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 …

Aerodynamic modeling plays an important role in multiphysics and design problems, in
addition to experiment and numerical simulation, due to its low-dimensional representation …

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

A common strategy for the dimensionality reduction of nonlinear partial differential equations
(PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced …

This book provides a basic introduction to reduced basis (RB) methods for problems
involving the repeated solution of partial differential equations (PDEs) arising from …

In this work we present a Reduced Order Model which is specifically designed to deal with
turbulent flows in a finite volume setting. The method used to build the reduced order model …

A data-driven framework is proposed towards the end of predictive modeling of complex
spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural …

This paper presents a novel model reduction method: deep learning reduced order model,
which is based on proper orthogonal decomposition and deep learning methods. The deep …

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven
reduced order modeling of dynamical systems relevant to fluid flows. We propose various …

Abstract Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the
Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they …