Deep Ensembles for Modeling Uncertain Phase Constraints In Compositionally Graded Alloy Design

Abstract Compositionally graded alloys (CGAs) are a specific class of multi-material functionally graded materials (FGMs) that use spatial variations in alloy composition to meet competing performance requirements in at different locations regions of a single part. Directed energy deposition (DED) metal additive technology has enabled the manufacturing of CGAs, but design these alloys remains a challenge. One important challenge is to avoid alloy compositions that result in the formation of deleterious phases during manufacturing. While designers can use CALculation of PHAse Diagram (CALPHAD) models predict the presence of deleterious phases, these calculations tend to be too costly to incorporate directly in a computational design framework. In this work, we apply deep ensembles, or ensembles of deep artificial neural networks (ANNs), to learn a surrogate model of deleterious phase boundaries based on CALPHAD simulations. The learned model is used as a constraint by a path planning algorithm to identify gradient pathway through metal composition space that can be successfully manufactured. We demonstrate the deep ensemble approach in the Fe-Ni-Cr-Ti quaternary system and benchmark it against individual ANNs and a K-nearest neighbors (KNN) approach reported previously. Additionally, we investigate the use of the predicted class probability threshold as a means for understanding surrogate model uncertainty and reasoning about the design space. Lastly, we illustrate how varying the thresholds on constraint probability results in a trade off between manufacturing risk and identifying solutions through narrow passageways.