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 …

Physics is a field of science that has traditionally used the scientific method to answer
questions about why natural phenomena occur and to make testable models that explain the …

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

Nearly all model-reduction techniques project the governing equations onto a linear
subspace of the original state space. Such subspaces are typically computed using methods …

In recent years, we have witnessed a significant shift toward ever-more complex and ever-
larger-scale systems in the majority of the grand societal challenges tackled in applied …

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate
physical simulations in which the intrinsic solution space falls into a subspace with a small …

Data science, and machine learning in particular, is rapidly transforming the scientific and
industrial landscapes. The aerospace industry is poised to capitalize on big data and …

A common strategy for the dimensionality reduction of nonlinear partial differential equations
(PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced …

A reduced basis method based on a physics-informed machine learning framework is
developed for efficient reduced-order modeling of parametrized partial differential equations …

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 …