Related papers: A Quadratic Manifold for Model Order Reduction of …
In this paper, a generalization of a quadratic manifold approach for the reduction of geometrically nonlinear structural dynamics problems is presented. This generalization is constructed by a linearization of the static force with respect…
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
The increasing size and complexity of modern power systems have led to a high-dimensional mathematical model for transient stability studies, rendering full-scale simulations computationally burdensome. While dimensionality reduction is…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov barrier that affects transport-dominated problems. In this work, we build on the reduced dynamics given by Neural Galerkin schemes and propose to…
A quadratic approximation manifold is presented for performing nonlinear, projection-based, model order reduction (PMOR). It constitutes a departure from the traditional affine subspace approximation that is aimed at mitigating the…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
Component Mode Synthesis methods, such as the Craig-Bampton (CB) approach, are widely used in structural dynamics due to their modularity and compatibility with substructuring workflows. While highly effective for linear systems, extending…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial…
The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…
Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…
Spatiotemporally chaotic systems, such as the solutions of some nonlinear partial differential equations, are dynamical systems that evolve toward a lower dimensional manifold. This manifold has an intricate geometry with heterogeneous…