用神经网络引导符号回归，从少量数据中发现可解释的钙钛矿催化活性描述符。
Neural Network-Guided Symbolic Regression for Interpretable Descriptor Discovery in Perovskite Catalysts
- 先用神经网络筛选特征，再结合符号回归生成可解释公式。
- 新公式预测误差低于21 meV，比已有方法更准且物理意义明确。
- 适合材料科学中需兼顾准确性和可解释性的研究者使用。
理解并预测氧化物钙钛矿催化剂在氧析出反应（OER）中的活性，需要既准确又具有物理可解释性的描述符。尽管符号回归（SR）能发现此类公式，但在高维输入和小样本情况下性能下降。本文提出两阶段框架：第一阶段基于小样本和七个结构特征，通过构建复合特征并应用符号回归，复现并改进了已知的μ/t描述符，训练与验证均方误差分别为22.8和20.8 meV；第二阶段扩展至164个特征，经降维后识别出LUMO能级为关键电子描述符。最终公式结合μ/t、μ/RA和LUMO能量，训练与验证误差分别降至22.1和20.6 meV，兼具高精度与强物理可解释性。结果表明，神经网络引导的符号回归可在数据稀缺条件下实现准确、可解释且物理意义明确的描述符发现，证明可解释性无需以牺牲准确性为代价。
原文摘要 · Abstract (English)
Understanding and predicting the activity of oxide perovskite catalysts for the oxygen evolution reaction (OER) requires descriptors that are both accurate and physically interpretable. While symbolic regression (SR) offers a path to discover such formulas, its performance degrades with high-dimensional inputs and small datasets. We present a two-phase framework that combines neural networks (NN), feature importance analysis, and symbolic regression (SR) to discover interpretable descriptors for OER activity in oxide perovskites. In Phase I, using a small dataset and seven structural features, we reproduce and improve the known μ/t descriptor by engineering composite features and applying symbolic regression, achieving training and validation MAEs of 22.8 and 20.8 meV, respectively. In Phase II, we expand to 164 features, reduce dimensionality, and identify LUMO energy as a key electronic descriptor. A final formula using μ/t, μ/RA, and LUMO energy achieves improved accuracy (training and validation MAEs of 22.1 and 20.6 meV) with strong physical interpretability. Our results demonstrate that NN-guided symbolic regression enables accurate, interpretable, and physically meaningful descriptor discovery in data-scarce regimes, indicating interpretability need not sacrifice accuracy for materials informatics.
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