational Monte Carlo -- bridging concepts of machine learning and high-dimensional partial differential equations

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Approximative Policy Iteration for Exit Time Feedback Control Problems Driven by Stochastic Differential Equations using Tensor Train Format

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Approximation of optimal control problems for the Navier-Stokes equation via multilinear HJB-POD

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

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Q3086656

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A continuous analogue of the tensor-train decomposition

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Stable als approximation in the TT-format for rank-adaptive tensor completion

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A literature survey of low-rank tensor approximation techniques

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Parallel tensor sampling in the hierarchical Tucker format

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Tensor Spaces and Numerical Tensor Calculus

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A new scheme for the tensor representation

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Solving high-dimensional partial differential equations using deep learning

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The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format

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Robust Feedback Control of Nonlinear PDEs by Numerical Approximation of High-Dimensional Hamilton--Jacobi--Isaacs Equations

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

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Order Reduction Methods for Solving Large-Scale Differential Matrix Riccati Equations

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Low-rank tensor completion by Riemannian optimization

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Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation

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

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SympOCnet: Solving Optimal Control Problems with Applications to High-Dimensional Multiagent Path Planning Problems

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Adaptive Deep Learning for High-Dimensional Hamilton--Jacobi--Bellman Equations

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Tensor-Train Decomposition

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TT-cross approximation for multidimensional arrays

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Approximating Optimal feedback Controllers of Finite Horizon Control Problems Using Hierarchical Tensor Formats

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Quasioptimality of maximum-volume cross interpolation of tensors

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Approximation rates for the hierarchical tensor format in periodic Sobolev spaces

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Riemannian Optimization for High-Dimensional Tensor Completion

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Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks

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Identifiers

zbMATH Open document ID

1523.49037

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arXiv ID

2205.05109

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6054276