Interpretable inverse design of optical multilayer thin films based on extended neural adjoint and regression activation mapping

We propose an extended neural adjoint (ENA) framework, which meets six key criteria for artificial intelligence-assisted inverse design of optical multilayer thin films (OMTs): accuracy, efficiency, diversity, scalability, flexibility, and interpretability. To enhance the scalability of the existing neural adjoint method, we present a novel forward neural network architecture for OMTs and introduce a material loss function into the existing neural adjoint loss function, facilitating the exploration of material configurations of OMTs. Furthermore, we present the detailed formulation of the regression activation mapping for the presented forward neural network architecture (F-RAM), a feature visualization method aimed at improving interpretability. We validated the efficacy of the material loss by conducting an ablation study, where each component of the loss function is systematically removed and evaluated. The results indicated that the inclusion of the material loss significantly improves accuracy and diversity. To substantiate the performance of the ENA-based inverse design, we compared it against the residual network-based global optimization network (Res-GLOnet). The ENA yielded the OMT solutions of an inverse design with higher accuracy and better diversity compared to the Res-GLOnet. To demonstrate the interpretability, we applied F-RAM to diverse OMT structures with similar optical properties, obtained by the proposed ENA method. We showed that distributions of feature importance for various OMT structures exhibiting analogous optical properties are consistent, despite variations in material configurations, layer number, and thicknesses. Furthermore, we demonstrate the flexibility of the ENA method by restricting the initial layer of OMTs to SiO2 and 100 nm.