Predictive Models of Multi-scale Behavior of Materials: Mechanistic versus Machine Learning Schemes

A model of a system is an approximate representation of its real structure and behavior. Computer simulations of a material mimic its model numerically, and their accuracy in prediction of material-specific behavior is singularly determined by how realistic the model is. The construction of a mechanistic model of a material involves identification of the degrees of freedom relevant to the property of interest. The model captures effective interactions between these by integrating out the rest, a step known as coarse-graining which filters out the features of short length and time scales. Reducing number of degrees of freedom while maintaining close similarity to material’s real behavior is the challenge and science of modeling. First-principles density functional theory provides the fundamental input at the shortest scales in hierarchical modeling to capture of phonons, phase transitions, dislocations and continuum description of materials. When separation between relevant and irrelevant variables is not straightforward or there are several coupled groups of relevant variables, machine learning can be useful in developing predictive models. While machine learning needs big data and result in uninterpretable models, machine learning combined with dimensional analysis and physical laws seems promising in developing insightful models of complex material behavior from relatively small data.