The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

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

This paper presents a randomized algorithm for computing the near-optimal low-rank
dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to …

We develop greedy algorithms to approximate the optimal solution to the multi-fidelity sensor
selection problem, which is a cost constrained optimization problem prescribing the …

In this paper, we overview, evaluate, and demonstrate the sparse processing particle image
velocimetry (SPPIV) as a real-time flow field estimation method using the particle image …

Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to
decompose complex, nonlinear systems into a set of modes, revealing underlying patterns …

Reconstruction of the distribution of ground motion due to an earthquake is one of the key
technologies for the prediction of seismic damage to infrastructure. Particularly, the …

Abstract The Koopman and Perron Frobenius transport operators are fundamentally
changing how we approach dynamical systems, providing linear representations for even …

Considerable financial resources are allocated for measuring ambient air pollution in the
United States, yet the locations for these monitoring sites may not be optimized to capture …

The problem of selecting an optimal set of sensors estimating a high-dimensional data is
considered. Objective functions based on D-, A-, and E-optimality criteria of optimal design …