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

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

Sparse model identification enables the discovery of nonlinear dynamical systems purely
from data; however, this approach is sensitive to noise, especially in the low-data limit. In this …

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 behavioral approach to systems theory, put forward 40 years ago by Jan C. Willems,
takes a representation-free perspective of a dynamical system as a set of trajectories. Till …

THE field of fluid mechanics involves a range of rich and vibrant problems with complex
dynamics stemming from instabilities, nonlinearities, and turbulence. The analysis of these …

Automated data-driven modeling, the process of directly discovering the governing
equations of a system from data, is increasingly being used across the scientific community …

Harnessing data to discover the underlying governing laws or equations that describe the
behavior of complex physical systems can significantly advance our modeling, simulation …

Abstract Kolmogorov–Arnold networks (KANs) as an alternative to multi-layer perceptrons
(MLPs) are a recent development demonstrating strong potential for data-driven 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 …