  High-entropy alloys are solid solutions of multiple principal elements,
capable of reaching composition and feature regimes inaccessible for dilute
materials. Discovering those with valuable properties, however, relies on
serendipity, as thermodynamic alloy design rules alone often fail in
high-dimensional composition spaces. Here, we propose an active-learning
strategy to accelerate the design of novel high-entropy Invar alloys in a
practically infinite compositional space, based on very sparse data. Our
approach works as a closed-loop, integrating machine learning with
density-functional theory, thermodynamic calculations, and experiments. After
processing and characterizing 17 new alloys (out of millions of possible
compositions), we identified 2 high-entropy Invar alloys with extremely low
thermal expansion coefficients around 2*10-6 K-1 at 300 K. Our study thus opens
a new pathway for the fast and automated discovery of high-entropy alloys with
optimal thermal, magnetic and electrical properties.
