Proper Orthogonal Decomposition (POD
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Related Articles from SNS
Multifidelity Proper Orthogonal Decomposition
Announce Type: replace Abstract: This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique for extracting a low-dimensional basis from training data to achieve subsequent dimension reduction or reduced-order modeling. In scientific and engineering applications, the training data are typically numerical snapshot...
A-priori error estimation for space-time Galerkin POD for linear evolution problems
arXiv:2604.22057v2 Announce Type: replace Abstract: In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only the space dimension but simultaneously the time dimension as well. The proposed a-priori error estimate is developed for a linear parabolic partial differential equation and estimates the error between the...
Multiscale POD of Transformer Attention Fields: Scale-Selective Analysis via Morlet Scalogram
Announce Type: new Abstract: We introduce scale-selective Proper Orthogonal Decomposition (POD) for transformer attention fields, inspired by the use of POD for extracting energetically dominant modes from turbulent flow ensembles. The Morlet continuous wavelet transform identifies dominant temporal scales in the attention lag structure across a document ensemble; POD then extracts the energetically dominant modes at each scale from the ensemble of attention fields. The resulting modes...
Multiscale POD of Transformer Attention Fields: Scale-Selective Analysis via Morlet Scalogram
arXiv:2606.06573v1 Announce Type: cross Abstract: We introduce scale-selective Proper Orthogonal Decomposition (POD) for transformer attention fields, inspired by the use of POD for extracting energetically dominant modes from turbulent flow ensembles. The Morlet continuous wavelet transform identifies dominant temporal scales in the attention lag structure across a document ensemble; POD then extracts the energetically dominant modes at each scale from the ensemble of attention fields. The...
Reduced order modeling for spatio-temporal pattern approximation in diffusive Lotka-Volterra equations
arXiv:2606.04030v1 Announce Type: new Abstract: This paper presents an efficient reduced order modeling (ROM) framework for simulating spatio-temporal pattern formation in three-species diffusive Lotka-Volterra systems. To alleviate the high computational cost associated with long-time simulations of the high-dimensional full order model (FOM), we apply proper orthogonal decomposition (POD) to project the solution onto a low-dimensional subspace. Further efficiency is achieved through...
Identifying sensitivity-dominant parameters via active subspaces in reduced-order modeling of fluid dynamics
new Abstract: Reduced-order models (ROMs) are widely employed to describe complex system dynamics when simulations with full-order models (FOMs) are computationally prohibitive. This study presents POD-AS-PRS, a novel model-reduction framework based on the active subspaces (AS) technique, which performs dimensionality reduction in both the state and parameter spaces, enabling efficient and high-fidelity approximations of quantities of interest (QoI). The approach employs proper orthogonal...
Data-efficient semi-supervised learning for flow estimation using unlabelled probe data
arXiv:2605.28245v2 Announce Type: replace Abstract: Estimating time-resolved velocity and pressure fields from Particle Image Velocimetry (PIV) remains challenging due to its limited temporal resolution in many applications. Data-driven approaches that combine snapshot PIV with high-frequency probe data have shown great promise in reconstructing the flow dynamics for advection-dominated flows; however, they typically exploit only the probe measurements directly synchronized with the PIV...
Constrained Extreme Gradient Boosting for Adapting Reduced-Order Models
arXiv:2605.04130v2 Announce Type: replace Abstract: High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization, and real-time control. Projection-based reduced-order models (ROMs) alleviate this cost by projecting the governing dynamics onto low-dimensional subspaces. However, their performance can deteriorate...
Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraints
arXiv:2606.02038v1 Announce Type: new Abstract: Reconstructing spatially continuous daily temperature fields from sparse observations is important for urban climate monitoring and heat-risk analysis, but practical deployments are limited by sensor budgets and spacing constraints. This study proposes an uncertainty-aware graph neural network (GNN) framework for reconstructing daily maximum temperature fields from sparse sensors while supporting distance-constrained sensor placement and...
Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraints
arXiv:2606.02038v1 Announce Type: cross Abstract: Reconstructing spatially continuous daily temperature fields from sparse observations is important for urban climate monitoring and heat-risk analysis, but practical deployments are limited by sensor budgets and spacing constraints. This study proposes an uncertainty-aware graph neural network (GNN) framework for reconstructing daily maximum temperature fields from sparse sensors while supporting distance-constrained sensor placement and...