“…The DL algorithms are employed in various fields, such as nature language processing [ 24 , 25 , 26 ], image recognition [ 27 ], finance [ 28 , 29 , 30 ], and medicine [ 31 , 32 , 33 ]. Especially for the aspect of nanophotonics, the DL approach has proved to be one of the most advanced tools to study many nonintuitive and nonlinear physics issues [ 34 , 35 , 36 , 37 ], including the problem of the inverse design of photonics devices [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]. Peurifpy et al [ 46 ] utilized 50,000 samples to train neural networks to design a multi-layer dielectric spherical nanoparticle in 2018, which was regarded as the landmark in this field.…”