ADVANCED MATERIALS & PROCESSES | NOVEMBER/DECEMBER 2025 16 7. Constraint Manager – Pass 2 • Rechecks optimized candidates against updated feasibility and printer constraints. • Applies uncertainty-weighted risk thresholds. 8. Parameter Optimizer • Balances objectives: maximize density, ensure stability, and minimize binder use/time. • Uses Pareto frontier analysis and weighted scoring for Top-K ranking. 9. Process Window (Output) • Delivers binder chemistry and saturation, roller speed and layer thickness, sintering temperature and atmosphere. • Provides confidence bands and provenance for industrial validation. EXPERIMENTAL METHODOLOGY AND VALIDATION The training dataset comprises 2847 BJAM experiments across 23 material systems with comprehensive parameter coverage. Metal systems (n = 1642) include 316L, Inconel 625, Ti6Al-4V, and 17-4 PH. Oxide ceramics (n = 743) encompass Al₂O₃, ZrO₂, and yttria-stabilized zirconia. Carbide systems (n = 462) include SiC, WC-Co, and TiB₂. Parameter distributions span: D₅₀ (8-85 µm, µ = 32.4 ± 15.2), layer thickness (30-200 µm, µ = 89.1 ± 28.7), roller speed (0.8-4.2 mm/s, µ = 1.9 ± 0.6), binder saturation (45-125%, µ = 78.3 ± 16.9), and final density (55-98%, µ = 87.2 ± 8.7). Stratified K-fold cross-validation (K=5) ensured representative sampling across material classes. Hyperparameter optimization employed Bayesian optimization with Expected Improvement acquisition functions. Feature engineering incorporated numerical variables through standard scaling and categorical variables via one-hot encoding, with interaction terms capturing material- specific scaling factors. MODEL TRAINING AND PERFORMANCE ANALYSIS The regression models were tuned using Bayesian optimization with a Tree-structured Parzen Estimator. The acquisition function was defined as α(x) = µ(x) + Κσ(x) with (Κ = 2.576), ensuring 99% confidence exploration. Search ranges covered learning rates, tree depth, subsampling ratios, and L₁/L₂ penalties. This strategy allowed the optimizer to balance exploration of new hyperparameters with exploitation of known good settings. To ensure robustness, stratified sampling preserved the ratio of metals, oxides, and carbides across folds; Dirichlet allocation introduced slight variation between folds, preventing bias from overrepresented classes; and temporal stratification respected the order in which experiments were collected, preventing data leakage from correlated builds. Across 2847 experiments, the system achieved: • Mean absolute error = 2.1 ± 0.3% density units. • Root mean square error = 3.4 ± 0.5% density units. • Prediction interval coverage = 87.3% (after temperature scaling calibration). Variance differed by material class (heteroscedastic behavior): • Metals: lowest prediction variance (σ ≈ 1.8), reflecting stable sintering pathways. Fig. 1 — Multi-agent prediction architecture showing Physics Agent, ML Regression Agent, Materials Agent, Uncertainty Agent, Constraint Manager, and Parameter Optimizer with data flow connections.
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