Many problems in mathematics, statistical mechanics, and computer science are computationally hard but can often be mapped onto a ground-state-search problem of the Ising model and approximately solved by artificial spin-networks of coupled degenerate optical parametric oscillators (DOPOs) in coherent Ising machines. To better understand their working principle and optimize their performance, we analyze the dynamics during the ground state search of 2D Ising models with up to 1936 mutually coupled DOPOs. For regular as well as frustrated and disordered 2D lattices, the machine finds the correct solution within just a few milliseconds. We determine that calculation performance is limited by freeze-out effects and can be improved by controlling the DOPO dynamics, which allows to optimize performance of coherent Ising machines in various tasks. Comparisons with Monte Carlo simulations reveal that coherent Ising machines behave like low temperature spin systems, thus making them suitable for optimization tasks.