Related papers: Optimizing Oblique Projections for Nonlinear Syste…
Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper…
This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
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…
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…
In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…
This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…
This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of…
High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…
Two comprehensive approaches are considered for constructing projection-based reduced-order computational models for linear dynamical systems. The first one reduces the governing equations written in the descriptor form, using a Galerkin or…
An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…
In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…
Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…
State-specific thermochemical collisional models are crucial to accurately describe the physics of systems involving nonequilibrium plasmas, but they are also computationally expensive and impractical for large-scale, multi-dimensional…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearization techniques. By directly leveraging structural properties…
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…
Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…
In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…