相关论文: RONOM: Reduced-Order Neural Operator Modeling

We propose KROM, a kernel-based reduced-order framework for fast solution of nonlinear partial differential equations. KROM formulates PDE solution as a minimum-norm (Gaussian-process) recovery problem in an RKHS, and accelerates the…

We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…

In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…

Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

This chapter provides an extended overview about Reduced Order Models (ROMs), with a focus on their features in terms of efficiency and accuracy. In particular, the aim is to browse the more common ROM frameworks, considering both intrusive…

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…

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…

In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two…

We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The…

In this paper, we introduce the neural empirical interpolation method (NEIM), a neural network-based alternative to the discrete empirical interpolation method for reducing the time complexity of computing the nonlinear term in a reduced…

One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domains discretizations employed. Moreover, very often complex…

This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis in the literature has been performed on fully-discrete…

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…

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…

This paper develops a direct data-driven framework for constructing reduced-order models (ROMs) of discrete-time linear dynamical systems with unknown dynamics and process disturbances. The proposed scheme enables controller synthesis on…

Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus,…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…