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

A dimension reduction method called discrete empirical interpolation is proposed and
shown to dramatically reduce the computational complexity of the popular proper orthogonal …

This paper presents a new method of missing point estimation (MPE) to derive efficient
reduced-order models for large-scale parameter-varying systems. Such systems often result …

We propose a new technique for obtaining reduced order models for nonlinear dynamical
systems. Specifically, we advocate the use of the recently developed dynamic mode …

The optimization of subsurface flow processes is important for many applications, including
oil field operations and the geological storage of carbon dioxide. These optimizations are …

The need for multiple interactive, real-time simulations using different parameter values has
driven the design of fast numerical algorithms with certifiable accuracies. The reduced basis …

We perform a comparative analysis using three reduced-order strategies–Missing Point
Estimation (MPE) method, Gappy POD method, and Discrete Empirical Interpolation Method …

We demonstrate the synthesis of sparse sampling and dimensionality reduction to
characterize and model nonlinear dynamical systems over a range of bifurcation …

System Gramian matrices are a well-known encoding for properties of input-output systems
such as controllability, observability or minimality. These so-called system Gramians were …

This paper discusses the integrated design of mechatronic systems with varying dynamics,
such as serial and parallel machine tools. This characteristic affects the machine stability …