Machine Learning Constrained with Dimensional Analysis and Scaling Laws: Simple, Transferable, and Interpretable Models of Materials from Small Datasets

Machine learning (ML) from materials databases can accelerate the design and discovery of new materials through the development of accurate, computationally inexpensive models to predict materials properties. These models in turn enable rapid screening of large materials search space. However, materials datasets describing functional properties are typically small, which creates challenges pertaining to interpretability and transferability when exploring them with conventional ML approaches. Further, correlations within the dataset can lead to instability (nonunique functional models relating inputs to outputs) and overfitting. In this work, we address these issues by developing a new approach, in which ML with the Bootstrapped projected gradient descent algorithm is constrained with Buckingham Pi theorem-based dimensional analysis and scaling laws of relationships between different input descriptors (properties). This constrained learning model enables us to learn from small data and develop predictive models that are accurate, computationally inexpensive, and physically interpretable. We demonstrate this approach by developing a simple model to predict the intrinsic dielectric breakdown field based on an available dataset of 82 compounds. Our approach is generic in nature and is expected to work effectively with other sparse materials datasets.