Fast simulation method speeds up nonlinear analog circuit training
Fast simulation of nonlinear deep resistive networks for energy-based computation
Emerging Technologies
Summary
Simulating nonlinear electronic circuits that perform computation can be very slow, especially when realistic components like diodes are involved. The authors developed a faster way to predict the behavior of these circuits by updating voltages at each node using mathematical techniques tailored to common nonlinearities. Their method closely matches standard simulation results but runs hundreds to thousands of times faster. They also showed this approach can efficiently train large analog networks to recognize handwritten digits, making the design of complex energy-based electronic systems more practical.
nonlinear circuitsresistive networkscoordinate descentKirchhoff's lawsShockley diodecircuit simulationenergy-based computationroot-finding methodsLambert W functionanalog neural networks
Authors
Filip Osana, Julie Grollier, Damien Querlioz
Abstract
Deep resistive networks are electronic energy-based systems in which computation is performed by the steady-state voltages of nonlinear circuits. Nonlinear devices enable expressive input-output transformations, but make the circuit equilibria costly to compute during simulation and training. Recent coordinate-descent solvers have achieved large speedups over SPICE-class circuit simulators, but only for nonlinearities modeled as ideal-diode models. This mathematical simplification is not sufficient for practical analog circuits. Here we extend coordinate-descent simulation to realistic monotone nonlinearities, including Shockley diodes, antiparallel diode pairs, and piecewise-linear current-voltage characteristics. With neighboring voltages fixed, each node update remains a scalar Kirchhoff-law solve. Single-exponential characteristics admit closed-form Lambert-(W) updates, while more general monotone characteristics can be handled with scalar root-finding methods. Across networks with one to three hidden layers and hidden widths from 64 to 1024, the solver reproduces matched SPICE steady-state voltages with relative $L_1$ errors below $1.1\times10^{-4}$ for 90% of validation samples, while achieving speedups up to $(1.7\times10^3)$. We further train a $1568\times100\times20$ double-Shockley network on MNIST, reaching about 3.0% test error and reducing the per-epoch training time by roughly $4.4\times10^2$. Together, these results establish a practical route to the circuit-level design and training of large-scale analog energy-based systems incorporating realistic nonlinear devices.