Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds
From MaRDI portal
Publication:6194167
DOI10.1016/j.cma.2023.116402arXiv2305.15490MaRDI QIDQ6194167
Hongliang Mu, Harsh Sharma, Silke Glas, Rudy J. M. Geelen, Boris Kramer, Patrick Buchfink
Publication date: 14 February 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2305.15490
Hamiltonian systemsquadratic manifoldsdata-driven modelingscientific machine learningsymplectic model reduction
Cites Work
- Unnamed Item
- Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing
- A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
- Dynamically orthogonal field equations for continuous stochastic dynamical systems
- Symplectic integration of Hamiltonian wave equations
- On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry
- Dynamical reduced basis methods for Hamiltonian systems
- POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition
- Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference
- A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation
- Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning
- A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
- The neural network shifted-proper orthogonal decomposition: a machine learning approach for non-linear reduction of hyperbolic equations
- Physics-informed cluster analysis and a priori efficiency criterion for the construction of local reduced-order bases
- Performance assessment of energy-preserving, adaptive time-step variational integrators
- A review of structure-preserving numerical methods for engineering applications
- An artificial neural network framework for reduced order modeling of transient flows
- Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
- Decay of the Kolmogorov \(N\)-width for wave problems
- Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems
- Data-driven operator inference for nonintrusive projection-based model reduction
- Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
- 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
- Operator inference for non-intrusive model reduction with quadratic manifolds
- Nonlinear model order reduction based on local reduced-order bases
- Efficient reduced models anda posteriorierror estimation for parametrized dynamical systems by offline/online decomposition
- Symplectic Model Reduction of Hamiltonian Systems
- Structure Preserving Model Reduction of Parametric Hamiltonian Systems
- The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena
- Structure-preserving reduced basis methods for Poisson systems
- Rank-adaptive structure-preserving model order reduction of Hamiltonian systems
- Reduced basis techniques for nonlinear conservation laws
- Localized Discrete Empirical Interpolation Method
- Dynamical Low‐Rank Approximation
- Numerical methods for Hamiltonian PDEs
- Geometric Numerical Integration
- The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate
- Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder
