硅酸盐学报

材料领域知识嵌入的分而治之机器学习

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杨正伟 ¹ , 刘子图 ¹ , 张王颖 ² , 左维 ¹ , 余振垚 ¹ , 邹欣欣 ¹ , 袁浩栋 ¹ , 苏玉凤 ¹ , 施思齐 ²^,³ , 刘悦 ¹

硅酸盐学报 | AI for Materials专题—研究论文 2026,54(1): 14-24

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硅酸盐学报 |AI for Materials专题—研究论文 2026 , 54 (1) : 14 -24

材料领域知识嵌入的分而治之机器学习

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杨正伟¹, 刘子图¹, 张王颖², 左维¹, 余振垚¹, 邹欣欣¹, 袁浩栋¹, 苏玉凤¹, 施思齐²^,³, 刘悦¹

作者信息

^1．上海大学核电关键材料全国重点实验室&计算机工程与科学学院，上海 200444

^2．上海大学核电关键材料全国重点实验室&材料科学与工程学院，上海 200444

^3．上海大学材料基因组工程研究院，上海 200444

通讯作者:

刘悦（1975—），女，博士，教授

施思齐（1978—），男，博士，教授。

作者简介:

杨正伟（1994—），男，博士研究生。

Divide-and-Conquer Machine Learning Embedded with Materials Domain Knowledge

Zhengwei YANG¹, Zitu LIU¹, Wangying ZHANG², Wei ZUO¹, Zhenyao YU¹, Xinxin ZOU¹, Haodong YUAN¹, Yufeng SU¹, Siqi SHI²^,³, Yue LIU¹

Affiliations

^1.State Key Laboratory of Materials for Advanced Nuclear Energy & School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China

^2.State Key Laboratory of Materials for Advanced Nuclear Energy & School of Materials Science and Engineering, Shanghai University, Shanghai 200444, China

^3.Materials Genome Institute, Shanghai University, Shanghai 200444, China

Corresponding Author:

LIU Yue (1975-), female, Ph.D., Professor. E-mail: yueliu@shu.edu.cn

SHI Siqi (1978-), male, Ph.D., Professor. E-mail: sqshi@shu.edu.cn

YANG Zhengwei (1994-), male, Doctoral candidate. E-mail: zhw_yann@shu.edu.cn

出版时间: 2026-01-20 doi: 10.14062/j.issn.0454-5648.20250867

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摘要

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纯数据驱动的机器学习能够快速挖掘复杂材料数据隐含的科学规律。然而，“成分-结构-工艺-性能”组成的复杂材料构效关系使得机器学习难以准确剖析其内在／外在因素的作用机理，这导致模型精度、建模复杂程度及其可解释性面临严峻挑战。因此，本工作提出了一种材料领域知识嵌入的分而治之机器学习建模策略，旨在依据领域知识将复杂材料问题进行有效拆解并利用领域知识嵌入的机器学习对拆解后子问题进行针对性的自适应建模，以精准且具有一定可解释性的方式挖掘其内部隐藏作用机理。同时，利用变分推断验证该策略的科学性与有效性。进一步，总结了在材料科学领域中依据不同领域知识进行“分而治之”机器学习建模的应用示例。最后，展望了该策略未来所面临的挑战及对策。

关键词

材料科学 / 机器学习 / 分而治之 / 领域知识

Abstract

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Data-driven machine learning (ML) has made significant progress in predicting structure-property relationships, discovering new materials, and optimizing processes within materials science. However, the factors influencing materials structure-property relationships are highly complex and multifaceted, resulting in extremely intricate distribution patterns in materials data. This complexity makes it difficult for traditional data-driven approaches, which attempt to establish a single mapping between a fixed set of descriptors and target properties, to accurately and comprehensively unravel these relationships. Through the analysis of the characteristics of materials data and the modeling principle of data-driven ML methods, we have clarified the three main contradictions occurring to the application of ML in materials science, i.e., the contradictions between high dimension and small sample, accuracy and usability of models, learning results and domain knowledge. To reconcile these three contradictions, we propose the framework of machine learning embedded with materials domain knowledge and a series of novel methods. Then, by analyzing the characteristics of materials research problems and the complex and diverse structure-property relationships inherent in materials data, we believe that it is possible to effectively decompose complex material problems and address them individually by leveraging materials domain knowledge. To this end, we here propose a divide-and-conquer ML modeling strategy embedded with materials domain knowledge.

Specifically, the "Divide and Conquer" strategy aims to leverage materials domain knowledge to decompose complicated material problems and construct ML models towards each sub-problem, which can effectively reduce the complexity of ML models and ensures that the learning results of models are both accurate and credible through the integration of domain knowledge. It can be regarded as an application of the algorithmic paradigm of divide-and-conquer to ML modeling, or alternatively, as a novel form of ensemble learning. This strategy consists of: i) "Divide": Guided by materials domain knowledge, a complicated materials problem can be decomposed into several sub-problems from multiple perspectives based on an analysis of underlying physicochemical mechanisms. ii) "Conquer": Individual models are constructed for each sub-problem, where domain-specific knowledge is injected into the sub-models, establishing mappings between different ML models and distinct physicochemical mechanisms. iii) "Combine": A fusion mechanism is designed to integrate the feature extraction or decision outputs from the sub-models. As a result, multi-faceted analysis from diverse perspectives yields more comprehensive and rational insights into complex materials problems. This aids domain experts in identifying the critical thresholds and transition boundaries of the intrinsic mechanisms governing material property variations, reduces the complexity of individual ML models within each subspace, and enhances both the predictive accuracy and interpretability of the models. A further investigation reveals that, although the concept of "divide and conquer" has been widely adopted, no attempt has yet been made to theoretically derive and validate its content. In this study, we employ variational inference to provide a formal symbolic representation for the divide-and-conquer ML modeling strategy and verify its rationality and scientific validity.

Currently, researchers have begun to leverage domain knowledge to decompose materials problems or data, giving rise to diverse "divide-and-conquer" ML modeling strategies. Specific implementations include: i) Stage divide-and-conquer. Deconstructing long-term, highly complex evolutionary processes into several substages with relatively singular and stable physicochemical mechanisms, thereby simplifying the intricate. This strategy can be applied to complex materials issues featuring multi-step transition characteristics, such as the glass transition temperature (T_g) and the battery rollover point, to enable accurate prediction. ii) Positive/negative examples divide-and-conquer. Samples are categorized into distinct subspace according to their positive or negative impact on the target performance. This strategy can be applied to complex materials problems that encompass samples from superior performance to degradation, such as in the optimal design of lithium-ion battery electrolytes and the hydrothermal synthesis of inorganic-organic hybrid materials. iii) Category divide-and-conquer. By leveraging explicit labels or implicit distributional features, heterogeneous data is decomposed into several isotropic subdomains with relatively consistent physicochemical mechanisms, thereby reducing the complexity of global modeling. This strategy can be applied to the precise prediction of heterogeneous samples, such as the creep life of nickel-based single-crystal superalloys, the hardness of steel, and the strength and ductility of lead-free solder alloys. iv) Attribute divide-and-conquer. Multiple sets of optimal descriptor combinations are screened out, thereby enabling the targeted construction of several high-precision models. This strategy is validated on six distinct material systems, such as NASICON-type inorganic solid-state electrolytes, demonstrating high predictive accuracy and interpretative capabilities. v) Modality divide-and-conquer. Decomposing heterogeneous data and representing it as multi-modal data to comprehensively unravel structure-property relationships. This strategy is applicable to complex materials problems with multi-modal information, such as dual-phase steels and lithium-ion solid-state electrolytes.

Summary and prospects

In this study, we propose a divide-and-conquer ML modeling strategy embedded with materials domain knowledge, which establishes mappings between different ML models and the distinct physicochemical mechanisms of materials. Future research efforts can focus on the following directions to further advance this strategy: i) Data quality remains the fundamental fuel driving the construction of high-accuracy models. When implementing this strategy, it is necessary to collect sufficient high-quality data for each sub-problem. ii) As material problems become increasingly complex, more and more divide-and-conquer ML modeling strategies can be introduced to comprehensively cover the dimensions of decomposing complex material problems. iii) Currently, divide-and-conquer ML relies on manual model selection and hyperparameter optimization based on expert experience. Automated machine learning (AutoML) can be introduced to eliminating the knowledge barriers to modeling. iv) The divide-and-conquer ML modeling strategy allows researchers to introduce inherently interpretable models for specific sub-problems and incorporate internal interpretation methods for models. In the future, as the paradigm of materials science research undergoes a profound shift towards digitalization and intelligence, this strategy is poised to gain renewed relevance and vitality. Through the deep integration of scientific deconstruction guided by domain expertise, the "divide and conquer" strategy is expected to propel a more thorough and systematic understanding of complex material behaviors. It will facilitate deeper revelation of intrinsic relationships and underlying mechanisms, thereby accelerating the process of precise design and development of high-performance materials.

Key words

materials science / machine learning / divide-and-conquer / domain knowledge

引用本文

杨正伟, 刘子图, 张王颖, 左维, 余振垚, 邹欣欣, 袁浩栋, 苏玉凤, 施思齐, 刘悦. 材料领域知识嵌入的分而治之机器学习. 硅酸盐学报, 2026 , 54 (1) : 14 -24 . DOI: 10.14062/j.issn.0454-5648.20250867

Zhengwei YANG, Zitu LIU, Wangying ZHANG, Wei ZUO, Zhenyao YU, Xinxin ZOU, Haodong YUAN, Yufeng SU, Siqi SHI, Yue LIU. Divide-and-Conquer Machine Learning Embedded with Materials Domain Knowledge[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (1) : 14 -24 . DOI: 10.14062/j.issn.0454-5648.20250867

基金

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国家自然科学基金(92270124; 92472207; 52073169和52472223)

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2026年第54卷第1期

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文章信息

doi: 10.14062/j.issn.0454-5648.20250867

接收时间：2025-11-26
首发时间：2026-10-27
出版时间：2026-01-20

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出版历史

收稿日期：2025-11-26
修回日期：2025-12-22

基金

国家自然科学基金(92270124; 92472207; 52073169和52472223)

作者信息

^1．上海大学核电关键材料全国重点实验室&计算机工程与科学学院，上海 200444

^2．上海大学核电关键材料全国重点实验室&材料科学与工程学院，上海 200444

^3．上海大学材料基因组工程研究院，上海 200444

通讯作者:

刘悦（1975—），女，博士，教授

施思齐（1978—），男，博士，教授。

参考文献

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20250867

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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