7 Manifold interpolation
From MaRDI portal
Publication:3384277
DOI10.1515/9783110498967-007zbMath1505.65189OpenAlexW3210764284MaRDI QIDQ3384277
Publication date: 15 December 2021
Published in: System- and Data-Driven Methods and Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/9783110498967-007
interpolationparametric model reductionmatrix manifoldRiemannian computingRiemannian normal coordinates
Interpolation in approximation theory (41A05) Large-scale systems (93A15) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to approximations and expansions (41-01) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30) Numerical linear algebra (65F99) Numerical computation of matrix exponential and similar matrix functions (65F60)
Related Items (4)
Computing the Riemannian Logarithm on the Stiefel Manifold: Metrics, Methods, and Performance ⋮ A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation ⋮ DRIPS: a framework for dimension reduction and interpolation in parameter space ⋮ Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Algorithmic advances in Riemannian geometry and applications. For machine learning, computer vision, statistics, and optimization
- A gradient-descent method for curve fitting on Riemannian manifolds
- Gradient-enhanced surrogate modeling based on proper orthogonal decomposition
- Geometric mean and geodesic regression on Grassmannians
- The left invariant metric in the general linear group
- Introduction to the theory of Lie groups. Translated from the French by Urmie Ray
- Reduced-order models for parameter dependent geometries based on shape sensitivity analysis
- Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements
- Choosing roots of polynomials smoothly
- A reduced-order method for simulation and control of fluid flows
- On the geometry of Riemannian cubic polynomials.
- Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
- Statistics on the Stiefel manifold: theory and applications
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- The Riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data
- The dynamic interpolation problem: on Riemannian manifolds, Lie groups, and symmetric spaces
- Parametric model reduction via interpolating orthonormal bases
- \(C^1\) interpolating Bézier path on Riemannian manifolds, with applications to 3D shape space
- De Casteljau's algorithm on manifolds
- Bézier curves and \(C^{2}\) interpolation in Riemannian manifolds
- Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations
- A two-step algorithm of smooth spline generation on Riemannian manifolds
- A Riemannian framework for tensor computing
- Geodesic finite elements of higher order
- Kernels on Riemannian Manifolds
- Canonical Correlation Analysis on SPD(n) Manifolds
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- An Accelerated Greedy Missing Point Estimation Procedure
- Quasi-interpolation in Riemannian manifolds
- On the Convergence of Gradient Descent for Finding the Riemannian Center of Mass
- A Locally Parametrized Reduced-Order Model for the Linear Frequency Domain Approach to Time-Accurate Computational Fluid Dynamics
- A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems
- Galerkin Models Enhancements for Flow Control
- A real time procedure for affinely dependent parametric model order reduction using interpolation on Grassmann manifolds
- Positive Definite Matrices: Data Representation and Applications to Computer Vision
- From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings
- Geometric Methods and Applications
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- Efficient reduced models anda posteriorierror estimation for parametrized dynamical systems by offline/online decomposition
- An Online Method for Interpolating Linear Parametric Reduced-Order Models
- Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds
- Local Parametrization of Subspaces on Matrix Manifolds via Derivative Information
- Cubic Splines on Curved Spaces
- Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis
- Riemannian Metric and Geometric Mean for Positive Semidefinite Matrices of Fixed Rank
- Rolling Stiefel manifolds
- Riemannian center of mass and mollifier smoothing
- The Geometry of Algorithms with Orthogonality Constraints
- Radial Basis Functions
- Endpoint Geodesics on the Stiefel Manifold Embedded in Euclidean Space
- Continuous Mode Interpolation for Control-Oriented Models of Fluid Flow
- A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank
- Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
- Interpolation-based reduced-order modelling for steady transonic flows via manifold learning
- Hermite Interpolation and Data Processing Errors on Riemannian Matrix Manifolds
- Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition
- Quotient Geometry with Simple Geodesics for the Manifold of Fixed-Rank Positive-Semidefinite Matrices
- Lie Groups and Geometric Aspects of Isometric Actions
- Lie Groups, Lie Algebras, and Representations
- A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
- A Matrix-Algebraic Algorithm for the Riemannian Logarithm on the Stiefel Manifold under the Canonical Metric
- Geometric Means in a Novel Vector Space Structure on Symmetric Positive‐Definite Matrices
- Functions of Matrices
- Multiscale Representations for Manifold-Valued Data
- DIFFERENTIAL GEOMETRY OF GRASSMANN MANIFOLDS
This page was built for publication: 7 Manifold interpolation
