Process Parameter Optimization for Additive Manufacturing

Define the LPBF parameter space to optimize: laser power (100–400 W), scan speed (200–1200 mm/s), hatch spacing (60–120 μm), and layer thickness (20–60 μm). These four parameters control the volumetric energy density delivered to the powder bed: E = P / (v × h × t), a key predictor of part quality.

Define two objective functions: minimize porosity (volume fraction of voids, target < 0.1%) and maximize ultimate tensile strength (UTS, target > 1000 MPa for Ti-6Al-4V). These objectives partially conflict — very high energy density eliminates porosity but can cause keyhole defects that reduce strength. Use published experimental data from literature (e.g., the NIST AM benchmark datasets) to create a realistic simulation of the objective functions, or build an analytical model based on energy density relationships.

Since you likely don't have access to an LPBF machine, create a synthetic objective function that mimics real AM physics. Model porosity as a function of energy density with a U-shaped curve (too little energy → lack-of-fusion porosity; too much → keyhole porosity). Model tensile strength as a function of porosity and microstructure (controlled by cooling rate, which depends on scan speed).

Add realistic noise to the simulator — real AM experiments have significant variability between builds. Use published regression models from AM literature (e.g., the Eagar-Tsai thermal model for melt pool dimensions) to make your simulator physically grounded. The simulator should take ~0.1 seconds per evaluation, mimicking the expensive nature of real experiments (which take hours).

Build a Gaussian process (GP) model using GPyTorch that learns the mapping from process parameters to quality outcomes. The GP provides both a mean prediction (best estimate of the objective) and an uncertainty estimate (how confident we are) — this uncertainty is what makes Bayesian optimization work.

Use a Matérn 5/2 kernel (standard for physical processes) with automatic relevance determination (ARD) — this lets the GP learn that some parameters matter more than others. Fit the GP on an initial set of 10–15 random experiments (the "seed" design). Validate the GP predictions against held-out points to verify the surrogate is accurate before using it for optimization.

Use BoTorch to implement the optimization loop. At each iteration: (1) fit the GP to all observations so far, (2) optimize the acquisition function to select the next experiment, (3) evaluate the objective at the selected parameters, (4) add the result to the dataset. Repeat for 50–100 iterations.

For single-objective optimization, use Expected Improvement (EI) as the acquisition function — it naturally balances exploration and exploitation. For multi-objective optimization (porosity AND strength simultaneously), use qNEHVI (q-Noisy Expected Hypervolume Improvement), which optimizes the Pareto frontier. BoTorch handles the acquisition function optimization via L-BFGS with random restarts.

Run the multi-objective BO campaign targeting both porosity minimization and strength maximization. After optimization, extract the Pareto frontier — the set of process parameter combinations where you cannot improve one objective without worsening the other.

Visualize the Pareto frontier in objective space (porosity vs. strength) with each point colored by a key process parameter (e.g., laser power). This reveals the fundamental trade-offs: achieving <0.05% porosity might require accepting 950 MPa instead of 1050 MPa strength. Also plot the parameter settings along the Pareto frontier — do they form physically interpretable patterns? (They should cluster around an optimal energy density band.)

Run the same optimization problem with random search and grid search (with the same total budget of function evaluations). Compare how quickly each method finds near-optimal solutions. BO should find competitive solutions in 30–50 evaluations where grid search needs 200+ to cover the 4D parameter space adequately.

Plot the optimization convergence curve: best-so-far objective value vs. number of evaluations. BO's curve should descend much faster than random search, demonstrating sample efficiency — the entire point of Bayesian optimization. Compute the hypervolume indicator for multi-objective runs to quantify how well each method approximates the true Pareto frontier.

Analyze the optimal parameters found by BO. Do they correspond to known good process windows from literature? For Ti-6Al-4V LPBF, the optimal energy density is typically 60–80 J/mm³ — does your optimizer converge to this range? If so, the BO successfully learned the physics from data alone.

Document the complete methodology in a format suitable for a journal paper or conference presentation. Include: problem formulation with physical motivation, GP model specification and validation, acquisition function choice and justification, optimization results with convergence plots, Pareto frontier analysis, and comparison against baselines. Discuss how this workflow would integrate into a real AM process development program — where each "evaluation" costs $500–2000 in machine time and materials, making sample efficiency genuinely valuable.