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

Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…

Suitable reduced order models (ROMs) are computationally efficient tools in characterizing key dynamical and statistical features of nature. In this paper, a systematic multiscale stochastic ROM framework is developed for complex systems…

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…

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

Neural operators as novel neural architectures for fast approximating solution operators of partial differential equations (PDEs), have shown considerable promise for future scientific computing. However, the mainstream of training neural…

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…

In this paper, we combine convolutional neural networks (CNNs) with reduced order modeling (ROM) for efficient simulations of multiscale problems. These problems are modeled by partial differential equations with high-dimensional random…

The Discrete Ordinates Method (DOM) is widely used for velocity discretization in radiative transport simulations. However, DOM tends to exhibit the ray effect when the velocity discretization is not sufficiently refined, a limitation that…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…

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…

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…

The domain decomposition (DD) nonlinear-manifold reduced-order model (NM-ROM) represents a computationally efficient method for integrating underlying physics principles into a neural network-based, data-driven approach. Compared to linear…

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…

Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within…

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…

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…