ADVANCED MATERIALS & PROCESSES | NOVEMBER/DECEMBER 2025 1 7 • Oxides: σ ≈ 2.6, due to grain growth and pore coalescence. • Carbides: σ ≈ 2.9, linked to reaction-limited kinetics and higher sintering temperatures. SHAP (SHapley Additive exPlanations) feature importance analysis reveals hierarchical parameter dependencies (as shown in Fig. 2). Binder saturation dominates with ϕi = 0.37 relative importance, reflecting direct control over capillary forces and interparticle bonding. Roller speed contributes ϕ i = 0.25, primarily through oxidation kinetics in metal systems and particle rearrangement dynamics. Layer/D₅₀ ratio importance (ϕi = 0.24) validates physics informed scaling relationships, while material type (ϕi = 0.14) exhibits lower direct importance due to effect mediation through interaction terms. QUANTITATIVE CASE STUDY VALIDATION In the Al₂O₃ (D₅₀ = 10 µm) test, physics-informed constraints predicted water-based PVA binder (contact angle θ = 65°, η = 2.3 mPa·s), saturation S = 75-85% based on measured porosity ϕ = 0.38. Washburn penetration depth of L = 38 µm validated capillary-driven infiltration within 40 µm layer thickness. Experimental validation across n = 12 builds yielded ⍴ = 91.2 ± 1.4% theoretical density, with confidence interval [89.8, 92.6%] capturing 91.7% of observations. For 316L stainless steel (D₅₀ = 25 µm), solvent-based phenolic resin (θ = 45°, η = 1.8 mPa·s) with reduced saturation S = 72-80% to minimize part swelling. Diffusion-controlled sintering at 1250°C (Q = 280 kJ/mol) achieved ⍴ = 96.8 ± 0.9% across n = 8 validation builds. Predictive accuracy within ±1.2% demonstrates robust physics machine learning integration. For silicon carbide (D₅₀ = 15 µm), aqueous binder with polyvinyl butyral additive (θ = 55°, η = 2.1 mPa·s), S = 7885%. Refractory sintering requirements (T > 2150°C, Q = 650 kJ/mol) incorporated through Arrhenius-constrained temperature bounds. Experimental density ⍴ = 91.4 ± 2.1% (n = 6 builds) validated high-temperature ceramic processing predictions. Predicted versus experimental correlation analysis (as shown in Fig. 3) demonstrates R² = 0.943 with residual heteroscedasticity χ² = 2.14 (⍴ > 0.05), confirming model validity across material classes. Durbin-Watson statistic d = 1.96 indicates absence of autocorrelation in prediction residuals. Predicted versus experimental correlation demonstrates agreement within ±2% across all material systems, validating the framework’s cross-material generalizability. The validation analysis shows excellent correlation for all three material classes, with prediction errors well within acceptable engineering tolerances. Feature importance analysis reveals material-dependent parameter sensitivity: Ceramics show higher binder saturation sensitivity (42% importance) due to lower intrinsic green strength, while metals exhibit greater speed sensitivity (28% importance) related to oxidation kinetics during spreading. QUANTILE-BASED UNCERTAINTY ANALYSIS The regression framework applies asymmetric loss functions to capture lower, median, and upper bounds of achievable density: ⍴τ(u) = u(τ−I(u<0)), τ∈{0.1,0.5,0.9} where u = y−y’ and I( ˙ ) is the indicator function. Each model is optimized with gradient boosting, minimizing Ltotal =∑⍴τ(y−y’) + Ω(f) where Ω(f) is an L2 regularization penalty on tree complexity to prevent overfitting. The three quantile models exhibit complementary behavior: • Q₁₀ : higher bias, lower variance for conservative bounds suitable for high-risk applications. • Q₅₀ : balanced estimates, optimized for central tendency. • Q₉₀ : lower bias, higher variance for optimistic bounds capturing upper performance. Binder saturation was analyzed across the optimal process window (S = 70-90%) as shown in Fig. 4. Prediction intervals (Q₁₀–Q₉₀) narrowed significantly within this range: • At S = 0.8, uncertainty reduced to σ ≈ 1.8%. • At the lower boundary S = 0.6, uncertainty expanded to σ ≈ 4.2%. This heteroscedastic pattern indicates that data variability decreases when saturation is well constrained by physics, while model uncertainty grows when extrapolating beyond training data. To provide rigorous uncertainty guarantees, conformal prediction was applied. For a new observation yt+1 Fig. 2 — Feature importance analysis for density prediction derived from SHAP parameter importance ranking. Fig. 3 — Predicted vs. experimental density validation scatter plot showing the material data points across various material systems.
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