Optimization and inverse design of optical activation functions based on neural networks

The development of all-optical and electro-optical neural networks represents a rapidly growing field of research, with nonlinear activation functions serving as essential components of these systems. In this study, we employ an artificial neural network model to optimize the performance parameters of two systems based on Mach-Zehnder interferometers and micro-ring resonators. The results demonstrate that the optimized devices can accurately approximate several of the 14 activation functions (with a minimum root mean square error (RMSE) value of-33.1 dB), including Clipped ReLU, Sine, and Exponential. The optimized functions are also applied to an image recognition task using the Modified National Institute of Standards and Technology (MNIST) database, achieving maximum training and validation accuracies of 99.9% and 99.3% in simulation, respectively. Additionally, we introduce an inverse model to design the structural parameters of the coupling regions. Our approach significantly reduces the design time of the MZI-MRR activation function structure and theoretically demonstrates its feasibility and flexibility, providing a valuable example for the broader application of inverse design and optimization methods in optical neural network chips.