相关论文: A new approach to proper orthogonal decomposition …

In this paper we study the approximation of a distributed optimal control problem for linear para\-bolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis…

The Dynamic Mode Decomposition (DMD)---a popular method for performing data-driven Koopman spectral analysis---has gained increased adoption as a technique for extracting dynamically meaningful spatio-temporal descriptions of fluid flows…

In this paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. In particular, we show in practice that there exists a…

In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…

We consider model order reduction based on proper orthogonal decomposition (POD) for unsteady incompressible Navier-Stokes problems, assuming that the snapshots are given by spatially adapted finite element solutions. We propose two…

A method is proposed to obtain full-domain spatial modes based on Proper Orthogonal Decomposition (POD) of Particle Image Velocimetry (PIV) measurements performed at different (overlapping) spatial locations. This situation occurs when…

The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…

Experimental spatio-temporal flow data often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised or missing regions, a data completion method based on spectral proper orthogonal decomposition…

Dynamic mode decomposition (DMD) gives a practical means of extracting dynamic information from data, in the form of spatial modes and their associated frequencies and growth/decay rates. DMD can be considered as a numerical approximation…

The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g.,…

We present a conditional space-time proper orthogonal decomposition (POD) formulation that is tailored to the eduction of the average, rare or intermittent event from an ensemble of realizations of a fluid process. By construction, the…

A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…

Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…

Out-of-distribution (OOD) detection is a crucial task for ensuring the reliability and safety of deep learning. Currently, discriminator models outperform other methods in this regard. However, the feature extraction process used by…

In this paper, we propose a multiscale method for heterogeneous Stokes problems. The method is based on the Localized Orthogonal Decomposition (LOD) methodology and has approximation properties independent of the regularity of the…

Traditional low-rank approximation is a powerful tool to compress the huge data matrices that arise in simulations of partial differential equations (PDE), but suffers from high computational cost and requires several passes over the PDE…

Defect concentrations in semiconductors are strongly influenced by thermal history during growth and cooldown, yet most defect calculations assume either instantaneous quenching from high temperature or that full-equilibrium is maintained -…

Direct Statistical Simulation (DSS) solves the equations of motion for the statistics of turbulent flows in place of the traditional route of accumulating statistics by Direct Numerical Simulation (DNS). That low-order statistics usually…

Contemporary deep learning, characterized by the training of cumbersome neural networks on massive datasets, confronts substantial computational hurdles. To alleviate heavy data storage burdens on limited hardware resources, numerous…

In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper…