Advances in experimental techniques and the ever-increasing fidelity of numerical
simulations have led to an abundance of data describing fluid flows. This review discusses a …

Numerical simulation of large-scale dynamical systems plays a fundamental role in studying
a wide range of complex physical phenomena; however, the inherent large-scale nature of …

This paper describes a method for learning low-dimensional approximations of nonlinear
dynamical systems, based on neural network approximations of the underlying Koopman …

Controllability and observability have long been recognized as fundamental structural
properties of dynamical systems, but have recently seen renewed interest in the context of …

Turbulence pervades our world, from weather patterns to the air entering our lungs. This
book describes methods that reveal its structures and dynamics. Building on the existence of …

In today's technological world, physical and artificial processes are mainly described by
mathematical models, which can be used for simulation or control. These processes are …

MODEL reduction is a powerful tool that has been applied throughout many different
disciplines, including controls, uid dynamics, and structural dynamics. In many situations …

Part I deals with the mathematical preliminaries: numerical linear algebra; system theory;
stochastic processes; and Kalman filtering. Part II explains realization theory as applied to …

In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and
wide applicability for simulating large-scale mathematical models in engineering and the …

Balanced truncation is one of the most common model reduction schemes. In this note, we
present a survey of balancing related model reduction methods and their corresponding …