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We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…

Numerical Analysis · Mathematics 2021-04-05 Ion Victor Gosea , Serkan Gugercin , Benjamin Unger

In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…

In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…

Dynamical Systems · Mathematics 2023-01-24 Pawan Goyal , Igor Pontes Duff , Peter Benner

We introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model and forecasting tool for global atmospheric chemistry dynamics. By exploiting a low-dimensional…

Machine Learning · Computer Science 2024-04-22 Meghana Velegar , Christoph Keller , J. Nathan Kutz

Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…

Machine Learning · Computer Science 2021-05-11 Gabriel F. Barros , Malú Grave , Alex Viguerie , Alessandro Reali , Alvaro L. G. A. Coutinho

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…

Machine Learning · Computer Science 2026-05-05 Tatsuya Naoi , Jun Ohkubo

We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of…

Dynamical Systems · Mathematics 2015-06-02 J. Nathan Kutz , Xing Fu , Steven L. Brunton

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for…

Computational Engineering, Finance, and Science · Computer Science 2018-10-25 J. Nagoor Kani , Ahmed H. Elsheikh

We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galerkin ROMs constructed from vibration…

Numerical Analysis · Mathematics 2025-12-09 Alexander Saccani , Paolo Tiso

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…

Numerical Analysis · Mathematics 2022-06-08 Alexander V. Mamonov , Maxim A. Olshanskii

We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…

Systems and Control · Electrical Eng. & Systems 2023-03-21 Paul Schwerdtner , Manuel Schaller

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

Reconstructing continuous state trajectories of chaotic dynamical systems from sparse, noisy observations remains a fundamental open problem in nonlinear science. We introduce the Physics-Informed Diffusion Model with Dormand-Prince…

Machine Learning · Computer Science 2026-05-27 Shailendra Dabral

Assessing IC manufacturing process fluctuations and their impacts on IC interconnect performance has become unavoidable for modern DSM designs. However, the construction of parametric interconnect models is often hampered by the rapid…

Hardware Architecture · Computer Science 2011-11-09 Peng Li , Frank Liu , Xin Li , Lawrence T. Pileggi , Sani R. Nassif

An adaptive scheme to generate reduced-order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the POD-Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively…

Numerical Analysis · Mathematics 2021-10-13 Sridhar Chellappa , Lihong Feng , Peter Benner

Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…

Systems and Control · Electrical Eng. & Systems 2025-08-05 Ziqin He , Mengqi Hu , Yifei Lou , Can Chen

Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with…

Fluid Dynamics · Physics 2026-05-05 Yutaro Tanaka , Hiroya Nakao

Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…

Numerical Analysis · Mathematics 2021-09-14 Neeraj Sarna , Peter Benner

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…

Computational Physics · Physics 2020-04-22 Suraj Pawar , Shady E. Ahmed , Omer San , Adil Rasheed

Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely…

Quantum Physics · Physics 2023-08-04 Wei Liu , Zi-Hao Chen , Yu Su , Yao Wang , Wenjie Dou