Related papers: Reduced order modeling for flow and transport prob…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Reduced-order models (ROMs) are widely used in fluid engineering to enable rapid prediction of flow fields for parametric analysis, design optimization, and control applications. Proper orthogonal decomposition (POD) is commonly employed to…
In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…
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…
Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…
In this paper we consider the numerical approximation of a semilinear reaction-diffusion model problem (PDEs) by means of reduced order methods (ROMs) based on proper orthogonal decomposition (POD). We focus on the time integration of the…
Reduced-order models (ROMs) have become an essential tool for reducing the computational cost of fluid flow simulations. While standard ROMs can efficiently approximate laminar flows, their accuracy often suffers in convection-dominated…
Deep neural networks trained using a softmax layer at the top and the cross-entropy loss are ubiquitous tools for image classification. Yet, this does not naturally enforce intra-class similarity nor inter-class margin of the learned deep…
We present a deep learning-based reduced order model (DL-ROM) for predicting the fluid forces and unsteady vortex patterns. We consider flow past a sphere to examine the accuracy of our DL-ROM predictions. The proposed methodology relies on…
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted…
For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…
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…
In recent years, numerical methods in industrial applications have evolved from a pure predictive tool towards a means for optimization and control. Since standard numerical analysis methods have become prohibitively costly in such…
Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…
Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control.…
Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the…
In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems…
Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial…