Efficient FGM optimization with a novel design space and DeepONet

This manuscript proposes an optimization framework to find the tailor-made functionally graded material (FGM) profiles for thermoelastic applications. This optimization framework consists of (1) a random profile generation scheme, (2) deep learning (DL) based surrogate models for the prediction of thermal and structural quantities, and (3) a genetic algorithm (GA). From the proposed random profile generation scheme, we strive for a generic design space that does not contain impractical designs, i.e., profiles with sharp gradations. We also show that the power law is a strict subset of the proposed design space. We use a dense neural network-based surrogate model for the prediction of maximum stress, while the deep neural operator DeepONet is used for the prediction of the thermal field. The point-wise effective prediction of the thermal field enables us to implement the constraint that the metallic content of the FGM remains within a specified limit. The integration of the profile generation scheme and DL-based surrogate models with GA provides us with an efficient optimization scheme. The efficacy of the proposed framework is demonstrated through various numerical examples.