Coherent Ising Machines (CIMs) are optical devices that employ parametric oscillators to tackle binary optimization problems, whose simplified dynamics are described by a series of coupled ordinary differential equations. In this study, we learn the deterministic dynamics of CIMs via the use of neural Deep Operator Networks (DeepONet). After training successfully the systems over multiple initial conditions and problem instances, we benchmark the comparative performance of the neural network. In our tests, the network is capable of delivering solutions of comparative quality to the exact dynamics up to 175 spins, but we do not identify roadblocks to go further: given sufficient training resources the CIM solvers could successfully be represented by a neural network at a large scale.