Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

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 …

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

Abstract Machine learning (ML) has been increasingly used to aid aerodynamic shape
optimization (ASO), thanks to the availability of aerodynamic data and continued …

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 …

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

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 …

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to
overcome common limitations shared by conventional reduced order models (ROMs)–built …

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 …

We develop a general framework for data-driven approximation of input-output maps
between infinitedimensional spaces. The proposed approach is motivated by the recent …