Related papers: Nonlinear Model Order Reduction via Lifting Transf…
This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical…
This work presents structure-preserving Lift & Learn, a scientific machine learning method that employs lifting variable transformations to learn structure-preserving reduced-order models for nonlinear partial differential equations (PDEs)…
In PDE-constrained optimization, proper orthogonal decomposition (POD) provides a surrogate model of a (potentially expensive) PDE discretization, on which optimization iterations are executed. Because POD models usually provide good…
AI for science (AI4Science) models often suffer from discretization: learned representations remain tied to the training grid, limiting transfer across resolutions, solvers and applications. We introduce Neural Proper Orthogonal…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in…
A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…
A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…
This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…
We are concerned with employing Model Order Reduction (MOR) to efficiently solve parameterized multiscale problems using the Localized Orthogonal Decomposition (LOD) multiscale method. Like many multiscale methods, the LOD follows the idea…
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…
In this paper, we propose and analyze a multiscale method for a class of quasilinear elliptic problems of nonmonotone type with spatially multiscale coefficient. The numerical approach is inspired by the Localized Orthogonal Decomposition…
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…
The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing Proper Orthogonal Decomposition (POD-MOR) for nonlinear parabolic evolution…
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…
We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…
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…