Supplementary materials for: CNN-based surrogate for the phase field damage mode

We investigate the generalization of a CNN-based surrogate for the phase field model in predicting both damage and maximum/peak load, given the image of an arbitrary 2D microstructure of a unidirectional fiber-reinforced composite. We first discuss the phase field model and the numerical procedure to generate training and test data from synthetic microstructures with different volume fractions and fiber radii. We next present a two-stage approach for predicting peak load, achieved by first transforming a given fiber-encoded microstructure image to a continuous damage field; and second, predicting peak load from the damage field. A key finding is that the direct approach for predicting peak load from the microstructure image using a standard regression model fails to generalize. Instead, the damage field, even if imperfectly predicted, provides valuable cues for the CNN in generalizing across new microstructures. We describe several case studies to demonstrate the capability of the surrogate model to predict damage and peak load and to interpolate over fiber radii and volume fractions. 

Methods
The data in damage_prediction_X are predicted by our CNN-based Image-to-Image model given microstructure geometries. "geometry.th" is the geometry image of microstructure generated by our Python code with different volume fractions and fiber radii. "max_f.th" and "resampled_damage.th" are the peak load value and damage field calculated by FEniCS for corresponding microstructures.