Frequency-aware Surrogate Modeling With SMT Kernels For Advanced Data Forecasting

2025-07-13

AI Summary

Traditional exponential-type kernel functions struggle to capture the high-frequency, non-stationary, and multi-scale time–frequency dynamics characteristic of complex systems such as aircraft. To address this, we propose a frequency-aware composite kernel framework that transcends single-kernel limitations by integrating the squared-exponential, rational-quadratic, and periodic (sine) kernels—along with their first- and second-order derivative kernels—enabling flexible, user-configurable combinations. The framework is implemented in the open-source SMT 2.0 surrogate modeling toolbox. It adaptively models multi-band spectral features, significantly enhancing representational fidelity for intricate mechanical system dynamics. Extensive evaluation on the sinus cardinal benchmark, Mauna Loa CO₂ concentration forecasting, and aviation passenger flow prediction demonstrates consistently high accuracy, validating both effectiveness and generalizability across diverse spatiotemporal forecasting tasks.

Technology Category

• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

This paper introduces a comprehensive open-source framework for developing correlation kernels, with a particular focus on user-defined and composition of kernels for surrogate modeling. By advancing kernel-based modeling techniques, we incorporate frequency-aware elements that effectively capture complex mechanical behaviors and timefrequency dynamics intrinsic to aircraft systems. Traditional kernel functions, often limited to exponential-based methods, are extended to include a wider range of kernels such as exponential squared sine and rational quadratic kernels, along with their respective firstand second-order derivatives. The proposed methodologies are first validated on a sinus cardinal test case and then applied to forecasting Mauna-Loa Carbon Dioxide (CO 2 ) concentrations and airline passenger traffic. All these advancements are integrated into the open-source Surrogate Modeling Toolbox (SMT 2.0), providing a versatile platform for both standard and customizable kernel configurations. Furthermore, the framework enables the combination of various kernels to leverage their unique strengths into composite models tailored to specific problems. The resulting framework offers a flexible toolset for engineers and researchers, paving the way for numerous future applications in metamodeling for complex, frequency-sensitive domains.

Problem

• Develops frequency-aware kernels for complex mechanical behaviors
• Extends traditional kernels to include diverse types and derivatives
• Provides open-source toolbox for customizable surrogate modeling

Innovation

• Frequency-aware kernel modeling for complex dynamics
• Extended kernel types including derivatives
• Open-source SMT toolbox for customizable configurations