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

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 …

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 …

Today's manufacturing processes are pushed to their limits to generate products with ever-
increasing quality at low costs. A prominent hurdle on this path arises from the multiscale …

Identifying governing equations from data and solving them to acquire spatio-temporal
responses is desirable, yet highly challenging, for many practical problems. Data-driven …

Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of
reduced-order models for a variety of scientific and engineering tasks. However, it is …

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems
is crucial in many scientific and engineering domains such as fluid dynamics, weather …

Data-driven science and technology offer transformative tools and methods to science. This
review article highlights the latest development and progress in the interdisciplinary field of …

Data-driven modeling continues to be enabled by modern machine learning algorithms and
deep learning architectures. The goals of such efforts revolve around the generation of …