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 …

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward
and inverse nonlinear problems described by partial differential equations (PDEs) and noisy …

Many dynamical systems of interest are nonlinear, with examples in turbulence,
epidemiology, neuroscience, and finance, making them difficult to control using linear …

In the context of science, the well-known adage" a picture is worth a thousand words" might
well be" a model is worth a thousand datasets." In this manuscript we introduce the SciML …

There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

The discovery of governing equations from scientific data has the potential to transform data-
rich fields that lack well-characterized quantitative descriptions. Advances in sparse …

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 …

Understanding the interplay of order and disorder in chaos is a central challenge in modern
quantitative science. Approximate linear representations of nonlinear dynamics have long …

Accurately modelling the nonlinear dynamics of a system from measurement data is a
challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm …