Gradient preserving operator inference: data-driven reduced-order models for equations with gradient structure
From MaRDI portal
Publication:6557793
DOI10.1016/j.cma.2024.117033MaRDI QIDQ6557793
Lili Ju, Zhu Wang, Jasdeep Singh, Yuwei Geng, Boris Kramer
Publication date: 18 June 2024
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
reduced-order modelingoperator inferencedata-driven modelingdissipative and conservative systemsgradient-flow equation
Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)
Cites Work
- Unnamed Item
- Discontinuous Hamiltonian finite element method for linear hyperbolic systems
- Backpropagation and stochastic gradient descent method
- Report 14/2006: Geometric Numerical Integration (March 19th -- March 25th, 2006)
- Interpolatory projection methods for structure-preserving model reduction
- Structure-preserving model reduction for mechanical systems
- Interior-point methods
- Energy preserving model order reduction of the nonlinear Schrödinger equation
- Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems
- Structure-preserving model reduction for dynamical systems with a first integral
- Dynamical reduced basis methods for Hamiltonian systems
- On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: energy conservation and multi-symplecticity
- A review of structure-preserving numerical methods for engineering applications
- Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
- Symplectic Hamiltonian finite element methods for linear elastodynamics
- Conservative numerical schemes with optimal dispersive wave relations: part I. Derivation and analysis
- Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems
- Data-driven operator inference for nonintrusive projection-based model reduction
- Structure-preserving finite difference schemes for the Cahn-Hilliard equation with dynamic boundary conditions in the one-dimensional case
- An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations with complete Coriolis force
- Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
- Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
- Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I
- Hamiltonian operator inference: physics-preserving learning of reduced-order models for canonical Hamiltonian systems
- A Mathematical View of Interior-Point Methods in Convex Optimization
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- CVXPY: A Python-Embedded Modeling Language for Convex Optimization
- Structure-Preserving Model Reduction for Nonlinear Port-Hamiltonian Systems
- A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction
- Topics in structure-preserving discretization
- Symplectic Model Reduction of Hamiltonian Systems
- Multilayer shallow water equations with complete Coriolis force. Part 1. Derivation on a non-traditional beta-plane
- $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
- Turbulence and the dynamics of coherent structures. I. Coherent structures
- Geometric integration using discrete gradients
- LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs
- Discrete gradient methods for solving ODEs numerically while preserving a first integral
- Structure Preserving Model Reduction of Parametric Hamiltonian Systems
- An Interior-Point Method for Semidefinite Programming
- Structure-preserving reduced basis methods for Poisson systems
- Data-Driven Science and Engineering
- Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
- Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
- A new class of energy-preserving numerical integration methods
- Geometric integrators for ODEs
- Conservation properties of a time FE method. Part IV: Higher order energy and momentum conserving schemes
- New POD Error Expressions, Error Bounds, and Asymptotic Results for Reduced Order Models of Parabolic PDEs
- Approximation of Large-Scale Dynamical Systems
- Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder
- Reduced basis methods for time-dependent problems
- Galerkin proper orthogonal decomposition methods for parabolic problems
- Canonical and noncanonical Hamiltonian operator inference
- Gradient-Preserving Hyper-Reduction of Nonlinear Dynamical Systems via Discrete Empirical Interpolation
- Energy-conserving explicit and implicit time integration methods for the multi-dimensional Hermite-DG discretization of the Vlasov-Maxwell equations
- Port-Hamiltonian Dynamic Mode Decomposition
- Nonintrusive Reduced-Order Models for Parametric Partial Differential Equations via Data-Driven Operator Inference
- Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds
- Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems
- Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems
- Learning nonlinear reduced models from data with operator inference
Related Items (1)
This page was built for publication: Gradient preserving operator inference: data-driven reduced-order models for equations with gradient structure
