Dynamically Orthogonal Runge–Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation
DOI10.1137/21m1431229zbMath1517.37087MaRDI QIDQ6039249
Unnamed Author, Pierre F. J. Lermusiaux
Publication date: 4 May 2023
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
curvatureretractionreduced-order modelingstochastic dynamical systemsdynamical low-rank approximationRiemannian matrix optimizationdynamically orthogonal equationsfixed-rank matrix manifold
Applications of differential geometry to physics (53Z05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solutions to stochastic differential and integral equations (65C30) Approximation methods and numerical treatment of dynamical systems (37M99)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Low-rank retractions: a survey and new results
- Reduced-order modelling for flow control. Papers based on the presentations at the course, Udine, Italy, September 2008
- Dynamical criteria for the evolution of the stochastic dimensionality in flows with uncertainty
- Dynamically orthogonal field equations for continuous stochastic dynamical systems
- From quantum to classical molecular dynamics: Reduced models and numerical analysis.
- Exact solvability of potentials with spatially dependent effective masses
- On Q-order and R-order of convergence
- The best \(L^ 2\)-approximation by finite sums of functions with separable variables
- Modeling uncertainty in flow simulations via generalized polynomial chaos.
- Perturbation expansions and error bounds for the truncated singular value decomposition
- Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations
- A rank-adaptive robust integrator for dynamical low-rank approximation
- Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors
- Symplectic dynamical low rank approximation of wave equations with random parameters
- Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries
- Projection methods for dynamical low-rank approximation of high-dimensional problems
- A projector-splitting integrator for dynamical low-rank approximation
- Exact solutions of the position-dependent mass Schrödinger equation in \(D\) dimensions
- Exactly solvable potentials for the Schrödinger equation with spatially dependent mass
- Uncertainty estimation and prediction for interdisciplinary ocean dynamics
- The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
- Minimum-correction second-moment matching: theory, algorithms and applications
- Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values
- D.D. Kosambi
- Low-Rank Matrix Completion by Riemannian Optimization
- Projection-like Retractions on Matrix Manifolds
- Computational Ocean Acoustics
- SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
- Geometric Methods on Low-Rank Matrix and Tensor Manifolds
- Convergence analysis of projected fixed‐point iteration on a low‐rank matrix manifold
- Dynamically Orthogonal Numerical Schemes for Efficient Stochastic Advection and Lagrangian Transport
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- Subspace Iteration Randomization and Singular Value Problems
- A Geometric Approach to Dynamical Model Order Reduction
- Dynamical Low‐Rank Approximation
- The Homogeneous Chaos
- Motion of Electrons and Holes in Perturbed Periodic Fields
- A note on \(Q\)-order of convergence
This page was built for publication: Dynamically Orthogonal Runge–Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation
