Surrogate Models Trained with Small Data Sets for a Thermoelectric Energy Harvester

Jan Lohbreier1, Eugen Vambolt1
1Technische Hochschule Nürnberg Georg Simon Ohm
Published in 2026

Empirical investigations allow for the characterization of physical systems under controlled conditions using systematic measurement protocols. However, experimental methods are often limited by high time and financial costs, safety risks, or the practical impossibility of reproducing certain phenomena. Computer simulations offer a complementary research paradigm by numerically solving mathematical models, such as partial differential equations, to represent system dynamics. While this approach improves economic efficiency and facilitates parameter studies, high-fidelity simulations can still require significant computation time, ranging from minutes to days. To address computational costs, surrogate modeling provides a useful alternative. These data-driven metamodels, trained via machine learning, emulate underlying physics without explicitly solving equations. They offer exceptional efficiency, delivering predictions with millisecond latencies. This speed is advantageous for optimization, uncertainty propagation, and sensitivity analysis. However, surrogate models typically have reduced accuracy compared to high-precision simulations and still rely on expensive simulation data for training, creating a bottleneck in data acquisition. Consequently, current research focuses on architectures that perform well even with limited data. This study investigates the performance and predictive fidelity of three surrogate modeling techniques — Polynomial Chaos Expansion (PCE), Deep Neural Network (DNN), and Gaussian Process Regression (GPR)—for the numerical characterization of Thermoelectric Generator (TEG) systems. TEGs serve as autonomous energy sources in Internet of Things (IoT) applications, particularly for powering wireless sensor nodes. For the design and optimization of application-specific TEG prototypes, comprehensive sensitivity analyses are required, necessitating the use of computationally efficient and numerically robust surrogate models. The present work conducts a quantitative assessment of the surrogate models’ predictive accuracy by systematically comparing their outputs against both experimental data and high-fidelity simulation results. All three modeling approaches are evaluated under identical input parameter conditions to ensure a consistent comparison of the resulting Quantities of Interest (QoI)s.

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