Data-driven stochastic optimization on manifolds for additive manufacturing

Laser powder-bed fusion is an increasingly attractive modality for additive manufacturing. Simulating the precise behavior of the process is infeasible, leading researchers to seek proxy solutions in machine learning. We demonstrate a novel adaptation of a technique called diffusion maps to infer the dependence structure between build parameters and material properties of interest on an approximated Riemannian manifold, when attaining a sufficient number of samples is cost prohibitive. We perform stochastic optimization to learn the efficient frontier of multi-objective combinations as well as to locate the set of parameters (hatch width, laser speed, and power) that putatively minimize the chance of failure, herein defined as lower bounds on the material properties (ultimate strength, yield strength, and elongation). Out-of-sample validation is performed and the results confirm our model's efficacy in optimizing coupons, and perhaps complex geometries in the future.