Enhancing Adjoint Optimization-Based Photonic Inverse Designwith Explainable Machine Learning

A fundamental challenge in the design of photonic devices, andelectromagnetic structures more generally, is the optimization of their overall architectureto achieve a desired response. To this end, topology or shape optimizers based on theadjoint variable method have been widely adopted due to their high computationalefficiency and ability to create complex freeform geometries. However, the functionalunderstanding of such freeform structures remains a black box. Moreover, unless a designspace of high-performance devices is known in advance, such gradient-based optimizerscan get trapped in local minima valleys or saddle points, which limits performanceachievable through this inverse design process. To elucidate the relationships betweendevice performance and nanoscale structuring while mitigating the effects of local minimatrapping, we present an inverse design framework that combines adjoint optimization,automated machine learning, and explainable artificial intelligence. Integrated with anumerical electromagnetic simulation method, our framework reveals structural contributions toward afigure-of-merit (FOM) ofinterest. Through an explanation-based reoptimization process, this information is then leveraged to minimize the FOM further thanthat obtained through adjoint optimization alone, thus overcoming the optimization's local minima. We demonstrate our frameworkin the context of waveguide splitter design and achieve between 39 and 74% increases in device performance relative to state-of-the-art adjoint optimization-based inverse design across a range of telecom wavelengths. Our results highlight machine learning strategiesthat can substantially extend and enhance the capabilities of a conventional, optimization-based inverse design algorithm whilerevealing deeper insights into the algorithm's designs

Automated summary

A fundamental challenge in the design of photonic devices is optimizing their overall architecture to achieve desired responses. Topology or shape optimizers based on the adjoint variable method are commonly used for their computational efficiency and ability to create complex freeform geometries. However, the functional understanding of such freeform structures remains unknown. Additionally, unless a design space of high-performance devices is known in advance, gradient-based optimizers can get stuck in local minima or saddle points, limiting the achievable performance. To address these issues, an inverse design framework combining adjoint optimization, automated machine learning, and explainable artificial intelligence is proposed. By integrating numerical electromagnetic simulation, this framework reveals structural contributions and uses explanation-based reoptimization to overcome local minima and further minimize the figure-of-merit (FOM). The framework is demonstrated in the context of waveguide splitter design and achieves significant increases in device performance compared to state-of-the-art adjoint optimization-based inverse design. These results showcase the potential of machine learning strategies to enhance conventional optimization-based inverse design algorithms while providing deeper insights into the designs.