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Deep-learning inverse techniques have attracted significant attention inrecent years. Among them, the neural adjoint (NA) method, which employs aneural network surrogate simulator, has demonstrated impressive performance inthe design tasks of artificial electromagnetic materials (AEM). However, theimpact of the surrogate simulators' accuracy on the solutions in the NA methodremains uncertain. Furthermore, achieving sufficient optimization becomeschallenging in this method when the surrogate simulator is large, andcomputational resources are limited. Additionally, the behavior underconstraints has not been studied, despite its importance from the engineeringperspective. In this study, we investigated the impact of surrogate simulators'accuracy on the solutions and discovered that the more accurate the surrogatesimulator is, the better the solutions become. We then developed an extensionof the NA method, named Neural Lagrangian (NeuLag) method, capable ofefficiently optimizing a sufficient number of solution candidates. We thendemonstrated that the NeuLag method can find optimal solutions even whenhandling sufficient candidates is difficult due to the use of a large andaccurate surrogate simulator. The resimulation errors of the NeuLag method wereapproximately 1/50 compared to previous methods for three AEM tasks. Finally,we performed optimization under constraint using NA and NeuLag, and confirmedtheir potential in optimization with soft or hard constraints. We believe ourmethod holds potential in areas that require large and accurate surrogatesimulators.

Enhancing Inverse Problem Solutions with Accurate Surrogate Simulators and Promising Candidates