Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction
technique for data sequences. In its most common form, it processes high-dimensional …

Numerical simulation of fluids plays an essential role in modeling many physical
phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well …

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

Seismic waves from earthquakes and other sources are used to infer the structure and
properties of Earth's interior. The availability of large-scale seismic datasets and the …

Signal propagation in complex networks drives epidemics, is responsible for information
going viral, promotes trust and facilitates moral behavior in social groups, enables the …

Abstract Machine learning is rapidly becoming a core technology for scientific computing,
with numerous opportunities to advance the field of computational fluid dynamics. Here we …

Controlling electromagnetic waves and information simultaneously by information
metasurfaces is of central importance in modern society. Intelligent metasurfaces are smart …

Machine learning (ML) provides novel and powerful ways of accurately and efficiently
recognizing complex patterns, emulating nonlinear dynamics, and predicting the spatio …

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