Today data-based learning methods and their implementations demands great amount of energy. Bigger computing center are needed, operating for hours for training and the energy consumption of the inference is also extensive, depending on the use of the models learned.

For materials, being able to learn from the process parameters, resulting material micro-structures or cell distributions and corresponding homogenized properties is a very appealing objective, especially considering the computational cost involved for doing structural, thermal or fluid flow simulations. This is because the numerical discretization of the solvers needs to resolve the micro- or cell-structure.

Neural Networks have shown to be already very useful for learning surrogate models for material applications, from given simulation data, provided enough data is available. They learn the relationship between material structure and homogenized properties by given process parameters. Also, the approach can be very useful for the inverse task of designing material structures that end up having specific properties.

Despite the prospects, neural networks demand considerable energy resources and are, as methodological component, black boxes. Therein the importance of developing methods that are “green” and “transparent”, in the sense that do not require so much energy for learning and the methodological components are not a black box.

We present the building blocks for such a “green” methodology. The approach is based on the geometry of the material structures, it derives features based on it so that the training phase for learning features is avoided. The approach computes, based on fewer data sets, as the ones needed for neural networks, a surrogate model. By these simplifications, accuracy could be compromised but we argue that having a lower accuracy by a fraction of a percentage is enough for most engineering applications. We also include a direct comparison with Neural Networks for specific use cases.