相关论文: Non-intrusive reduced order modeling of natural co…

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…

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…

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…

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations…

We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a…

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…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

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…

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…

Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods…

Multivariate time series anomaly detection is a crucial problem in many industrial and research applications. Timely detection of anomalies allows, for instance, to prevent defects in manufacturing processes and failures in cyberphysical…

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…

A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics…

This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

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 propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…

Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear…

An autoencoder is a self-supervised machine-learning network trained to output a quantity identical to the input. Owing to its structure possessing a bottleneck with a lower dimension, an autoencoder works to achieve data compression,…