Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction
technique for data sequences. In its most common form, it processes high-dimensional …

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

Digital twin can be defined as a virtual representation of a physical asset enabled through
data and simulators for real-time prediction, optimization, monitoring, controlling, and …

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

Fast and accurate airflow simulations in the built environment are critical to provide
acceptable thermal comfort and air quality to the occupants. Computational Fluid Dynamics …

This paper discusses the spectral proper orthogonal decomposition and its use in identifying
modes, or structures, in flow data. A specific algorithm based on estimating the cross …

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 …

This document presents comprehensive historical accounts on the developments of finite
element methods (FEM) since 1941, with a specific emphasis on developments related to …

Recent attempts to use deep learning for super-resolution reconstruction of turbulent flows
have used supervised learning, which requires paired data for training. This limitation …

We consider the frequency domain form of proper orthogonal decomposition (POD), called
spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space …