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

TL;DR

This paper presents an open-source framework for frequency-aware surrogate modeling using advanced SMT kernels, enabling better capture of complex dynamics in data forecasting tasks like CO2 levels and airline traffic.

Contribution

It introduces a comprehensive, customizable kernel-based surrogate modeling framework with frequency-aware elements, extending traditional kernels and integrating them into SMT 2.0.

Findings

Validated on sinus cardinal test case

Successfully applied to CO2 concentration forecasting

Enhanced modeling of frequency-dependent behaviors

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.