Related papers: Hyper-Reduced Autoencoders for Efficient and Accur…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Hard visual attention is a promising approach to reduce the computational burden of modern computer vision methodologies. Hard attention mechanisms are typically non-differentiable. They can be trained with reinforcement learning but the…

Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model…

We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity…

Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to the embedded data in downstream learning steps is ignored. In…

A nonlinear-manifold reduced order model (NM-ROM) is a great way of incorporating underlying physics principles into a neural network-based data-driven approach. We combine NM-ROMs with domain decomposition (DD) for efficient computation.…

High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization,…

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…

In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that…

This study proposes an intrusive projection-based model-order reduction framework for nonlinear problems with a polynomial structure, solved iteratively using a Newton solver in the reduced space. It is demonstrated that for the targeted…

Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…

The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…

We present a method to construct reduced-order models for duct flows of Bingham media. Our method is based on proper orthogonal decomposition (POD) to find a low-dimensional approximation to the velocity and artificial neural network to…

In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…

Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…