Model reduction on manifolds: a differential geometric framework
DOI10.1016/J.PHYSD.2024.134299zbMATH Open1544.34019MaRDI QIDQ6599870
Silke Glas, Bernard Haasdonk, Patrick Buchfink, Benjamin Unger
Publication date: 6 September 2024
Published in: Physica D (Search for Journal in Brave)
Hamiltonian systemsLagrangian systemsPetrov-Galerkinnonlinear projectiondata-driven projectionmodel reduction on manifolds
Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Geometric methods in ordinary differential equations (34A26) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Dynamical systems in numerical analysis (37N30) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürnberg
- A-posteriori error estimation for second order mechanical systems
- Reduced order methods for modeling and computational reduction
- Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing
- From quantum to classical molecular dynamics: Reduced models and numerical analysis.
- A paradigm for joined Hamiltonian and dissipative systems
- Reconstructing phase space from PDE simulations
- Structure-preserving model reduction for mechanical systems
- Reconstruction equations and the Karhunen-Loève expansion for systems with symmetry
- Note on exchange phenomena in the Thomas atom.
- Reduced order models for Lagrangian hydrodynamics
- Modal decomposition of flow data via gradient-based transport optimization
- Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference
- Lift \& learn: physics-informed machine learning for large-scale nonlinear dynamical systems
- Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric
- Non intrusive method for parametric model order reduction using a bi-calibrated interpolation on the Grassmann manifold
- A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
- Registration-based model reduction of parameterized two-dimensional conservation laws
- Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
- Decay of the Kolmogorov \(N\)-width for wave problems
- Kolmogorov \(n\)-widths for linear dynamical systems
- Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems
- Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
- Hamiltonian operator inference: physics-preserving learning of reduced-order models for canonical Hamiltonian systems
- Quadratic approximation manifold for mitigating the Kolmogorov barrier in nonlinear projection-based model order reduction
- Energetically consistent model reduction for metriplectic systems
- Operator inference for non-intrusive model reduction with quadratic manifolds
- Introduction to Smooth Manifolds
- Active Subspaces
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- A real time procedure for affinely dependent parametric model order reduction using interpolation on Grassmann manifolds
- 7 Manifold interpolation
- Symplectic Model Reduction of Hamiltonian Systems
- $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
- A method for interpolating on manifolds structural dynamics reduced-order models
- Reduction and reconstruction for self-similar dynamical systems
- Structure Preserving Model Reduction of Parametric Hamiltonian Systems
- Model Reduction and Approximation
- Transport Reversal for Model Reduction of Hyperbolic Partial Differential Equations
- The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena
- Freezing Solutions of Equivariant Evolution Equations
- Structure-preserving reduced basis methods for Poisson systems
- Projection-based model reduction with dynamically transformed modes
- Riemannian Optimization on the Symplectic Stiefel Manifold
- Port-Hamiltonian Systems Theory: An Introductory Overview
- Optimizing Oblique Projections for Nonlinear Systems using Trajectories
- A Registration Method for Model Order Reduction: Data Compression and Geometry Reduction
- Model Order Reduction for Problems with Large Convection Effects
- Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
- Geometric Numerical Integration
- Reduced Basis Methods for Partial Differential Equations
- Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder
- Control of port-Hamiltonian differential-algebraic systems and applications
- Neural-network-augmented projection-based model order reduction for mitigating the Kolmogorov barrier to reducibility
- Canonical and noncanonical Hamiltonian operator inference
- Front transport reduction for complex moving fronts
- Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems
- Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds
- Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders
- Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems
- Energy-based model reduction of transport-dominated phenomena
This page was built for publication: Model reduction on manifolds: a differential geometric framework
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6599870)