Two-stage surrogate modeling for data-driven design optimization with application to composite microstructure generation

Design optimization or inverse problems, which involve determining input parameters to achieve specific desired outputs, are essential in many engineering applications. Conventional artificial intelligence methods for solving inverse problems rely on single-stage surrogate modeling. However, these methods can be limited in their ability to fully represent the complex relationship between inputs and outputs, hindering a comprehensive exploration of potential solutions and overlooking valid alternatives. To address this challenge, this paper presents a novel two-stage framework that combines two distinct machine learning models: a "learner"and an "evaluator". The learner identifies a subset of candidate inputs whose predicted outputs closely match the target. The evaluator then refines this selection by further narrowing the input space, resulting in more precise predictions. A key innovation is the incorporation of conformal inference, a statistical technique that quantifies prediction uncertainty in a distribution-free setting and is applicable to any machine learning model. The framework's effectiveness is validated through extensive benchmark testing using a simulated data set and an engineering case study on artificial microstructure generation of fiber-reinforced composites. The results demonstrate that this two-stage approach significantly outperforms traditional single-stage methods, consistently delivering more accurate and reliable solutions. For instance, the framework consistently identifies input configurations that closely align with two desired descriptors across varying fiber counts, while single surrogate models yield solutions far from the targets without any precautions. This paper is concluded by discussing potential future enhancements, including the integration of deep learning models and strategies for addressing distribution shifts within the framework.