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

In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal…

This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced…

Numerical simulations of contaminant dispersion, as after a gas leakage incident on a chemical plant, can provide valuable insights for both emergency response and preparedness. Simulation approaches combine incompressible Navier-Stokes…

This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…

We propose a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code code…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…

The G-equation is a well-known model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing \textcolor{black}{regular solutions} of viscous G-equations in…

In Laser Powder Bed Fusion (LPBF), the applied laser energy produces high thermal gradients that lead to unacceptable final part distortion. Accurate distortion prediction is essential for optimizing the 3D printing process and…

POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…

This work aims to interpolate parametrized Reduced Order Model (ROM) basis constructed via the Proper Orthogonal Decomposition (POD) to derive a robust ROM of the system's dynamics for an unseen target parameter value. A novel non-intrusive…

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves.…

This paper introduces the $3^{rd}$-order Spectral Representation Method for simulation of non-stationary and non-Gaussian stochastic processes. The proposed method extends the classical $2^{nd}$-order Spectral Representation Method to…

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…

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…

In this paper, a parametric model order reduction (pMOR) technique is proposed to find a simplified system representation of a large-scale and complex thermal system. The main principle behind this technique is that any change of the…

Parametric partial differential equations (PDEs) serve as fundamental mathematical tools for modeling complex physical phenomena, yet repeated high-fidelity numerical simulations across parameter spaces remain computationally prohibitive.…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

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…