Data-driven process maps for functionally graded foams in foam additive manufacturing: Accuracy and interpretability across six models

Foam Additive Manufacturing (FAM) couples gas-assisted foaming with material extrusion to produce lightweight PLA components, yet the combined influence of solubilization and extrusion variables remains poorly quantified. We analyze an experimental PLA–CO2 FAM dataset and model strand density ρ as a function of six controllable parameters (Pa,ta,td,Te,Se,Dn). Six regressors were compared under a common held-out test partition and a standardized map-generation protocol: polynomial regression, PCA + polynomial regression, SVR-RBF, Random Forest, RF-distilled polynomial surrogate, and Bayesian-regularized MLP. On the common test set, the MLP and Random Forest achieved comparable best performance, with the MLP marginally attaining the lowest errors (MAE=0.1058gcm−3,RMSE=0.1421gcm−3,R2=0.7895), closely followed by Random Forest (MAE=0.1063gcm−3,RMSE=0.1435gcm−3,R2=0.7853). The RF-distilled polynomial surrogate provides a closed-form differentiable approximation useful for exploratory sensitivity inspection, although it does not improve predictive accuracy over the direct polynomial baseline. The resulting maps quantify interactions between Te and Se at fixed (Pa,ta,td), revealing empirical trends that are qualitatively consistent with expected foaming behavior. Independent external-validation experiments further support the use of these maps as a basis for future uncertainty-aware process planning in FAM.