The macroscopic mechanical response of a material is fundamentally governed by its underlying fine-scale structure. Conventional constitutive models aim to approximate the influence of such features, but these approaches become inadequate when mechanical phenomena exhibit an inseparable coupling across multiple scales. Concurrent multiscale frameworks are designed to establish a reliable link between fine-scale features and continuum-level behavior. In this paradigm, local deformation kinematics are transferred from the macro-scale to a representative volume element (RVE) containing fine-scale features, and the resulting homogenized stress is upscaled back to the continuum model. Accurate modeling of fine-scale structures demands significant computational resources, as it requires resolving numerous degrees of freedom and solving complicated nonlinear material laws. FFT-based homogenization provides an efficient framework for this purpose as it inherently outperforms conventional finite element methods. However, high-resolution simulations of complex microstructures remain computationally prohibitive in practical applications, even with highly optimized implementations. This fundamental limitation motivates the development of surrogate models that provide a scalable and robust pathway toward real-time, data-driven multiscale simulations. In this contribution, we present a deep learning-based surrogate model for the plastic return-mapping process within a concurrent multiscale framework. Following the use of artificial neural networks to replace theoretical constitutive models, our surrogate model learns the underlying constitutive response directly from training data generated via FFT-based homogenization of heterogeneous RVEs. The trained neural network bypasses the need for expensive nested numerical solves, enabling extremely fast stress updates based on the local deformation kinematics provided by the macroscopic model. Key contributions of this work include: a framework for constructing frame-indifferent fine-scale data; guidelines for incremental FFT-based modeling and data generation; strategies for efficient and representative training datasets; implementation requirements for data-driven return-mapping algorithms; and a sensitivity study with respect to data population, increment size, and finite element discretization.