Probabilistic Inverse Design of Nanoporous Fabry–Perot Color Filters via Mixture Density Networks

Nanophotonic inverse design is inherently nonunique because different structural configurations can produce similar optical responses, which limits deterministic approaches. Here, we propose a probabilistic inverse design framework based on a mixture density network (MDN) to address this limitation. Using an anodic aluminum oxide (AAO)-based metal–insulator–metal (MIM) structural color filter as a model system, the MDN learns the conditional probability distribution of structural parameters for a target optical response and enables multiple physically valid solutions. A forward neural network (FNN) surrogate model is to validate predicted structures efficiently and removes the burden of repeated parametric electromagnetic simulations. The proposed approach achieves high color accuracy, and a large fraction of test samples reaches the perceptual threshold (ΔE 2000 ≤ 2), while the method captures multiple valid solutions within the design space. These results show that inverse design in nanophotonic systems is better formulated as a distribution learning problem rather than a deterministic mapping and provides multiple FDTD-supported candidate solutions for further evaluation under structural parameter variations. This approach offers a transferable workflow to address nonuniqueness across a wide range of nanophotonic systems, including metasurfaces, photonic crystals, and multilayer thin-film structures, provided that the MIDAS models are trained with simulation data specific to each system.