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Optimizing shapes and topology of physical devices is crucial for bothscientific and technological advancements, given its wide-ranging implicationsacross numerous industries and research areas. Innovations in shape andtopology optimization have been seen across a wide range of fields, notablystructural mechanics, fluid mechanics, and photonics. Gradient-based inversedesign techniques have been particularly successful for photonic and opticalproblems, resulting in integrated, miniaturized hardware that has set newstandards in device performance. To calculate the gradients, there aretypically two approaches: implementing specialized solvers using automaticdifferentiation or deriving analytical solutions for gradient calculation andadjoint sources by hand. In this work, we propose a middle ground and present ahybrid approach that leverages and enables the benefits of automaticdifferentiation and machine learning frameworks for handling gradientderivation while using existing, proven solvers for numerical solutions.Utilizing the adjoint method, we turn existing numerical solvers differentiableand seamlessly integrate them into an automatic differentiation framework.Further, this enables users to integrate the optimization environment withmachine learning applications which could lead to better photonic designworkflows. We illustrate the approach through two distinct examples: optimizingthe Purcell factor of a magnetic dipole in the vicinity of an opticalnanocavity and enhancing the light extraction efficiency of a {\textmu}LED.

Merging automatic differentiation and the adjoint method for photonic inverse design