  Ising machines based on nonlinear analog systems are a promising method to
accelerate computation of NP-hard optimization problems. Yet, their analog
nature is also causing amplitude inhomogeneity which can deteriorate the
ability to find optimal solutions. Here, we investigate how the system's
nonlinear transfer function can mitigate amplitude inhomogeneity and improve
computational performance. By simulating Ising machines with polynomial,
periodic, sigmoid and clipped transfer functions and benchmarking them with
MaxCut optimization problems, we find the choice of transfer function to have a
significant influence on the calculation time and solution quality. For
periodic, sigmoid and clipped transfer functions, we report order-of-magnitude
improvements in the time-to-solution compared to conventional polynomial
models, which we link to the suppression of amplitude inhomogeneity induced by
saturation of the transfer function. This provides insights into the
suitability of systems for building Ising machines and presents an efficient
way for overcoming performance limitations.
