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We introduce a Nemytskii neural operator framework for nonlinear model reduction of parametrized steady-state partial differential equations. The method generalizes reduced basis approaches by replacing linear combinations of basis…

Numerical Analysis · Mathematics 2026-03-03 Jingye Li , Alex Bespalov , Jinglai Li

This paper develops a general approach to nonlinear circuit modelling aimed at preserving the intrinsic symmetry of electrical circuits when formulating reduced models. The goal is to provide a framework accommodating such reductions in a…

Systems and Control · Electrical Eng. & Systems 2020-06-02 Ricardo Riaza

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

Numerical Analysis · Mathematics 2023-11-17 Junming Duan , Jan S. Hesthaven

Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model…

Optimization and Control · Mathematics 2024-10-17 Min Tao , Panagiotis Petsagkourakis , Jie Li , Constantinos Theodoropoulos

This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…

Systems and Control · Electrical Eng. & Systems 2025-04-08 Arshiya Taj Abdul , Augustinos D. Saravanos , Evangelos A. Theodorou

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

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Computational Engineering, Finance, and Science · Computer Science 2021-09-24 Thomas Simpson , Nikolaos Dervilis , Eleni Chatzi

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Fluid Dynamics · Physics 2020-04-13 Ali Thari , Vito Pasquariello , Niels Aage , Stefan Hickel

Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…

Systems and Control · Electrical Eng. & Systems 2026-02-20 Jan C. Schulze , Alexander Mitsos

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

Dynamical Systems · Mathematics 2021-01-07 Elliott Skomski , Soumya Vasisht , Colby Wight , Aaron Tuor , Jan Drgona , Draguna Vrabie

In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are…

Systems and Control · Electrical Eng. & Systems 2020-11-09 Arash Sadeghzadeh , Roland Toth

Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…

Robotics · Computer Science 2021-01-29 David Hägele , Moataz Abdelaal , Ozgur S. Oguz , Marc Toussaint , Daniel Weiskopf

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

Numerical Analysis · Mathematics 2022-03-02 Davide Papapicco , Nicola Demo , Michele Girfoglio , Giovanni Stabile , Gianluigi Rozza

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

Machine Learning · Statistics 2025-02-20 Patrick Héas , Cédric Herzet , Benoit Combès

Parameter estimation of nonlinear state-space models from input-output data typically requires solving a highly non-convex optimization problem prone to slow convergence and suboptimal solutions. This work improves the reliability and…

Signal Processing · Electrical Eng. & Systems 2026-02-27 Merijn Floren , Jan Swevers

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Numerical Analysis · Mathematics 2026-01-09 Jiaming Guo , Dunhui Xiao

The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…

Numerical Analysis · Mathematics 2014-09-18 Christopher Beattie , Serkan Gugercin

We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…

Numerical Analysis · Mathematics 2015-06-23 Remi Abgrall , David Amsallem

Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…

Optimization and Control · Mathematics 2022-01-17 Samuel E. Otto , Alberto Padovan , Clarence W. Rowley

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Systems and Control · Electrical Eng. & Systems 2022-06-13 Steeven Janny , Quentin Possamai , Laurent Bako , Madiha Nadri , Christian Wolf