We conclude by emphasising that it is imperative to develop new machine learning and deep learning methodologies for tackling problems pertaining to the continuum mechanics of heterogeneous and anisotropic solids that adhere to the strong forms of essential physical principles both on a global and on a local scale. Doing so offers several advantages: firstly, it enhances the interpretability and generalizability of machine learning-based surrogate models. Secondly, it reduces the amount of required training data. Thirdly, it can enhance solver performance by up to several thousand times compared to conventional solution methods such as FEM or spectral methods. As an initial endeavour in this direction, we have demonstrated how to construct machine learning surrogate models that inherently produce divergence-free stress fields, thereby satisfying mechanical equilibrium conditions. Learning suitable lowdimensional latent representations not only reduces online inference time but also facilitates engineering studies with minimal computational resources. Additionally, acquiring training data for engineering applications is both economically expensive and time-consuming. Therefore, it is crucial to devise strategies for cleverly gathering training data, ensuring that the limited data covers a wide range of parameter space.