相关论文: Nonlinear Reduced-Order Modeling of Compressible F…

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…

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…

We propose an online learning framework for forecasting nonlinear spatio-temporal signals (fields). The method integrates (i) dimensionality reduction, here, a simple proper orthogonal decomposition (POD) projection; (ii) a generalized…

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual…

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of…

We develop an on-the-fly reduced-order model (ROM) integrated with a flow simulation, gradually replacing a corresponding full-order model (FOM) of a physics solver. Unlike offline methods requiring a separate FOM-only simulation prior to…

We investigate the applicability of machine learning based reduced order model (ML-ROM) to three-dimensional complex flows. As an example, we consider a turbulent channel flow at the friction Reynolds number of $Re_\tau=110$ in a minimum…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

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…

In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting…

Artificial intelligence-based three-dimensional(3D) fluid modeling has gained significant attention in recent years. However, the accuracy of such models is often limited by the processing of irregular flow data. In order to bolster the…

This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…

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…

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…

In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

The reconstruction and prediction of full-state flows from sparse data are of great scientific and engineering significance yet remain challenging, especially in applications where data are sparse and/or subjected to noise. To this end,…

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…

Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…

In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…

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…