The prediction of temperature effects from first principles is computationally demanding and typically too approximate for the engineering of high-temperature processes. Here, we introduce a hybrid approach combining zero-Kelvin first-principles calculations with a Gaussian process regression model trained on temperature-dependent reaction free energies. We apply this physics-based machine-learning model to the prediction of metal oxide reduction temperatures in high-temperature smelting processes that are commonly used for the extraction of metals from their ores and from electronics waste and have a significant impact on the global energy economy and greenhouse gas emissions. The hybrid model predicts accurate reduction temperatures of unseen oxides, is computationally efficient, and surpasses in accuracy computationally much more demanding first-principles simulations that explicitly include temperature effects. The approach provides a general paradigm for capturing the temperature dependence of reaction free energies and derived thermodynamic properties when limited experimental reference data is available.

根据第一原理预测温度效应的计算要求很高，并且对于高温过程的工程来说通常过于近似。在这里，我们引入了一种混合方法，将零开尔文第一原理计算与基于温度相关反应自由能训练的高斯过程回归模型相结合。我们将这种基于物理的机器学习模型应用于高温冶炼过程中金属氧化物还原温度的预测，这些过程通常用于从矿石和电子废物中提取金属，对全球能源经济产生重大影响和温室气体排放。该混合模型可以准确预测看不见的氧化物的还原温度，计算效率高，并且在精度上超越了对计算要求更高的第一性原理模拟（明确包含温度影响）。该方法提供了一个通用范例，用于在有限的实验参考数据可用时捕获反应自由能的温度依赖性和导出的热力学性质。