  Analog electrical networks have long been investigated as energy-efficient
computing platforms for machine learning, leveraging analog physics during
inference. More recently, resistor networks have sparked particular interest
due to their ability to learn using local rules (such as equilibrium
propagation), enabling potentially important energy efficiency gains for
training as well. Despite their potential advantage, the simulations of these
resistor networks has been a significant bottleneck to assess their
scalability, with current methods either being limited to linear networks or
relying on realistic, yet slow circuit simulators like SPICE. Assuming ideal
circuit elements, we introduce a novel approach for the simulation of nonlinear
resistive networks, which we frame as a quadratic programming problem with
linear inequality constraints, and which we solve using a fast, exact
coordinate descent algorithm. Our simulation methodology significantly
outperforms existing SPICE-based simulations, enabling the training of networks
up to 327 times larger at speeds 160 times faster, resulting in a 50,000-fold
improvement in the ratio of network size to epoch duration. Our approach can
foster more rapid progress in the simulations of nonlinear analog electrical
networks.
