Dynamic tensor approximation of high-dimensional nonlinear PDEs (Q2124324)

scientific article; zbMATH DE number 7505902

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English	Dynamic tensor approximation of high-dimensional nonlinear PDEs	scientific article; zbMATH DE number 7505902

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instance of

scholarly article

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title

Dynamic tensor approximation of high-dimensional nonlinear PDEs (English)

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Journal of Computational Physics

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publication date

8 April 2022

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full work available at URL

https://arxiv.org/abs/2007.09538

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zbMATH Keywords

hierarchical tensor methods

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functional tensor train

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Fokker-Planck equation

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describes a project that uses

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Spatiotemporal analysis of complex signals: Theory and applications

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Spatiotemporal and statistical symmetries.

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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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Spectral tensor-train decomposition

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Parallel tensor methods for high-dimensional linear PDEs

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Tensor methods for the Boltzmann-BGK equation

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Sparse grids

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Q3621214

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The Boltzmann equation and its applications

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Stiefel and Grassmann manifolds in quantum chemistry

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

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Numerical methods for high-dimensional probability density function equations

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On the equivalence of dynamically orthogonal and bi-orthogonal methods: theory and numerical simulations

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Dynamically orthogonal tensor methods for high-dimensional nonlinear PDEs

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Numerical methods for kinetic equations

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A mean-field optimal control formulation of deep learning

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Multi-element probabilistic collocation method in high dimensions

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Unnormalized optimal transport

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A continuous analogue of the tensor-train decomposition

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On the Decay Rate of the Singular Values of Bivariate Functions

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Tensor Spaces and Numerical Tensor Calculus

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Spectral Methods for Time-Dependent Problems

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On manifolds of tensors of fixed TT-rank

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

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Dynamical Low‐Rank Approximation

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Dynamical Tensor Approximation

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Tensor Decompositions and Applications

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

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Time Integration of Tensor Trains

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Dynamical approximation by hierarchical Tucker and tensor-train tensors

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Dual dynamically orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions

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Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

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

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Dynamical low-rank approximation: Applications and numerical experiments

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Constructive representation of functions in low-rank tensor formats

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

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Stability analysis of hierarchical tensor methods for time-dependent PDEs

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Differential geometry and mathematical physics. II: Fibre bundles, topology and gauge fields

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Dynamically orthogonal field equations for continuous stochastic dynamical systems

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The geometry of algorithms using hierarchical tensors

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The numerical approximation of nonlinear functionals and functional differential equations

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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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Optimal Transport

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

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2021.110295

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Sitelinks

Mathematics(1 entry)

mardi Publication:2124324