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 …

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 …

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

State estimation is concerned with reconciling noisy observations of a physical system with
the mathematical model believed to predict its behaviour for the purpose of inferring …

Uncertainty quantification (UQ) in machine learning is currently drawing increasing research
interest, driven by the rapid deployment of deep neural networks across different fields, such …

A central challenge in data-driven model discovery is the presence of hidden, or latent,
variables that are not directly measured but are dynamically important. Takens' theorem …

Discovering governing equations of complex dynamical systems directly from data is a
central problem in scientific machine learning. In recent years, the sparse identification of …

Partial differential equations (PDEs) are concise and understandable representations of
domain knowledge, which are essential for deepening our understanding of physical …

The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to
a series of computational techniques for numerical solutions. Although numerous latest …