Heterogeneous nanocrystalline high-entropy alloys (HEAs) have excellent mechanical properties. However, it is still difficult to obtain the optimized grain size in the heterogeneous-grained HEAs, which achieves their outstanding mechanical properties. Here, using a novel integration method of machine learning, a physical model and atomic simulation, the optimal grain size is designed for achieving high yield strength of heterogeneous-grained CrCoFeNi HEAs. Atomic simulations give the stress–strain curve, yielding strength and microstructure with the increase of small grain size. The physical-based strength model expands the data from the atomic simulations and obtains the transition region from the Hall–Petch to inverse Hall–Petch relationship. The results show that the strength of CrCoFeNi HEAs derives mainly from the contribution of the grain boundary compared to lattice friction stress. The machine learning model shows that the obvious transition point from the Hall–Petch to inverse Hall–Petch relationship occurs at the grain size of 38.4 nm for the heterogeneous-grained CrCoFeNi HEAs with the large grain size of 165 nm. This result agrees with the prediction from the subsequent atomic simulation. This integrated model makes significant contributions to understanding deformation and designing the microstructure of heterogeneous-grained HEAs. Importantly, the developed model including simulation, a theoretical model, experiment and machine learning can be widely applied to explore the advanced material with the desired performance.

异质纳米晶高熵合金（HEA）具有出色的机械性能。但是，仍然很难在异质HEA中获得最佳的晶粒尺寸，从而实现其出色的机械性能。在这里，使用新型的机器学习，物理模型和原子模拟的集成方法，设计了最佳晶粒尺寸，以实现异质晶粒CrCoFeNi HEA的高屈服强度。原子模拟给出了随小晶粒尺寸增加的应力-应变曲线，屈服强度和微观结构。基于物理的强度模型扩展了原子模拟的数据，并获得了从Hall-Petch到逆Hall-Petch关系的过渡区域。结果表明，与晶格摩擦应力相比，CrCoFeNi HEA的强度主要来自晶界的贡献。机器学习模型表明，对于大晶粒尺寸为165 nm的不均匀晶粒CrCoFeNi HEA，在38.4 nm的晶粒尺寸处出现了从Hall-Petch到逆Hall-Petch关系的明显过渡点。该结果与后续原子模拟的预测相符。该集成模型为理解变形和设计异质HEA的微观结构做出了重要贡献。重要的是，包括仿真，理论模型，实验和机器学习在内的开发模型可以广泛应用于探索具有所需性能的高级材料。机器学习模型表明，对于粒径为165 nm的不均匀晶粒CrCoFeNi HEA，从霍尔-Petch关系到霍尔-Petch逆关系的明显过渡点出现在38.4 nm的晶粒上。该结果与后续原子模拟的预测相符。该集成模型为理解变形和设计异质HEA的微观结构做出了重要贡献。重要的是，包括仿真，理论模型，实验和机器学习在内的开发模型可以广泛应用于探索具有所需性能的高级材料。机器学习模型表明，对于粒径为165 nm的不均匀晶粒CrCoFeNi HEA，从霍尔-Petch关系到霍尔-Petch逆关系的明显过渡点出现在38.4 nm的晶粒上。该结果与后续原子模拟的预测相符。该集成模型为理解变形和设计异质HEA的微观结构做出了重要贡献。重要的是，包括仿真，理论模型，实验和机器学习在内的开发模型可以广泛应用于探索具有所需性能的高级材料。对于165nm的大晶粒，异质晶粒CrCoFeNi HEA为4 nm。该结果与后续原子模拟的预测相符。该集成模型为理解变形和设计异质HEA的微观结构做出了重要贡献。重要的是，包括仿真，理论模型，实验和机器学习在内的开发模型可以广泛应用于探索具有所需性能的高级材料。对于165nm的大晶粒，异质晶粒CrCoFeNi HEA为4 nm。该结果与后续原子模拟的预测相符。该集成模型为理解变形和设计异质HEA的微观结构做出了重要贡献。重要的是，包括仿真，理论模型，实验和机器学习在内的开发模型可以广泛应用于探索具有所需性能的高级材料。