Dynamical Low‐Rank Approximation
From MaRDI portal
Publication:5460547
DOI10.1137/050639703zbMath1145.65031OpenAlexW2152279941MaRDI QIDQ5460547
Publication date: 29 April 2008
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/050639703
numerical experimentserror analysisprojection methodmatrix differential equationslow-rank approximationcontinuous updatingsmooth decompositiontime-varying matrices
Related Items
Efficient 6D Vlasov simulation using the dynamical low-rank framework \texttt{Ensign} ⋮ Low-rank tensor methods for partial differential equations ⋮ Full-rank and low-rank splitting methods for the Swift-Hohenberg equation ⋮ Front transport reduction for complex moving fronts ⋮ A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations ⋮ Neural Galerkin schemes with active learning for high-dimensional evolution equations ⋮ Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems ⋮ Accelerating the simulation of kinetic shear Alfvén waves with a dynamical low-rank approximation ⋮ Reduced-order modeling of neutron transport eigenvalue problems separated in energy by proper generalized decomposition ⋮ Solving the Boltzmann Equation with a Neural Sparse Representation ⋮ Stable Rank-Adaptive Dynamically Orthogonal Runge–Kutta Schemes ⋮ Rank-1 Matrix Differential Equations for Structured Eigenvalue Optimization. ⋮ Reduced-Order Modeling with Time-Dependent Bases for PDEs with Stochastic Boundary Conditions ⋮ Asymptotic-Preserving and Energy Stable Dynamical Low-Rank Approximation ⋮ A Grassmann manifold handbook: basic geometry and computational aspects ⋮ A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations ⋮ Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds ⋮ Continuous-time balanced truncation for time-periodic fluid flows using frequential Gramians ⋮ A low-rank solver for parameter estimation and uncertainty quantification in time-dependent systems of partial differential equations ⋮ Adaptive symplectic model order reduction of parametric particle-based Vlasov–Poisson equation ⋮ A low-rank method for two-dimensional time-dependent radiation transport calculations ⋮ Dynamic tensor approximation of high-dimensional nonlinear PDEs ⋮ Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization ⋮ On the Stability of Robust Dynamical Low-Rank Approximations for Hyperbolic Problems ⋮ Manifold Approximations via Transported Subspaces: Model Reduction for Transport-Dominated Problems ⋮ Reduced basis methods for time-dependent problems ⋮ An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation ⋮ A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds ⋮ A high-order/low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations ⋮ A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations ⋮ Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory ⋮ A dynamical low-rank approach to the chemical master equation ⋮ Solving the master equation without kinetic Monte Carlo: tensor train approximations for a CO oxidation model ⋮ Numerical low-rank approximation of matrix differential equations ⋮ Rank-adaptive structure-preserving model order reduction of Hamiltonian systems ⋮ Computation of the nearest structured matrix triplet with common null space ⋮ Adaptive integration of nonlinear evolution equations on tensor manifolds ⋮ An adaptive dynamical low rank method for the nonlinear Boltzmann equation ⋮ Minimum-correction second-moment matching: theory, algorithms and applications ⋮ A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations ⋮ Dynamically Orthogonal Numerical Schemes for Efficient Stochastic Advection and Lagrangian Transport ⋮ The geometry of algorithms using hierarchical tensors ⋮ On the Nearest Singular Matrix Pencil ⋮ On the approximation of high-dimensional differential equations in the hierarchical Tucker format ⋮ Dynamically Orthogonal Runge–Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation ⋮ A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy ⋮ Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems ⋮ Dynamical low-rank approximation to the solution of parabolic differential equations ⋮ Convergence Results for Projected Line-Search Methods on Varieties of Low-Rank Matrices Via Łojasiewicz Inequality ⋮ Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors ⋮ Adaptive sparse interpolation for accelerating nonlinear stochastic reduced-order modeling with time-dependent bases ⋮ Real-time reduced-order modeling of stochastic partial differential equations via time-dependent subspaces ⋮ A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems ⋮ Low-rank parareal: a low-rank parallel-in-time integrator ⋮ Dynamical low-rank integrators for second-order matrix differential equations ⋮ Matrix Stabilization Using Differential Equations ⋮ Quantum Dynamics with the Parallel Transport Gauge ⋮ On manifolds of tensors of fixed TT-rank ⋮ Locating coalescing singular values of large two-parameter matrices ⋮ Fast, low-memory numerical methods for radiative transfer via \(hp\)-adaptive mesh refinement ⋮ Reduced order model in cardiac electrophysiology with approximated Lax pairs ⋮ Dual dynamically orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions ⋮ Restricted Riemannian geometry for positive semidefinite matrices ⋮ Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations ⋮ A robust and conservative dynamical low-rank algorithm ⋮ Desingularization of Bounded-Rank Matrix Sets ⋮ A Geometric Approach to Dynamical Model Order Reduction ⋮ An optimization approach for dynamical Tucker tensor approximation ⋮ Geometric multiscale decompositions of dynamic low-rank matrices ⋮ Symplectic dynamical low rank approximation of wave equations with random parameters ⋮ Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling ⋮ A projector-splitting integrator for dynamical low-rank approximation ⋮ A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction ⋮ Mathematical methods in quantum chemistry. Abstracts from the workshop held March 18--24, 2018 ⋮ Computing low-rank rightmost eigenpairs of a class of matrix-valued linear operators ⋮ Geometric Methods on Low-Rank Matrix and Tensor Manifolds ⋮ Mini-workshop: Computational optimization on manifolds. Abstracts from the mini-workshop held November 15--21, 2020 (online meeting) ⋮ Low-rank retractions: a survey and new results ⋮ Time Integration of Tree Tensor Networks ⋮ On-the-fly reduced order modeling of passive and reactive species via time-dependent manifolds ⋮ An efficient method for non-negative low-rank completion ⋮ An observation-driven time-dependent basis for a reduced description of transient stochastic systems ⋮ Stochastic dynamical low-rank approximation method ⋮ An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics ⋮ Riemannian conjugate gradient methods with inverse retraction ⋮ A Low-Rank Algorithm for Weakly Compressible Flow ⋮ A Low-Rank Projector-Splitting Integrator for the Vlasov--Poisson Equation ⋮ A numerical solver for high dimensional transient Fokker-Planck equation in modeling polymeric fluids ⋮ Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values ⋮ Low rank differential equations for Hamiltonian matrix nearness problems ⋮ A computational framework of gradient flows for general linear matrix equations ⋮ Dynamical reduced basis methods for Hamiltonian systems ⋮ Localized bases of eigensubspaces and operator compression ⋮ Dynamical low-rank approximation: Applications and numerical experiments ⋮ Rank-adaptive tensor methods for high-dimensional nonlinear PDEs ⋮ An Efficient Dynamical Low-Rank Algorithm for the Boltzmann-BGK Equation Close to the Compressible Viscous Flow Regime ⋮ Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations ⋮ A gradient system for low rank matrix completion ⋮ Tensor neural network models for tensor singular value decompositions ⋮ Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods ⋮ The Extrinsic Geometry of Dynamical Systems Tracking Nonlinear Matrix Projections ⋮ Convergence of a Low-Rank Lie--Trotter Splitting for Stiff Matrix Differential Equations ⋮ Existence of dynamical low-rank approximations to parabolic problems ⋮ A Quasi-Conservative Dynamical Low-Rank Algorithm for the Vlasov Equation ⋮ Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces ⋮ A low-rank power iteration scheme for neutron transport criticality problems ⋮ Efficient dynamical low-rank approximation for the Vlasov-Ampère-Fokker-Planck system ⋮ Time Integration of Tensor Trains ⋮ Differential Equations for Real-Structured Defectivity Measures ⋮ Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit ⋮ Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs ⋮ Tensor Spaces and Hierarchical Tensor Representations ⋮ Finding the Nearest Passive or Nonpassive System via Hamiltonian Eigenvalue Optimization ⋮ A rank-adaptive robust integrator for dynamical low-rank approximation ⋮ A literature survey of low-rank tensor approximation techniques ⋮ Continuous Decompositions and Coalescing Eigenvalues for Matrices Depending on Parameters ⋮ A sweep-based low-rank method for the discrete ordinate transport equation ⋮ Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy ⋮ An unconventional robust integrator for dynamical low-rank approximation
