Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …

A multitude of cyber-physical system (CPS) applications, including design, control,
diagnosis, prognostics, and a host of other problems, are predicated on the assumption of …

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

Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling
and control efforts, providing a tremendous opportunity to extend the reach of model …

We establish the convergence of a class of numerical algorithms, known as dynamic mode
decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite …

PySINDy is a Python package for the discovery of governing dynamical systems models
from data. In particular, PySINDy provides tools for applying the sparse identification of …

For prediction and real-time control tasks, machine-learning (ML)-based digital twins are
frequently employed. However, while these models are typically accurate, they are custom …

The sparse identification of nonlinear dynamics (SINDy) is a recently proposed data-driven
modelling framework that uses sparse regression techniques to identify nonlinear low-order …

Effective inclusion of physics-based knowledge into deep neural network models of
dynamical systems can greatly improve data efficiency and generalization. Such a priori …

We propose using operator learning to approximate the dynamical response of non-
autonomous systems, such as nonlinear control systems. Unlike classical function learning …