Nonlinear computational analysis of composite materials is often time-consuming and expensive, necessitating the development of novel methods. Machine learning methods have shown great potential to develop computationally efficient and accurate material models. Artificial Neural Networks (ANNs) have been used in multi-scale modelling approaches to replace expensive lower-scale micro- and/or meso-scale material models. Using ANNs, it is possible to develop structure-property relationships at different length scales. Required training data can be obtained from high-fidelity models that have the potential to provide accurate predictions at lower length scales. To evaluate the effect of different geometrical and material variations on a composite behaviour, a data-driven framework of this type must explore ample design space to feed the training of surrogate machine-learning models. This study aims to replace meso-scale finite element analysis of woven composites with recurrent neural networks trained on two sets of data of two different levels of complexity. The first data set (for initial training) is obtained through fast mean-field simulations on a one-layer 2D woven unit cell. This data set explores the whole possible design space and represents the general nonlinear behaviour of the meso-scale woven composite. A Recurrent Neural Network (RNN) is trained using the mean-field data set. Then, a second data set is obtained from full-field simulations of a woven unit cell. In both data generation methods, yarn nonlinearity is taken into account at the meso-scale as a consequence of considering elasto-plastic material behaviour with isotropic hardening for the matrix. Since the full-field simulations model better captures the detailed behaviour of composite (compared to the mean-field simulations), it serves as the so-called target data set for the RNN training. Thereby, path-dependent RNNs are trained using the representational inductive transfer method [1]. The idea behind this method is that the knowledge gained from the low-quality big data set (mean-field simulations) is transferred to the high-quality, computationally expensive data set (full-field simulations), allowing RNNs to predict plasticity in composites accurately. As a result, the detailed nonlinear behaviour of woven composites is predicted at a remarkably lower computational cost (compared to the original FE simulations.)