Aerodynamic modeling plays an important role in multiphysics and design problems, in
addition to experiment and numerical simulation, due to its low-dimensional representation …

In recent years, we have witnessed a significant shift toward ever-more complex and ever-
larger-scale systems in the majority of the grand societal challenges tackled in applied …

Data-driven discovery is revolutionizing how we model, predict, and control complex
systems. Now with Python and MATLAB®, this textbook trains mathematical scientists 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 …

THE field of fluid mechanics involves a range of rich and vibrant problems with complex
dynamics stemming from instabilities, nonlinearities, and turbulence. The analysis of these …

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate
physical simulations in which the intrinsic solution space falls into a subspace with a small …

In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

A common strategy for the dimensionality reduction of nonlinear partial differential equations
(PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced …

Optimal sensor and actuator placement is an important unsolved problem in control theory.
Nearly every downstream control decision is affected by these sensor and actuator …

Closed-loop turbulence control is a critical enabler of aerodynamic drag reduction, lift
increase, mixing enhancement, and noise reduction. Current and future applications have …