Modeling the relationship between mechanical yield stress and material geometry using convolutional neural networks

Neural networks have proved to be able to capture the relevant and informative features of a wide variety of data types and predict the desired output for different regression or classification problems. Finding a mapping between materials’ structure and a given physical property of those systems is an example of a problem that could be approached with machine learning methods like neural networks. Especially when we are dealing with systems with a very large design space where using classical computational methods like molecular dynamics can be very time and resource-consuming for the study of a very large number of systems, a well-trained neural network can be greatly faster and more efficient for computing the relevant properties. In this work, we study α-quartz crystals with one porous layer with simplex noise as the shape of porosity. Simplex noise is a gradient based procedural algorithm that can produce irregular geometries with surface morphology resembling what is observed in nature. The property that we want the neural network to learn is the yield stress of these systems under both shear and tensile deformation. Molecular dynamics simulations are used for a randomly selected sample of possible structures in order to generate the ground truth to be used as the training data. We employ deep convolutional neural networks (CNN) which are commonly used when dealing with image or image-like data since the input data for the problem in hand is a binary 2-D structure of the porous layer of the systems. The trained model is compared with a basic polynomial fit of stress versus porosity. The trained CNN is successful in predicting the yield stress of a system based on the geometry of that given system, with lower variability and higher precision compared to the base polynomial regression method. The saliency maps created with the trained model show the model to be successful in capturing the physics of the problem when compared with the stress fields calculated using molecular dynamics simulations. This method of modeling materials can be further developed for the inverse design of structures with desired properties without the need for a huge number of simulations on a wide domain of possible systems.