An Operator-Theoretic Framework to Simulate Neuromorphic Circuits

Splitting algorithms are well-established in convex optimization and are designed to solve large-scale problems. Using such algorithms to simulate the behavior of nonlinear circuit networks provides scalable methods for the simulation and design of neuromorphic systems. For circuits made of linear capacitors and inductors with nonlinear resistive elements, we propose a splitting that breaks the network into its LTI lossless component and its static resistive component. This splitting has both physical and algorithmic advantages and allows for separate calculations in the time domain and in the frequency domain. To demonstrate the scalability of this approach, a network made from one hundred neurons modeled by the well-known FitzHugh-Nagumo circuit with all-to-all diffusive coupling is simulated.