Composite materials are crucial for advancing sustainable engineering practices as they offer high strength-to-weight ratios, making them ideal for applications in aerospace, automotive and civil engineering. Meeting global sustainability goals demands a shift towards efficient materials, resulting in composites becoming increasingly significant. Besides difficulties in producing highly complex composites there are also challenges in computational methods to accurately predict the behavior of structures made from composite materials within a reasonable computational time frame. In most civil engineering practices, the Finite Element Analysis (FEA) is a useful method to derive stress-strain paths. However, these methods often rely on homogenized material assumptions which fail to capture complex microstructural stresses in high-performance composites. A more suitable method to predict the behavior of these materials under complex loading conditions is available using multi-scale modeling techniques. This approach is essential but computationally expensive, especially when high accuracy at the microscale is needed. Surrogate models based on a machine learning framework have been investigated in prior research. These models typically make predictions on homogenized average stress at macroscale rather than the maximum stress at microscale, which identifies as the research gap. The maximum microscopic stress has been recently used as a failure indicator. The main objective of this research is to design a surrogate model, based on the physically recurrent neural network (PRNN) designed in previous research, that can accurately predict the local maximum stress at the microscale in heterogeneous composite materials. Additionally, this research explores how knowledge from existing models that predict average stresses can be leveraged to enhance new models that predict local quantities at the microscale through transfer learning and multi-task learning techniques. Among the three developed models, two models using an encoder-decoder architecture performed poorly because the decoder averages the results instead of being able to find the limits. The decoder was removed in the third model and this yielded promising results. This model maintains high fidelity in stress predictions with lower computational costs because the number of trainable parameters in this model is limited. Transfer learning yielded faster convergence but did overall not improve significantly in terms of error. The decrease in computational time is very limited when transfer learning is applied over direct training as the models used in this thesis are small and do not need extensive datasets or epochs to converge. The multi-task approach achieved very promising results as it enables accurate predictions for average and maximum stresses in a single model. Cross validation showed strong model robustness and flexibility across unseen loading scenarios. Finally, a triple-task model showed that the PRNN is able to act as a modular framework as also the minimum microscopic stress can be accurately predicted without increasing the model and or training set size. The developed surrogate model shows that the architecture of the PRNN developed in previous research can be effectively modified to make predictions on other tasks. It provides a viable tool for simulating composite materials behavior at microscale.