Related papers: Reduced-order modeling of advection-dominated syst…

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-driven modeling approach for nonlinear dynamical systems when…

A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two but the novel…

Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional…

Many reduced order models are neither robust with respect to the parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework…

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…

We study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous…

Understanding intraventricular hemodynamics requires compact and physically interpretable representations of the underlying flow structures, as characteristic flow patterns are closely associated with cardiovascular conditions and can…

Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…

Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks…

The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear…

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 variables when the control parameter values vary. Our…

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…

This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the…

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of $\mathrm{CO_2}$ sequestration). Here, we present a non-intrusive reduced order model of natural…

In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…

Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order…