Gaussian process-based surrogate framework for efficient prediction of geometrical inaccuracy in Wire Electrical Discharge Machining of thin-wall miniature components

High aspect ratio, thin-walled miniature structures are critical in applications such as microfluidics and micromechanical cooling. Wire Electrical Discharge Machining (Wire EDM) presents a commercially viable alternative to specialized micromachining setups for fabricating such features. However, as part size decreases, conventional Wire EDM faces challenges in achieving accurate profiles due to intensified thermal effects and reduced part stiffness, leading to increased geometrical errors. To address this, a reduced-order surrogate framework based on Gaussian Process Regression (GPR) is developed to predict key geometrical deviations specifically, reduced wall thickness and wall deformation as functions of process parameters. The framework integrates four GPR models trained on hybrid datasets combining experimental data and physics-based numerical results. A discrepancy model further refines numerical predictions by accounting for deviations from experimental data. The final GPR models achieve mean absolute errors of 3.39 $\mu$m and 6.08 $\mu$m for wall thickness and deformation, with $R^2$ values of 0.96 and 0.99. K-fold cross-validation and validation experiments confirm model reliability, with prediction errors around 14.3 $\mu$m and 12.1 $\mu$m. The discrepancy model reduces the deviation of numerical predictions from actual values by 55%. Process parameter optimization is performed to fabricate thin walls with targeted deformation levels, achieving reasonable accuracy within 22.3 $\mu$m. Furthermore, sensitivity analysis is conducted to quantify both individual and interactive influences of major process parameters on geometrical errors.