Machine learning-based surrogate models trained with limited datasets for a thermoelectric energy harvester

Thermoelectric energy harvesters (TEH) serve as autonomous energy sources in Internet of Things applications, particularly for powering wireless sensor nodes. However, they often require complex, computationally expensive multi-physical finite element method (FEM) simulations for precise optimization. Machine learning-based surrogate models offer a computationally efficient alternative. This study presents a comprehensive comparative analysis of three prominent surrogate modeling techniques: Polynomial Chaos Expansion (PCE), Gaussian Process Regression (GPR), and Deep Neural Networks (DNN). These models are trained using high-fidelity datasets derived from multi-physical FEM simulations, with a specific focus on limited data regimes to emulate realistic computational constraints. The predictive performance and generalization capabilities of PCE, GPR, and DNN are rigorously evaluated against unseen reference data across varying training set sizes. This approach allows for a quantified assessment of how data sparsity impacts model fidelity. Furthermore, the models’ capacity to forecast the influence of individual parameters is directly validated through comparison with empirical data obtained from a simplified experimental setup. The findings reveal distinct operational regimes for each methodology. While GPR demonstrates superior robustness and predictive accuracy in single-parameter optimization, PCE intrinsically offers excellent interpretability and efficiency for smooth parametric dependencies. Conversely, DNNs exhibit strong scalability as dataset sizes increase and deals well with the high-dimensional parameter space. Notably, while a single high-fidelity FEM simulation requires approximately 30 min per parameter set, the trained surrogate models deliver predictions virtually in real-time.