Recent years have seen a significant increase in the use of machine
intelligence for predicting electronic structure, molecular force fields, and
the physicochemical properties of various condensed systems. However,
substantial challenges remain in developing a comprehensive framework capable
of handling a wide range of atomic compositions and thermodynamic conditions.
This perspective discusses potential future developments in liquid-state
theories leveraging on recent advancements of functional machine learning. By
harnessing the strengths of theoretical analysis and machine learning
techniques including surrogate models, dimension reduction and uncertainty
quantification, we envision that liquid-state theories will gain significant
improvements in accuracy, scalability and computational efficiency, enabling
their broader applications across diverse materials and chemical systems.

近年来，机器智能在预测电子结构、分子力场以及各种凝聚系统的物理化学性质方面得到了显著增长。然而，对于处理广泛的原子组成和热力学条件的全面框架仍面临重大挑战。本文展望了液态理论在利用最新功能性机器学习进展方面的潜在未来发展。通过发挥理论分析和机器学习技术的优势，包括代理模型、降维和不确定性量化，我们预见液态理论将在准确性、可扩展性和计算效率方面取得显著改进，从而实现在各种材料和化学体系中的广泛应用。