A study of machine-learning-derived formulas using artificially generated dataset

IF 0.8 4区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY
Donggeon Lee, Sooran Kim
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Abstract

In this study, we investigate the effectiveness of machine learning (ML) models in constructing empirical formulas for the superconducting transition temperature (Tc) by comparing ML-derived equations with McMillan’s equation. We utilized artificially generated data with a size of 10,000 from McMillan’s equation and employed the parametric brute force searching (BFS) algorithm to search for model equations varying model complexity and dataset size. The BFS models with features of the Debye temperature and electron–phonon coupling exhibit the RMSE of 0.830 K and R2 of 0.976 even with a small dataset size of 100. The ML-derived formula is also close to McMillan’s equation showing a linear relationship between the Debye temperature and Tc, as well as a cubic relationship between electron–phonon coupling and Tc. Furthermore, we analyzed feature contributions using non-parametric random forest (RF) regression and found the strong relevance of electron–phonon coupling on Tc. Our results demonstrate the importance of feature selection and model complexity in effectively predicting Tc rather than simply adding more data.

Abstract Image

利用人工生成的数据集研究机器学习得出的公式
在本研究中,我们通过比较机器学习(ML)模型与麦克米兰方程,研究了机器学习(ML)模型在构建超导转变温度(Tc)经验公式方面的有效性。我们利用从麦克米兰方程中人工生成的 10,000 个数据,并采用参数蛮力搜索(BFS)算法来搜索不同模型复杂度和数据集大小的模型方程。具有德拜温度和电子-声子耦合特征的 BFS 模型显示,即使数据集规模只有 100 个,RMSE 也达到了 0.830 K,R2 为 0.976。ML 衍生公式也接近麦克米兰方程,显示出德拜温度与 Tc 之间的线性关系,以及电子-声子耦合与 Tc 之间的立方关系。此外,我们还使用非参数随机森林(RF)回归分析了特征贡献,发现电子-声子耦合与 Tc 有很大关系。我们的研究结果证明了特征选择和模型复杂性在有效预测 Tc 方面的重要性,而不是简单地增加更多数据。
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来源期刊
Journal of the Korean Physical Society
Journal of the Korean Physical Society PHYSICS, MULTIDISCIPLINARY-
CiteScore
1.20
自引率
16.70%
发文量
276
审稿时长
5.5 months
期刊介绍: The Journal of the Korean Physical Society (JKPS) covers all fields of physics spanning from statistical physics and condensed matter physics to particle physics. The manuscript to be published in JKPS is required to hold the originality, significance, and recent completeness. The journal is composed of Full paper, Letters, and Brief sections. In addition, featured articles with outstanding results are selected by the Editorial board and introduced in the online version. For emphasis on aspect of international journal, several world-distinguished researchers join the Editorial board. High quality of papers may be express-published when it is recommended or requested.
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