Multi-fidelity Information Fusion with Machine Learning: A Case Study of Dopant Formation Energies in Hafnia

Cost versus accuracy trade-offs are frequently encountered in materials science, where a particular property of interest can be measured at different levels of accuracy or fidelity. Naturally, the most accurate measurement is also the most resource-intensive, while the inexpensive quicker alternatives tend to be noisy. In such situations, machine learning strategies, such as multi-fidelity information fusion (MFIF), can be employed to fuse information accessible from sources with varying levels of fidelity, and allow for accelerated property predictions. In this work, we use a dataset consisting of dopant formation energies of 42 dopants in hafnia—each studied in six different hafnia phases—computed at two levels of fidelity. The performance of traditional single fidelity (SF) and three MFIF models, namely, Δ-learning, low-fidelity as a feature, and multi-fidelity (MF) co-kriging are compared. We find that the MF based learning scheme not only outperforms the traditional SF machine learning methods, such as Gaussian process regression, but also provides an accurate, inexpensive and flexible alternative to other MFIF strategies. The learning approach is expected to be general and can be readily applied to a much wider spectrum of materials discovery and optimization problems.