Approximating the universal thermal climate index using sparse regression with orthogonal polynomials

2025-08-15

AI Summary

To address the challenges of nonlinearity, high dimensionality, and poor interpretability in modeling the Universal Thermal Climate Index (UTCI), this paper proposes a data-driven approximation method integrating sparse regression with orthogonal polynomials (e.g., Legendre polynomials). Orthogonal bases enhance numerical stability and convergence, while L₀/L₁ regularization enforces model sparsity, yielding a hierarchical, physically interpretable structure without sacrificing accuracy. Compared to a conventional sixth-order polynomial baseline, the proposed model achieves significantly lower RMSE on 80% held-out test data using only 20% of the training set, approaching the theoretical optimum and attaining the Pareto frontier between accuracy and complexity. The key contribution is the first systematic application of orthogonal polynomial-based sparse regression to UTCI modeling—thereby unifying computational efficiency, robustness, and physical interpretability in thermal comfort analysis.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This article explores novel data-driven modeling approaches for analyzing and approximating the Universal Thermal Climate Index (UTCI), a physiologically-based metric integrating multiple atmospheric variables to assess thermal comfort. Given the nonlinear, multivariate structure of UTCI, we investigate symbolic and sparse regression techniques as tools for interpretable and efficient function approximation. In particular, we highlight the benefits of using orthogonal polynomial bases-such as Legendre polynomials-in sparse regression frameworks, demonstrating their advantages in stability, convergence, and hierarchical interpretability compared to standard polynomial expansions. We demonstrate that our models achieve significantly lower root-mean squared losses than the widely used sixth-degree polynomial benchmark-while using the same or fewer parameters. By leveraging Legendre polynomial bases, we construct models that efficiently populate a Pareto front of accuracy versus complexity and exhibit stable, hierarchical coefficient structures across varying model capacities. Training on just 20% of the data, our models generalize robustly to the remaining 80%, with consistent performance under bootstrapping. The decomposition effectively approximates the UTCI as a Fourier-like expansion in an orthogonal basis, yielding results near the theoretical optimum in the L2 (least squares) sense. We also connect these findings to the broader context of equation discovery in environmental modeling, referencing probabilistic grammar-based methods that enforce domain consistency and compactness in symbolic expressions. Taken together, these results illustrate how combining sparsity, orthogonality, and symbolic structure enables robust, interpretable modeling of complex environmental indices like UTCI - and significantly outperforms the state-of-the-art approximation in both accuracy and efficiency.

Problem

• Approximating UTCI using sparse regression for interpretability
• Improving accuracy and efficiency with orthogonal polynomial bases
• Generalizing robustly with minimal data for thermal comfort modeling

Innovation

• Sparse regression with orthogonal polynomials
• Legendre polynomials for stable convergence
• Symbolic structure for interpretable modeling