Finite Element (FE) simulations involving many loading cycles with nonlinear material models can lead to high computational costs. One approach to accelerate the cyclic simulations is to use cycle-domain modeling as proposed by Suiker and de Borst. The model framework builds upon standard plasticity theory and is formulated as a viscoplastic model to predict the evolution of plastic deformations in the material over many cycles. A key challenge, however, with cycle-domain material models is to formulate a suitable per-cycle evolution law for the plastic strains. In our previous work, we investigated the feasibility and accuracy of Machine Learning (ML) to formulate such an equation. The proposed ML-based cycle domain model was able to produce very accurate results while only taking a single increment per cycle. However, that approach requires a lot of training data even for uniaxial loading. In this contribution, based on a time-domain model, we present a novel approach to speed up cyclic simulations by taking large time increments. This approach aims to take much larger time steps than standard time integration schemes. Specifically, we propose to use ML to train an explicit model that learns the solutions of the evolution equations for internal variables. We evaluate different methods for incorporating knowledge from the underlying ODE to guide the ML-based enhancement and reduce the need for training data. The ML model is trained against artificially generated data obtained from a cyclic plasticity model under multiaxial, non-proportional cyclic loading. Using a novel training data generation strategy, we prepare training data with varying time steps, enabling training across a wide range of increment sizes without requiring a large number of loading cycles.