Related papers: Efficient space-time reduced order model for linea…

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…

In this study, we present a non-intrusive reduced order modeling (ROM) framework for large-scale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM)…

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…

Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…

The Kolmogorov $n$-width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue,…

Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows…

In this paper, a dynamic closure modeling approach has been derived to stabilize the projection-based reduced order models in the long-term evolution of forced-dissipative dynamical systems. To simplify our derivation without losing…

Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of the bath have to be included in the computation to…

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of…

While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…

We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate topology optimization, we replace the large-scale finite…

The impact of chemical reactions on the robustness and accuracy of projection-based Reduced-Order Models (ROMs) of fluid flows is investigated. Both Galerkin and Least-Squares Petrov Galerkin ROMs are shown to be less robust in reacting…

Machine learning and artificial intelligence algorithms typically require large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden…

Advection driven problems are known to be difficult to model with a reduced basis because of a slow decay of the Kolmogorov $N$-width. This paper investigates how this challenge transfers to the context of solidification problems and tries…

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such…

The discontinuous Petrov-Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and…

Though high-performance computing enables high-fidelity simulations of complex engineering systems, accurately resolving multi-scale physics for real-world problems remains computationally prohibitive, particularly in many-query…

We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…

The main goal of this work is to develop a data-driven Reduced Order Model (ROM) strategy from high-fidelity simulation result data of a Full Order Model (FOM). The goal is to predict at lower computational cost the time evolution of…

The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of…