Nonlinear dynamics and mathematical programming with neuromorphic integrated silicon photonic circuits in Verilog-A

Abstract

The rise in machine learning applications and the availability of larger datasets has motivated the investigation of new application-specific integrated circuits (ASICs), that can solely be dedicated to performing complex calculations at a much higher speed than conventional computers. Recent advances in integrated photonic neuromorphic architectures promise to deliver computations with higher speed than electronics by exploiting the parallel nature of light through wavelength-division multiplexing (WDM) and the passive nature of optical waveguides. In particular, photonic implementation of continuous-time recurrent networks (CTRNNs) have a potential to solve problems related to nonlinear optimization, model predictive control, and scientific computing. In recent developments, the dynamical behaviour of the photonic recurrent neural networks has been demonstrated using a combination of on-chip and off-chip components. One of the major challenges in an entirely on-chip implementation of neuromorphic photonic CTRNNs is the lack of sufficient tools to simulate fully integrated large-scale photonic integrated circuits. It is very crucial to perform simulations on a single platform to capture the behaviour of the circuit in the presence of both optical and electrical components. In this work, we have adopted a Verilog-A based approach to model photonic neuromorphic circuits. We developed Verilog-A models for the primary photonic devices (lasers, phase shifters, couplers, photodetector, and waveguide), which are the building blocks of photonic neural networks. The physical parameters of the devices are extracted from the experimental data and implemented in the Verilog-A models. The device simulations are also validated by comparing the measured and simulation results. Subsequently, we showed the dynamical isomorphism between the fully integrated silicon photonic recurrent neural circuit and the CTRNN model by simulating dynamical bifurcations and winner-takes-all algorithm. We have also demonstrated the application of the photonic CTRNNs by simulating a 4-node recurrent neural network to solve a quadratic programming (QP) problem, which has enormous applications in optimization, and model predictive control. The work done in this thesis would significantly increase the capability of optical-electrical co-simulation that would improve the efficiency of optimizing the devices and provide an accurate simulation of the circuit performance before fabrication.