Stability analysis of hierarchical tensor methods for time-dependent PDEs (Q778308)

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English	Stability analysis of hierarchical tensor methods for time-dependent PDEs	scientific article

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instance of

scholarly article

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title

Stability analysis of hierarchical tensor methods for time-dependent PDEs (English)

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zbMATH Open document ID

1435.65149

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DOI

10.1016/j.jcp.2020.109341

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Journal of Computational Physics

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publication date

2 July 2020

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full work available at URL

https://arxiv.org/abs/1908.09803

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Mathematics Subject Classification ID

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hierarchical tensor methods

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high-dimensional PDEs

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linear multistep integrators

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Fokker-Plank equation

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describes a project that uses

htucker

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MaRDI profile type

MaRDI publication profile

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Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations

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Optimal Randomized Multilevel Algorithms for Infinite-Dimensional Integration on Function Spaces with ANOVA-Type Decomposition

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High dimensional polynomial interpolation on sparse grids

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

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Q3241581

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Parallel tensor methods for high-dimensional linear PDEs

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Sparse grids

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Q3621214

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Probabilistic Theory of Mean Field Games with Applications II

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The proper generalized decomposition for advanced numerical simulations. A primer

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High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs

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Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

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Dynamically orthogonal tensor methods for high-dimensional nonlinear PDEs

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A mean-field optimal control formulation of deep learning

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Parallel ALS Algorithm for Solving Linear Systems in the Hierarchical Tucker Representation

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Multi-element probabilistic collocation method in high dimensions

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Unnormalized optimal transport

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Hierarchical Singular Value Decomposition of Tensors

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Distributed hierarchical SVD 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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Geometric Numerical Integration

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Q4000061

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A Riemannian trust-region method for low-rank tensor completion

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Spectral Methods for Time-Dependent Problems

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Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications

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Dynamical Tensor Approximation

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Tensor Decompositions and Applications

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Algorithm 941

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A Multilinear Singular Value Decomposition

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Survey of the stability of linear finite difference equations

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Regularized random-sampling high dimensional model representation (RS-HDMR)

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Time Integration of Rank-Constrained Tucker Tensors

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Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation

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Tensor-Train Decomposition

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Hidden physics models: machine learning of nonlinear partial differential equations

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

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Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues

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Stability of the method of lines

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The Fokker-Planck equation. Methods of solution and applications.

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On Local Convergence of Alternating Schemes for Optimization of Convex Problems in the Tensor Train Format

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Optimization on the hierarchical Tucker manifold - applications to tensor completion

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Optimization Techniques on Riemannian Manifolds

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Q4663944

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Random heterogeneous materials. Microstructure and macroscopic properties

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The geometry of algorithms using hierarchical tensors

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Low-Rank Matrix Completion by Riemannian Optimization

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The numerical approximation of nonlinear functionals and functional differential equations

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New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs

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Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

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A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems

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Q5755052

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Optimal Transport

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Q4714145

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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

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Mathematics(1 entry)

mardi Publication:778308