Optical computing for neural ordinary differential equations

Increasing the layer number can improve the model performance of on-chip optical neural networks (ONNs). However, this results in larger integrated photonic chip areas due to the successive cascading of network hidden layers. We introduce a novel architecture for optical computing based on neural ordinary differential equations (ODEs) that employing optical ODE solvers to parameterize the continuous dynamics of hidden layers. The architecture comprises ONNs followed by a photonic integrator and an optical feedback loop, which can be configured to represent residual neural networks (ResNets) and implement the function of recurrent neural networks with effectively reduced chip area occupancy. For the interference-based optoelectronic nonlinear hidden layer, we demonstrate that the single hidden layer architecture can achieve approximately the same accuracy as the two-layer optical ResNets in image classification tasks. Furthermore, the architecture improves the model classification accuracy for the diffraction-based all-optical linear hidden layer. We also utilize the time-dependent dynamics property of architecture for trajectory prediction with high accuracy.