Enhancing Inverse Problem Solutions with Accurate Surrogate Simulators and Promising Candidates

Deep-learning inverse techniques have attracted significant attention in recent years. Among them, the neural adjoint (NA) method, which employs a neural network surrogate simulator, has demonstrated impressive performance in the design tasks of artificial electromagnetic materials (AEM). However, the impact of the surrogate simulators' accuracy on the solutions in the NA method remains uncertain. Furthermore, achieving sufficient optimization becomes challenging in this method when the surrogate simulator is large, and computational resources are limited. Additionally, the behavior under constraints has not been studied, despite its importance from the engineering perspective. In this study, we investigated the impact of surrogate simulators' accuracy on the solutions and discovered that the more accurate the surrogate simulator is, the better the solutions become. We then developed an extension of the NA method, named Neural Lagrangian (NeuLag) method, capable of efficiently optimizing a sufficient number of solution candidates. We then demonstrated that the NeuLag method can find optimal solutions even when handling sufficient candidates is difficult due to the use of a large and accurate surrogate simulator. The resimulation errors of the NeuLag method were approximately 1/50 compared to previous methods for three AEM tasks. Finally, we performed optimization under constraint using NA and NeuLag, and confirmed their potential in optimization with soft or hard constraints. We believe our method holds potential in areas that require large and accurate surrogate simulators.