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Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…

Many reduced order models are neither robust with respect to the parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework…

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

To describe non-equilibrium transport processes in a quantum device with infinite baths, we propose to formulate the problems as a reduced-order problem. Starting with the Liouville-von Neumann equation for the density-matrix, the…

We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians…

Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…

In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system…

In time-limited model order reduction, a reduced-order approximation of the original high-order model is obtained that accurately approximates the original model within the desired limited time interval. Accuracy outside that time interval…

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…

Equilibrium or stationary solutions usually proceed through the exact balance between hyperbolic transport terms and source terms. Such equilibrium solutions are affected by truncation errors that prevent any classical numerical scheme from…

Non-intrusive reduced-order modeling techniques are necessary for systems that are simulated using black-box solvers or known only from data. For systems exhibiting large transients and operating far away from equilibria, current…

This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin…

We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced…

This work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov-)Galerkin…

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…