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We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…

Numerical Analysis · Mathematics 2022-02-22 Gobat G. , Opreni A. , Fresca S. , Manzoni A. , Frangi A

A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the…

Numerical Analysis · Mathematics 2023-08-08 Francesco Romor , Giovanni Stabile , Gianluigi Rozza

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…

Machine Learning · Computer Science 2021-08-30 Rachel Cooper , Andrey A. Popov , Adrian Sandu

We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…

Numerical Analysis · Mathematics 2026-01-13 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…

This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and…

Computational Engineering, Finance, and Science · Computer Science 2017-05-22 Shobhit Jain , Paolo Tiso , Daniel J. Rixen , Johannes B. Rutzmoser

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Numerical Analysis · Mathematics 2020-05-19 Oleg Balabanov , Anthony Nouy

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…

Numerical Analysis · Mathematics 2026-05-27 Rudy Geelen , Laura Balzano , Stephen Wright , Karen Willcox

We develop a Reduced Order Model (ROM) for a Large Eddy Simulation (LES) approach that combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies…

Numerical Analysis · Mathematics 2021-07-28 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…

Numerical Analysis · Mathematics 2020-09-16 Jiahua Jiang , Yanlai Chen

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

Numerical Analysis · Mathematics 2026-04-27 Dawid Kotowski , Mario Ohlberger

In the early stages of aerospace design, reduced order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy…

Machine Learning · Computer Science 2024-02-28 Bilal Mufti , Christian Perron , Dimitri N. Mavris

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…

Dynamical Systems · Mathematics 2022-10-03 Peter Benner , Pawan Goyal , Jan Heiland , Igor Pontes

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

Computational Engineering, Finance, and Science · Computer Science 2026-01-26 Alejandro N Diaz , Shane A McQuarrie , John T Tencer , Patrick J Blonigan

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box.…

Computational Physics · Physics 2024-10-16 Aviral Prakash , Yongjie Jessica Zhang

We propose a general --- i.e., independent of the underlying equation --- registration method for parameterized Model Order Reduction. Given the spatial domain $\Omega \subset \mathbb{R}^d$ and a set of snapshots $\{ u^k \}_{k=1}^{n_{\rm…

Numerical Analysis · Mathematics 2019-11-12 Tommaso Taddei

Convection-dominated problems are known for their slow Kolmogorov $n$-width decays and are challenging for model order reduction (MOR). In this work, we propose a hybrid surrogate modeling approach and a non-intrusive variant that overcome…

Dynamical Systems · Mathematics 2026-05-29 Lihong Feng , Ali Hassan , Shuwen Sun

We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and…

Machine Learning · Computer Science 2025-06-17 Vinicius L. S. Silva , Claire E. Heaney , Nenko Nenov , Christopher C. Pain

We propose a new framework to design controllers for high-dimensional nonlinear systems. The control is designed through the iterative linear quadratic regulator (ILQR), an algorithm that computes control by iteratively applying the linear…

Optimization and Control · Mathematics 2021-10-12 Yizhe Huang , Boris Kramer

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…

Fluid Dynamics · Physics 2021-10-13 Pranshu Pant , Ruchit Doshi , Pranav Bahl , Amir Barati Farimani