Thin film growth by pulsed laser deposition involves multiple process parameters — substrate temperature, oxygen pressure, laser fluence, repetition rate — that simultaneously affect film quality. Optimizing these parameters is typically treated as a single high-dimensional search: find the point in parameter space that maximizes some figure of merit. The implicit assumption is that all properties respond to all parameters together.
They don't (arXiv:2603.21814). In β-Ga₂O₃ epitaxy on sapphire, interpretable machine learning (quadratic polynomial ridge regression with SHAP analysis) reveals that crystalline quality and surface morphology are controlled by different dominant parameters. Temperature primarily governs bulk crystallinity — the X-ray rocking curve width that measures long-range order. Oxygen pressure primarily governs surface kinetics — the roughness and morphology that reflect how atoms arrange on the growing surface.
The optimization is effectively two independent problems masquerading as one. Temperature handles the bulk; pressure handles the surface. The coupling between them is secondary.
This decoupling enabled a remarkably efficient optimization: three experimental rounds reduced the rocking curve width by 70%, from over 3° to 0.92° — the best reported value for this material system on sapphire. The efficiency came not from clever algorithms but from recognizing the low-dimensional structure in what appeared to be a high-dimensional landscape.
The structural insight: when two quality metrics respond to different control parameters, optimizing them jointly is wasteful. The search space is the Cartesian product of the individual spaces, but the optimization factorizes into independent subproblems. The curse of dimensionality is real only if the dimensions are coupled. Finding that they aren't collapses the exponential search into a linear one. The machine learning model's value was not in finding the optimum but in revealing that the problem was simpler than it appeared.