Model reduction of dynamical systems on nonlinear manifolds using ...

[WCCM2022] Nonlinear manifold to component-wise reduced order ...

This is the presentation I gave at WCCM-APCOM Yokohama 2022 ( https://www.wccm2022.org ). I talked about various data-driven physical ...

Model Reduction on Approximate Inertial Manifolds for NS ... - OUCI

Rega, G., and H. Troger. 2005. Dimension reduction of dynamical systems: Methods, models, applications. Nonlinear Dynamics 41(1): 1–15. https:// ...

Learning Nonlinear Reduced Models from Data with Operator ...

The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model ...

symplectic-model-reduction-Hamiltonian-systems-data-driven ...

reduction of dynamical systems on nonlinear manifolds using interpretable (e.g., polynomial) manifold constructions ... model reduction of large-scale, nonlinear ...

SOME THEMES IN NONLINEAR MODEL REDUCTION WITH ...

Most of the established reduction techniques involve Galerkin projection of full system of governing equations onto linear subspaces for the reduction of ...

Nonlinear balanced truncation: Computing energy functions and ...

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders. Journal of Computational Physics, 404 ...

Fei Lu's Homepage - Johns Hopkins University

... model reduction for complex systems in computation such as fluid dynamics and molecular dynamics simulation. I view dynamical systems as a description of ...

Dynamical model reduction method for solving parameter ...

This strategy has also been considered in [28, 12, 21, 34] for the solution of nonlinear problems, including nonlinear dynamical systems. In [34] ...

Nonlinear Model Reduction for Slow-Fast Stochastic Systems Near ...

... manifold with slow dynamics and high-dimensional, large fast modes. Given only access to a black-box simulator from which short bursts of simulation can be ...

panchgonzalez/nmor: Deep learning framework for model reduction ...

... model reduction of dynamical systems - panchgonzalez ... dynamics of low-dimensional representation on its underlying nonlinear manifold.

Center manifold reduction - dynamical systems - Math Stack Exchange

Center manifold reduction ... Again (0,0) is an equilibrium point and the system is in canonical form JX(0,0)=[000−1]. ... and ˙y=−h(x)+x2=−(a−1)x2− ...

Dynamical Reduced-Order Models for High-Dimensional Systems

Even further, our numerical schemes automatically detect when the dynamics depart the nonlinear manifold and may jump to a new nonlinear manifold that better ...

MathAlgoDB | Query and Explore the Algorithm Knowledge Graph

Lee, Carlberg (2020) Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders ...

Advancing the Field of Reduced-order Modeling – News

The use of nonlinear manifold projection (autoencoders) has resulted in a significant improvement in solution accuracy over more well-established linear methods ...

Operator inference for non-intrusive model reduction with nonlinear ...

Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non- ...

REDUCED-ORDER OPTIMAL CONTROL BASED ON ... - jstor

dynamics results in the ability to control the full underlying control system. ... Model reduction for control design for distributed parameter systems, in Re.

Data-driven modeling and prediction of non-linearizable dynamics ...

Low-dimensional reduced models of high-dimensional nonlinear dynamical systems are critically needed in various branches of applied science and ...

A quadratic decoder approach to nonintrusive reduced‐order ...

Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally ...

Model Reduction: The Manifold Boundary Approximation Method

This particular model had 48 parameters and 29 differential equations. However, because the model was made of many inhomogeneous components interacting in ...

Structure-preserving model reduction for port-Hamiltonian systems ...

We discuss structure-preserving model order reduction for port-Hamiltonian systems based on a nonlinear approximation ansatz which is linear with respect to ...