Predicting phosphor particle distribution in white-LED phosphor films using a NAS-optimized physics-constrained neural network

The spatial distribution of phosphor particles within phosphor films is a key factor governing the optical performance of phosphor-converted white LEDs (pc-LEDs). However, real phosphor particles typically exhibit complex morphologies such as non-sphericity and agglomeration, making it difficult for Mie-theory-based models under ideal spherical assumptions to fully reproduce the coupled scattering-absorption-re-emission processes at an engineering scale. Meanwhile, the approach of relying on extensive experimental screening to obtain target spectra is disadvantageous in terms of both cost and time. Further investigation is needed to understand the relationship between LED spectra, considering multiple physical factors, and the distribution of phosphor particles within the phosphor film. To address this challenge, we constructed a spectral dataset based on realistic phosphor particles with varied spectral responses. A double-Sigmoid function and film-layered processing were employed to capture physically informative spectral descriptors and particle-distribution descriptors, respectively. Using the key parameters of the fitted function as inputs and the particle-distribution parameters as outputs, we trained an optimally structured neural network via data augmentation and neural architecture search (NAS). During training, physics-constrained loss terms derived from a one-dimensional transport approximation were further incorporated, yielding representative feasible solutions under the specified constrained assumptions (rather than physically unique solutions). The results show that the model achieves inverse-inference performance <i>R</i>² values of 0.913-0.994 for particle-number prediction and 0.831-0.960 for particle-size prediction. Finally, a Monte Carlo-based optical simulation model was adopted as a forward-validation benchmark: both the ground-truth and the machine-learning-predicted particle-distribution features were fed into the simulator to generate spectra, which were then compared with the measured spectra. The reconstructed spectra exhibit forward spectral consistency <i>R</i>² values of 0.974-0.983 relative to measurements. In terms of efficiency, the proposed approach requires approximately 1.71 s per target for a single inference, which is substantially lower than optical simulation and conventional experimental screening, demonstrating the potential for orders-of-magnitude acceleration.