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 …

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 …

We consider the use of probabilistic neural networks for fluid flow surrogate modeling and
data recovery. This framework is constructed by assuming that the target variables are …

This paper proposes a supervised machine learning framework for the non-intrusive model
order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state …

We study the performance of long short-term memory networks (LSTMs) and neural ordinary
differential equations (NODEs) in learning latent-space representations of dynamical …

We present a new non‐intrusive model reduction method for the Navier–Stokes equations.
The method replaces the traditional approach of projecting the equations onto the reduced …

Most modeling approaches lie in either of the two categories: physics‐based or data‐driven.
Recently, a third approach which is a combination of these deterministic and statistical …

We study the use of feedforward neural networks (FNN) to develop models of nonlinear
dynamical systems from data. Emphasis is placed on predictions at long times, with limited …

For over a century, reduced order models (ROMs) have been a fundamental discipline of
theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr …

Autoencoder techniques find increasingly common use in reduced order modeling as a
means to create a latent space. This reduced order representation offers a modular data …