Multi-fidelity learning in materials informatics: methodologies, applications, and outlook

Data-driven methods are transforming materials design by accelerating the discovery of new compounds and the optimization of existing systems. However, the progress of such approaches is often constrained by the scarcity of high-fidelity data from experiments and advanced simulations. Multi-fidelity (MF) learning has emerged as a powerful strategy to address this challenge by integrating information from diverse data sources that vary in accuracy and cost. In this review, we provide a systematic overview of the major methodologies for MF learning, including statistical and parametric models, machine learning models with fidelity features, correction-based models such as co-kriging, deep learning frameworks, and active learning frameworks. We discuss the strengths, limitations, and typical applications of each method in materials science, with illustrative examples spanning electronic structure modeling, alloy design, and interatomic potential development. Cross-cutting issues are also examined, including the bias-variance trade-off, data requirements for nested vs. non-nested designs, and computational scalability. Finally, we highlight outstanding challenges and outline emerging opportunities, such as physics-informed and generative MF models, standardized datasets, and integration with autonomous laboratories. Together, these perspectives define a roadmap for advancing MF learning as a core enabler of next-generation materials discovery.