Intelligent Prediction of Mechanical Properties in Metallic Materials based on Machine Learning: A Review & Perspective
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摘要: 机器学习正推动金属材料力学性能研究从经验驱动向数据驱动范式转变. 本文系统综述了机器学习在金属材料力学性能智能预测中的研究进展与挑战. 首先, 概述了常用机器学习算法的原理与流程, 重点介绍了可解释人工智能 与物理信息机器学习等前沿方法. 进而, 从微介观性能 (如微观结构演化、断裂行为)、宏观性能 (如硬度、应力响应、疲劳寿命) 与跨尺度耦合性能 (如流变应力、屈服强度、本构参数反演) 三个层面, 评述了机器学习模型的典型应用与预测效果, 突出其在高通量计算与多尺度建模中的优势. 最后, 指出该领域面临数据稀缺、异构性及宽温域/宽应变率条件下预测精度不足等挑战, 并提出迁移学习、大型语言模型与多模态融合等解决路径. 展望未来, 本文构建了融合多模态数据与物理机制的机器学习技术路径, 旨在实现对极端环境下金属材料力学行为的精准预测, 推动材料力学研究向数字化、智能化方向发展.Abstract: The rapid advancement of machine learning is transforming the research paradigm of mechanical properties of metallic materials from experience-driven to data-driven. This review systematically summarizes recent progress and challenges in machine learning based prediction of mechanical properties in metallic materials. We first outline commonly used ML algorithms and workflows, with an emphasis on cutting-edge methods such as explainable AI and physics-informed machine learning. We then review typical applications and predictive performance of ML models across three scales: micro/mesoscopic properties (e.g., microstructural evolution, fracture behavior), macroscopic properties (e.g., hardness, stress response, fatigue life), and cross-scale coupling properties (e.g., flow stress, yield strength, constitutive parameter inversion), highlighting their advantages in high-throughput computation and multi-scale modeling. Finally, we identify persistent challenges such as data scarcity, heterogeneity, and insufficient accuracy under wide temperature/strain-rate ranges, and propose potential solutions including transfer learning, large language models, and multi-modal fusion. Looking forward, we outline a technical pathway integrating multi-modal data and physical mechanisms for accurate prediction of mechanical behavior under extreme conditions, aiming to advance materials mechanics toward digitalization and intelligence.
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图 5 微观结构演化预测结果对比图. (a) PolyLMSE预测结果(Hu Y et al. 2025), (b) MOEP-ANN预测结果(Saidi et al. 2022)
图 6 机器学习预测裂纹长度结果对比图. (a) ConvLSTM裂纹长度预测结果(Hsu et al. 2020), (b) LSTM裂纹长度预测结果(Fernández-Godino et al. 2021)
图 8 材料力学行为预测物理信息神经网络结构与预测结果对比. (a)有限应变弹性塑性的PINN结构, (b)有限应变弹性塑性的PINN预测结果(Niu S et al. 2023), (c)数据驱动识别力学行为PINN结构, (d)数据驱动识别力学行为PINN预测结果(Jeong et al. 2024), (e) Finite-PINN模型结构, (f) Finite-PINN模型预测结果(Li H et al. 2025), (g)金属材料数字化框架模型结构, (h)金属材料数字化框架预测结果(Razaei et al. 2025)
图 10 流变应力预测模型结果对比图. (a) MDN预测结果与理论结果对比(Gu Y et al. 2024), (b) SR预测结果与经典模型对比(Versino et al. 2017)
表 1 机器学习算法特征汇总
算法 核心思想 优势 局限性 适用场景 应用案例 支持向
量机在数据集中寻找最优分割超平面, 使得超平面周围正负样本间隔最大化. 在高维空间中有效, 内存效率高. 对参数和核函数的选择敏感. 在材料科学的早期数据挖掘中应用广泛, 适合处理高维度的数据集. 预测铝合金硬度和电导率(Fang F S et al. 2009). K近邻
算法基于某种距离度量方法找出训练集中与样本最近的k个训练样本进行预测. 原理简单易实现, 无需训练过程. 对高维数据与不平衡数据敏感. 常用于快速原型验证或作为基线模型, 适用于小规模数据集. 预测D16T铝合金疲劳断裂图(Yasnii et al. 2018). 树集成
算法每个节点代表一个逻辑条件用于将输入数据划分为不同类别或分配数值. 具有可解释性, 能输出特征重要性排序. 模型参数较多, 调参过程复杂. 根据材料成分、工艺参数预测其性能特征, 或筛选潜力材料. 建立多组分钛合金成分与杨氏模量的关系(Yang F et al. 2020). 人工神经网络 利用多层神经元结构实现信息传递与特征映射. 能拟合复杂的非线性关系, 对特征要求较低. 预测能力严重依赖于数据集质量. 用于构建各类结构化材料描述符到目标性能的复杂非线性映射模型. 预测铝合金DMD轨迹横截面几何参数(Caiazzo & Caggiano 2018). 循环神经网络 对上一层神经元的输出进行记忆并应用于当前神经元的计算中. 有记忆功能, 可以处理长度不一的序列数据. 难以实现高效并行化计算. 处理序列相关的数据, 如金属材料的力学性能演化等. 纤维增强复合材料的疲劳寿命预测(Al-Assaf & El Kadi 2007). Transformer模型 通过注意力机制建立序列内部各个位置之间的全局依赖关系, 从而捕捉序列中各元素之间的关联. 具有强大的全局依赖建模能力, 可以实现高效的并行计算. 具有极高的计算复杂度, 需要大规模数据和较高的计算资源. 用于处理原子排列、晶格结构等微观结构序列以及文本描述等大规模序列化数据. 预测合金耐腐蚀性能(Sasidhar et al. 2023), 预测材料的电导率、带隙等性能(Xu C et al. 2023). 卷积神经网络 通过局部连接、权重共享和多层堆叠, 逐级提取图像中的特征. 能自动提取特征, 具有平移不变性, 在图像相关任务上性能卓越. 仅能处理规则网格数据, 并且需要大量标注数据. 专门用于处理具有空间网格结构的材料数据, 如微观结构图像等. 基于微观结构预测增材制造316L不锈钢有效屈服强度(Herriott & Spear 2020). 图神经
网络通过信息传递机制整合节点及其邻居节点的信息, 迭代地更新节点表示. 兼具强大表征能力与可解释性. 难以处理长程相互作用, 对图结构定义敏感. 用于表征材料的分子或晶体结构等不规则形状图结构. 预测材料原子力并支撑分子动力学模拟(Park et al. 2021). 可解释
模型通过约束模型结构或事后解析, 确保其决策逻辑与已知的因果关系或特征贡献度保持一致. 透明度高, 能够揭示输入变量与输出目标之间的作用关系. 难以兼顾预测精度与机制解释的深度, 且其结论多为统计相关性. 常用于分析输入与输出之间的潜在机理, 指导材料设计. 基于热轧钢板成分与工艺参数预测屈服强度等力学性能(Xie Q et al. 2021). 物理信息机器学习 将已知的物理定律显式地融入到机器学习模型的构建、训练和推理过程中. 泛化能力更强, 缓解模型对于数据的依赖. 需要将物理知识数学化, 实现更复杂. 用于数据获取困难, 成本高昂, 需要对物理过程进行高精度模拟的领域. 预测材料均质化位移场, 计算弹性模量(Li X et al. 2024). 
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表 2 损失函数及其适用场景
损失函数 公式 适用场景 均方误差 $ L=\dfrac{1}{n}\displaystyle\sum\nolimits_{i=1}^{n}{\left({y}_{i}-{\widehat{y}}_{i}\right)}^{2} $ 对异常值敏感, 适用于回归任务. 平均绝对误差 $ L=\dfrac{1}{n}\displaystyle\sum\nolimits_{i=1}^{n}\left\| {{y}_{i}-{\widehat{y}}_{i}} \right\| $ 对异常值不敏感, 适用于回归任务. 交叉熵损失 $ L=-\displaystyle\sum\nolimits_{i=1}^{n}{\widehat{y}}_{i}\log\left({\widehat{y}}_{i}\right) $ 适用于分类任务. 二元交叉熵 $ L=-\dfrac{1}{n}\displaystyle\sum\nolimits_{i=1}^{n}\left[{\widehat{y}}_{i}\log\left({\widehat{y}}_{i}\right) + \left(1-{\widehat{y}}_{i}\right)\log\left({1-\widehat{y}}_{i}\right)\right] $ 二分类任务专用. Hinge Loss $ L=\max\left(\mathrm{0,1}-{y}_{i}\cdot {\widehat{y}}_{i}\right) $ 适用于SVM模型, 确保间隔最大化.
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表 3 评估指标及其特点
评估指标 公式 特点 准确率 $ Accuracy=\dfrac{TP + TN}{TP + TN + FP + FN} $ 简单直观, 但类别不平衡时失效. 精确率 $ Precision=\dfrac{TP}{TP + FP} $ 关注预测为正类的准确性. 召回率 $ Recall=\dfrac{TP}{TP + FN} $ 关注真实正类的覆盖率. F1分数 $ F1=2\times \dfrac{Precision\times Recall}{Precision + Recall} $ 平衡精确率与召回率. 均方误差 $ MSE=\dfrac{1}{n}\displaystyle\sum\nolimits_{i=1}^{n}{\left({y}_{i}-{\widehat{y}}_{i}\right)}^{2} $ 对异常值更加敏感. 均方根误差 $ RMSE=\sqrt{\dfrac{1}{n}\displaystyle\sum\nolimits_{i=1}^{n}{\left({y}_{i}-{\widehat{y}}_{i}\right)}^{2}} $ 可直接与真实值对比. 相对均方根误差 $ RRMSE=\sqrt{\dfrac{1}{n}\displaystyle\sum\nolimits_{i=1}^{n}{\left(\dfrac{{y}_{i}-{\widehat{y}}_{i}}{{y}_{i}}\right)}^{2}} $ 以百分比形式表示误差相对大小. 平均绝对误差 $ MAE=\dfrac{1}{n}\displaystyle\sum\nolimits_{i=1}^{n}\left\| {{y}_{i}-{\widehat{y}}_{i}} \right\| $ 简单直观, 鲁棒性强. 平均绝对百分比误差 $ MAPE=\dfrac{1}{n}\displaystyle\sum\nolimits_{i=1}^{n}\left\| {\dfrac{{y}_{i}-{\widehat{y}}_{i}}{{y}_{i}}} \right\| $ 以百分比形式表示误差相对大小. 决定系数 $ {R}^{2}=1-\dfrac{\displaystyle\sum {\left({y}_{i}-{\widehat{y}}_{i}\right)}^{2}}{\displaystyle\sum {\left({y}_{i}-\stackrel{-}{{y}_{i}}\right)}^{2}} $ 衡量预测结果与真实情况的拟合程度.
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表 4 高熵合金相选择性能对比(Huang W et al. 2019)
机器学习算法 测试准确率 限制因素 SVM 64.3% 不擅长处理多分类非线性问题 KNN (k = 2) 66.8% 数据分布不均衡 加权KNN (k = 3) 68.6% 数据分布不均衡 ANN 74.3% 选取特征并非决定相选择的最关键因素
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表 5 不同硬度预测模型的性能比较
模型 输入特征 预测性能 SVR (Whitman & Latypov 2025) ViT提取微观结构特征、成分特征 $ MAPE=12.6\% $ DNN (Li Y et al. 2020) 微观结构特征、$ \gamma ' $析出相面积分布、冷却速率 $ {R}^{2}=0.945 $ RFR (Xiong J et al. 2021) 平均价电子浓度、混合焓、电负性失配度、平均原子序数、摩尔热容失配度、平均热导率 $\begin{array}{l} {R}^{2}=0.821 \\ RRMSE=16.7\% \end{array}$ GBDT (Yu A et al. 2024) 激光功率、扫描速度、体能量密度、线能量密度 $\begin{array}{l}{R}^{2}=0.963 \\ MAE=2.059 \\ RMSE=3.844 \end{array}$ SR (Xiong J et al. 2020) 回火温度、碳含量、铬含量、钼含量 $\begin{array}{l} {R}^{2} > 0.888 \\ RRMSE < 3.25\% \end{array}$ RF (Xiong J et al. 2020) $ \begin{array}{l} {R}^{2} > 0.912 \\ RRMSE < 3.75\% \end{array}$
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表 6 金属材料疲劳寿命预测性能汇总
文献 模型 材料 预测性能 (Zhang Z et al. 2022) CDM-MLP 300M-AerMet100钢 $ {R}^{2}=0.650 $ (Wang H et al. 2022) SVM AlSi10Mg合金 $ {R}^{2}=0.927 $
$ MAPE=24.5\% $RF AlSi10Mg合金 $ {R}^{2}=0.874 $
$ MAPE=32.8\% $(Wang L et al. 2023) $ \delta \sigma $-ANN(框架A) Al-Mg4.5Mn合金 $ {R}^{2}=0.975 $
$ MAPE=12.3\% $$ \delta \sigma $-SVR(框架A) Al-Mg4.5Mn合金 $ {R}^{2}=0.942 $
$ MAPE=15.7\% $$ \delta \sigma $-ANN(框架B) Al-Mg4.5Mn合金 $ {R}^{2}=0.833 $
$ MAPE=22.6\% $$ \delta \sigma $-SVR(框架B) Al-Mg4.5Mn合金 $ {R}^{2}=0.925 $
$ MAPE=20.2\% $Paris-ANN(框架A) Al-Mg4.5Mn合金 $ {R}^{2}=0.943 $
$ MAPE=15.5\% $Paris-SVR(框架A) Al-Mg4.5Mn合金 $ {R}^{2}=0.939 $
$ MAPE=15.3\% $Paris-ANN(框架B) Al-Mg4.5Mn合金 $ {R}^{2}=0.912 $
$ MAPE=16.8\% $Paris-SVR(框架B) Al-Mg4.5Mn合金 $ {R}^{2}=0.984 $
$ MAPE=9.8\% $(Feng F et al. 2025) MPIBNN 316L不锈钢 $ {R}^{2}=0.895 $
$ MSE=0.014 $MPIBNN AlMg4.5Mn合金 $ {R}^{2}=0.902 $
$ MSE=0.032 $MPIBNN Ti6.5Al2ZrMoV合金 $ {R}^{2}=0.867 $
$ MSE=0.037 $
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表 7 金属材料屈服强度预测性能汇总
文献 模型 材料 预测性能 (Jiang L et al. 2022) $ {\mathrm{\sigma }}_{\mathrm{y}}=79\mathrm{W}/\left({\mathrm{S}}^{3}\sqrt{{\mathrm{l}}_{\mathrm{t}}}\right) + 1.2\sqrt{\mathrm{\gamma }\mathrm{E}/{\mathrm{l}}_{\mathrm{t}}}{\mathrm{d}}^{-0.5} $ 多晶金属 $ {R}^{2}=0.960 $ (Lee et al. 2024) $ \begin{aligned} {\mathrm{\sigma }}_{\mathrm{y}}=&{\mathrm{\sigma }}_{\mathrm{o}}^{\mathrm{*}}\mathrm{exp}\left(-\dfrac{2.526\mathrm{R}\mathrm{T}}{\Delta \mathrm{E}}\mathrm{l}\mathrm{n}\left(\dfrac{0.237{\dot{\mathrm{\varepsilon }}}_{\mathrm{*}}}{\dot{\mathrm{\varepsilon }}}\right)\right) +\\ &\mathrm{\alpha }\dfrac{\mathrm{G}}{\sqrt{\mathrm{\beta }\cdot \left(\dfrac{\mathrm{d}}{\mathrm{b}}\right)} + \mathrm{\gamma }\cdot 4\sqrt{\dfrac{\mathrm{\delta }{\mathrm{D}}_{\mathrm{g}\mathrm{b}}}{\dot{\mathrm{\varepsilon }}{\mathrm{d}}^{3}}} + \mathrm{\omega }}\end{aligned} $ 中熵合金
$ {Fe}_{60}{Co}_{15}{Ni}_{15}{Cr}_{10} $$ {R}^{2}=0.957 $
$ MAE=35.0MPa $集成树回归 $ {R}^{2}=0.925 $
$ MAE=53.7MPa $(Li Z et al. 2023) $ {\mathrm{\sigma }}_{\mathrm{y}}=0.4734 + 2.713\times {10}^{-5}\cdot \dfrac{{T}_{m}^{2}\cdot VED}{{V}_{m}\cdot {\chi }_{p}^{2}} $ 非晶合金 $ {R}^{2}=0.930 $ (Peng J et al. 2020) 随机森林 (RF) 9Cr钢 $ {R}^{2}=0.983 $
$ MAE=16.4MPa $(Kateb & Safarian 2025) 随机森林 (RF) 钢 $ {R}^{2}=0.845 $
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