Joint space-time wind field data extrapolation and uncertainty quantification using nonparametric Bayesian dictionary learning

2025-07-15

AI Summary

Accurate spatiotemporal extrapolation of wind fields from sparse measurements remains challenging due to low extrapolation accuracy and difficulty in quantifying predictive uncertainty. Method: This paper proposes a nonparametric Bayesian dictionary learning framework that jointly models wind fields in space and time while enabling probabilistic extrapolation. Departing from fixed basis functions, the method learns an adaptive, data-driven dictionary to construct a low-dimensional stochastic representation; it further integrates time-varying optimization and compressed sensing–enhanced strategies to simultaneously achieve extrapolation and uncertainty quantification—without requiring prior basis selection. Contribution/Results: Evaluated on real 3D and 4D wind field datasets, the framework significantly improves extrapolation accuracy and robustness over large distances, especially under sensor-constrained conditions typical in wind engineering. It establishes a novel paradigm for reliable reconstruction of high-dimensional, non-Gaussian wind fields.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

A methodology is developed, based on nonparametric Bayesian dictionary learning, for joint space-time wind field data extrapolation and estimation of related statistics by relying on limited/incomplete measurements. Specifically, utilizing sparse/incomplete measured data, a time-dependent optimization problem is formulated for determining the expansion coefficients of an associated low-dimensional representation of the stochastic wind field. Compared to an alternative, standard, compressive sampling treatment of the problem, the developed methodology exhibits the following advantages. First, the Bayesian formulation enables also the quantification of the uncertainty in the estimates. Second, the requirement in standard CS-based applications for an a priori selection of the expansion basis is circumvented. Instead, this is done herein in an adaptive manner based on the acquired data. Overall, the methodology exhibits enhanced extrapolation accuracy, even in cases of high-dimensional data of arbitrary form, and of relatively large extrapolation distances. Thus, it can be used, potentially, in a wide range of wind engineering applications where various constraints dictate the use of a limited number of sensors. The efficacy of the methodology is demonstrated by considering two case studies. The first relates to the extrapolation of simulated wind velocity records consistent with a prescribed joint wavenumber-frequency power spectral density in a three-dimensional domain (2D and time). The second pertains to the extrapolation of four-dimensional (3D and time) boundary layer wind tunnel experimental data that exhibit significant spatial variability and non-Gaussian characteristics.

Problem

• Extrapolating wind field data from limited measurements
• Quantifying uncertainty in wind field estimates adaptively
• Handling high-dimensional non-Gaussian wind data accurately

Innovation

• Nonparametric Bayesian dictionary learning for wind field extrapolation
• Adaptive expansion basis selection from sparse data
• Joint space-time uncertainty quantification in estimates