卷积神经网络机器学习外文文献翻译中英文2020

1、 卷积神经网络机器学习相关外文翻译中英文 2020英文Prediction of composite microstructure stress-strain curves usingconvolutional neural networksCharles Yang，Youngsoo Kim，Seunghwa Ryu，Grace GuAbstractStress-strain curves are an important representation of a materialsmechanical properties, from which important properties su

2、ch as elasticmodulus, strength, and toughness, are defined. However, generatingstress-strain curves from numerical methods such as finite elementmethod (FEM) is computationally intensive, especially when consideringthe entire failure path for a material. As a result, it is difficult to performhigh t

3、hroughput computational design of materials with large designspaces, especially when considering mechanical responses beyond theelastic limit. In this work, a combination of principal component analysis(PCA) and convolutional neural networks (CNN) are used to predict theentire stress-strain behavior

4、 of binary composites evaluated over theentire failure path, motivated by the significantly faster inference speed ofempirical models. We show that PCA transforms the stress-strain curvesinto an effective latent space by visualizing the eigenbasis of PCA.Despite having a dataset of only 10-27% of po

5、ssible microstructureconfigurations, the mean absolute error of the prediction is 10% of the1 range of values in the dataset, when measuring model performance basedon derived material descriptors, such as modulus, strength, and toughness.Our study demonstrates the potential to use machine learning t

6、oaccelerate material design, characterization, and optimization.Keywords：Machine learning，Convolutional neural networks，Mechanical properties，Microstructure，Computational mechanicsIntroductionUnderstanding the relationship between structure and property formaterials is a seminal problem in material

7、science, with significantapplications for designing next-generation materials. A primarymotivating example is designing composite microstructures forload-bearing applications, as composites offer advantageously highspecific strength and specific toughness. Recent advancements in additivemanufacturin

8、g have facilitated the fabrication of complex compositestructures, and as a result, a variety of complex designs have beenfabricated and tested via 3D-printing methods. While more advancedmanufacturing techniques are opening up unprecedented opportunities foradvanced materials and novel functionalit

9、ies, identifying microstructureswith desirable properties is a difficult optimization problem.One method of identifying optimal composite designs is byconstructinganalyticaltheories.Forconventionalparticulate/fiber-reinforced composites, a variety of homogenization2 theories have been developed to p

10、redict the mechanical properties ofcomposites as a function of volume fraction, aspect ratio, and orientationdistribution of reinforcements. Because many natural composites,synthesized via self-assembly processes, have relatively periodic andregular structures, their mechanical properties can be pre

11、dicted if the loadtransfer mechanism of a representative unit cell and the role of theself-similar hierarchical structure are understood. However, theapplicability of analytical theories is limited in quantitatively predictingcomposite properties beyond the elastic limit in the presence of defects,b

12、ecause such theories rely on the concept of representative volumeelement (RVE), a statistical representation of material properties, whereasthe strength and failure is determined by the weakest defect in the entiresample domain. Numerical modeling based on finite element methods(FEM) can complement

13、analytical methods for predicting inelasticproperties such as strength and toughness modulus (referred to astoughness, hereafter) which can only be obtained from full stress-straincurves.However, numerical schemes capable of modeling the initiation andpropagation of the curvilinear cracks, such as t

14、he crack phase field model,are computationally expensive and time-consuming because a very finemesh is required to accommodate highly concentrated stress field nearcrack tip and the rapid variation of damage parameter near diffusive crack3 surface. Meanwhile, analytical models require significant hu

15、man effortand domain expertise and fail to generalize to similar domain problems.In order to identify high-performing composites in the midst of largedesign spaces within realistic time-frames, we need models that canrapidly describe the mechanical properties of complex systems and begeneralized eas

16、ily to analogous systems. Machine learning offers thebenefit of extremely fast inference times and requires only training data tolearn relationships between inputs and outputs e.g., compositemicrostructures and their mechanical properties. Machine learning hasalready been applied to speed up the opt

17、imization of several differentphysical systems, including graphene kirigami cuts, fine-tuning spin qubitparameters, and probe microscopy tuning. Such models do not requiresignificant human intervention or knowledge, learn relationshipsefficiently relative to the input design space, and can be genera

18、lized todifferent systems.In this paper, we utilize a combination of principal componentanalysis (PCA) and convolutional neural networks (CNN) to predict theentire stress-strain curve of composite failures beyond the elastic limit.Stress-strain curves are chosen as the models target because they are

19、difficult to predict given their high dimensionality. In addition,stress-strain curves are used to derive important material descriptors suchas modulus, strength, and toughness. In this sense, predicting stress-strain4 curves is a more general description of composites properties than anycombination

20、 of scaler material descriptors. A dataset of 100,000 differentcomposite microstructures and their corresponding stress-strain curves areused to train and evaluate model performance. Due to the highdimensionality of the stress-strain dataset, several dimensionalityreduction methods are used, includi

21、ng PCA, featuring a blend of domainunderstanding and traditional machine learning, to simplify the problemwithout loss of generality for the model.We will first describe our modeling methodology and the parametersof our finite-element method (FEM) used to generate data. Visualizationsof the learned

22、PCA latent space are then presented, along with modelperformance results.CNN implementation and trainingA convolutional neural network was trained to predict this lowerdimensional representation of the stress vector. The input to the CNN wasa binary matrix representing the composite design, with 0s

23、correspondingto soft blocks and 1s corresponding to stiff blocks. PCA wasimplemented with the open-source Python package scikit-learn, using thedefault hyperparameters. CNN was implemented using Keras with aTensorFlow backend. The batch size for all experiments was set to 16 andthe number of epochs

24、to 30; the Adam optimizer was used to update theCNN weights during backpropagation.5 A train/test split ratio of 95:5 is used we justify using a smallerratio than the standard 80:20 because of a relatively large dataset. With aratio of 95:5 and a dataset with 100,000 instances, the test set size sti

25、ll hasenough data points, roughly several thousands, for its results to generalize.Each column of the target PCA-representation was normalized to have amean of 0 and a standard deviation of 1 to prevent instable training.Finite element method data generationFEM was used to generate training data for

26、 the CNN model.Although initially obtained training data is compute-intensive, it takesmuch less time to train the CNN model and even less time to makehigh-throughput inferences over thousands of new, randomly generatedcomposites. The crack phase field solver was based on the hybridformulation for t

27、he quasi-static fracture of elastic solids and implementedin the commercial FEM software ABAQUS with a user-elementsubroutine (UEL).Visualizing PCAIn order to better understand the role PCA plays in effectivelycapturing the information contained in stress-strain curves, the principalcomponent repres

28、entation of stress-strain curves is plotted in 3dimensions. Specifically, we take the first three principal components,which have a cumulative explained variance 85%, and plot stress-straincurves in that basis and provide several different angles from which to6 view the 3D plot. Each point represent

29、s a stress-strain curve in the PCAlatent space and is colored based on the associated modulus value. itseems that the PCA is able to spread out the curves in the latent spacebased on modulus values, which suggests that this is a useful latent spacefor CNN to make predictions in.CNN model design and

30、performanceOur CNN was a fully convolutional neural network i.e. the onlydense layer was the output layer. All convolution layers used 16 filterswith a stride of 1, with a LeakyReLU activation followed byBatchNormalization. The first 3 Conv blocks did not have 2DMaxPooling, followed by 9 conv blocks

31、 which did have a 2DMaxPooling layer, placed after the BatchNormalization layer. AGlobalAveragePooling was used to reduce the dimensionality of theoutput tensor from the sequential convolution blocks and the final outputlayer was a Dense layer with 15 nodes, where each node corresponded toa principa

32、l component. In total, our model had 26,319 trainable weights.Our architecture was motivated by the recent development andconvergence onto fully-convolutional architectures for traditionalcomputer vision applications, where convolutions are empiricallyobserved to be more efficient and stable for lea

33、rning as opposed to denselayers. In addition, in our previous work, we had shown that CNNs were7 a capable architecture for learning to predict mechanical properties of 2Dcomposites 30. The convolution operation is an intuitively good fit forpredicting crack propagation because it is a local operati

34、on, allowing it toimplicitly featurize and learn the local spatial effects of crackpropagation.After applying PCA transformation to reduce the dimensionality ofthe target variable, CNN is used to predict the PCA representation of thestress-strain curve of a given binary composite design. After train

35、ing theCNN on a training set, its ability to generalize to composite designs it hasnot seen is evaluated by comparing its predictions on an unseen test set.However, a natural question that emerges is how to evaluate a modelsperformance at predicting stress-strain curves in a real-world engineeringco

36、ntext. While simple scaler metrics such as mean squared error (MSE)and mean absolute error (MAE) generalize easily to vector targets, it isnot clear how to interpret these aggregate summaries of performance. It isdifficult to use such metrics to ask questions such as “Is this model goodenough to use

37、 in the real world” and “On average, how poorly will agiven prediction be incorrect relative to some given specification”.Although being able to predict stress-strain curves is an importantapplication of FEM and a highly desirable property for any machinelearning model to learn, it does not easily l

38、end itself to interpretation.Specifically, there is no simple quantitative way to define whether two8 stress-strain curves are “close” or “simi-lwaro”rld uwniitt sh. realGiven that stress-strain curves are oftentimes intermediaryrepresentations of a composite property that are used to derive moremea

39、ningful descriptors such as modulus, strength, and toughness, wedecided to evaluate the model in an analogous fashion. The CNNprediction in the PCA latent space representation is transformed back to astress-strain curve using PCA, and used to derive the predicted modulus,strength, and toughness of t

40、he composite. The predicted materialdescriptors are then compared with the actual material descriptors. In thisway, MSE and MAE now have clearly interpretable units and meanings.The average performance of the model with respect to the error betweenthe actual and predicted material descriptor values

41、derived fromstress-strain curves are presented in Table. The MAE for materialdescriptors provides an easily interpretable metric of model performanceand can easily be used in any design specification to provide confidenceestimates of a model prediction. When comparing the mean absolute error(MAE) to

42、 the range of values taken on by the distribution of materialdescriptors, we can see that the MAE is relatively small compared to therange. The MAE compared to the range is 10% for all materialdescriptors. Relatively tight confidence intervals on the error indicate thatthis model architecture is sta

43、ble, the model performance is not heavilydependent on initialization, and that our results are robust to different9 train-test splits of the data.Future workFuture work includes combining empirical models with optimizationalgorithms, such as gradient-based methods, to identify compositedesigns that

44、yield complementary mechanical properties. The ability of atrained empirical model to make high-throughput predictions overdesigns it has never seen before allows for large parameter spaceoptimization that would be computationally infeasible for FEM. Inaddition, we plan to explore different visualiz

45、ations of empirical modelsin an effort to “open up the black-box” of such models. Applying machinelearning to finite-element methods is a rapidly growing field with thepotential to discover novel next-generation materials tailored for a varietyof applications. We also note that the proposed method c

46、an be readilyapplied to predict other physical properties represented in a similarvectorized format, such as electron/phonon density of states, andsound/light absorption spectrum.ConclusionIn conclusion, we applied PCA and CNN to rapidly and accuratelypredict the stress-strain curves of composites b

47、eyond the elastic limit. Indoing so, several novel methodological approaches were developed,including using the derived material descriptors from the stress-straincurves as interpretable metrics for model performance and dimensionality10 reduction techniques to stress-strain curves. This method has

48、the potentialto enable composite design with respect to mechanical response beyondthe elastic limit, which was previously computationally infeasible, andcan generalize easily to related problems outside of microstructuraldesign for enhancing mechanical properties.中文基于卷积神经网络的复合材料微结构应力-应变曲线预测查尔斯，吉姆，瑞恩

49、，格瑞斯摘要应力-应变曲线是材料机械性能的重要代表，从中可以定义重要的性能，例如弹性模量，强度和韧性。但是，从数值方法（例如有限元方法（FEM）生成应力-应变曲线的计算量很大，尤其是在考虑材料的整个失效路径时。结果，难以对具有较大设计空间的材料进行高通量计算设计，尤其是在考虑超出弹性极限的机械响应时。在这项工作中，主成分分析（PCA）和卷积神经网络（CNN）的组合被用于预测在整个失效路径上评估的二元复合材料的整体应力 -应变行为，这是由于经验模型的推断速度显着加快的缘故。我们展示了 PCA 通过可视化 PCA 的本征基础将应力-应变曲线转换为有效的潜在空间。尽管只有可能的微观结构配置的 10-

50、27的数据集，但在基于派生的材料描述符（例如模量，强度）测量模型性能时，预测的平均绝对误差小于数据集中值范围的 10和韧性。我们的研究表明使用机器学习11 来加速材料设计，表征和优化的潜力。关键词：机器学习，卷积神经网络，力学性能，微观结构，计算力学引言理解材料的结构与性能之间的关系是材料科学中的一个重要问题，在设计下一代材料方面有重要的应用。一个主要的动机示例是设计用于承重应用的复合材料微结构，因为复合材料可提供有利的高比强度和比韧性。增材制造的最新进展促进了复杂复合结构的制造，结果，通过 3D 打印方法制造并测试了各种复杂设计。尽管更先进的制造技术为先进的材料和新颖的功能性开辟了前所未有的

51、机遇，但要确定具有所需性能的微结构却是一个困难的优化问题。确定最佳组合设计的一种方法是构建分析理论。对于常规的颗粒/纤维增强复合材料，已开发出多种均质化理论来预测复合材料的机械性能随增强材料的体积分数，纵横比和取向分布的变化。由于许多通过自组装过程合成的天然复合材料具有相对周期性和规则的结构，因此，如果了解代表性单位晶格的载荷传递机理和自相似分层结构的作用，则可以预测其机械性能。但是，在存在缺陷的情况下，分析理论的应用范围仅限于定量预测超出弹性极限的复合材料性能，因为此类理论依赖于代表体积元素（RVE）的概念，即材料性能的统计表示，而强度和强度失败取决于整个样本域中最弱的缺陷。基于有限元方法（

52、FEM）的数值建模可以补充用于预测非弹性属性（例如强度和韧性模量，以下简称韧性）的分析方法，这些方法只能从完整的应力 -应12 变曲线获得。但是，由于需要非常细的网格来适应裂纹尖端附近的高度集中的应力场，因此能够模拟曲线裂纹的萌生和扩展的数值模式（例如裂纹相场模型）在计算上是昂贵且费时的。扩散裂纹表面附近损伤参数的变化。同时，分析模型需要大量的人力和领域专业知识，并且不能推广到类似的领域问题。为了在现实的时间内在大型设计空间中识别出高性能的复合材料，我们需要能够快速描述复杂系统的机械性能并易于推广到类似系统的模型。机器学习提供了极快的推理时间的优势，并且仅需训练数据即可学习输入和输出之间的关系

53、，例如复合微结构及其机械性能。机器学习已被应用来加速几个不同物理系统的优化，包括石墨烯 kirigami 切割，微调自旋 qubit 参数和探针显微镜微调。这样的模型不需要大量的人工干预或知识，不需要相对于输入设计空间有效地学习关系，并且可以推广到不同的系统。在本文中，我们结合主成分分析（PCA）和卷积神经网络（CNN）来预测超出弹性极限的复合材料破坏的整个应力 -应变曲线。选择应力-应变曲线作为模型的目标，因为鉴于它们的高维数，它们很难预测。另外，应力-应变曲线用于导出重要的材料描述，如模量，强度和韧性。从这个意义上讲，预测应力 -应变曲线是比定标器材料描述符的任何组合更全面的复合材料性能描

54、述。100,000 个不同的复合微结构及其对应的应力-应变曲线的数据集用于训练和评估模型性能。由于应力 -应变数据集的高维性，因此使用了多种降维方法，包括PCA，该方法将领域理解和传统机器学习相结合，从而简化了问题，13 而又不损失模型的一般性。我们将首先描述建模方法和用于生成数据的有限元方法（FEM）的参数。然后呈现学习到的 PCA 潜在空间的可视化以及模型性能结果。CNN 的实施和培训卷积神经网络经过训练可以预测应力向量的这种较低维表示。CNN 的输入是代表复合设计的二进制矩阵，其中 0 对应于软块，而 1对应于硬块。 PCA 是使用默认的超参数通过开源 Python 软件包scikit-

55、learn 实现的。 CNN 是使用 Keras 与 TensorFlow 后端实现的。所有实验的批次大小均设置为 16，历时数设置为 30。 Adam 优化器用于在反向传播期间更新 CNN 权重。使用的火车/测试拆分比率为 95：5 由于数据集相对较大，因此我们使用比标准 80:20 小的比率进行验证。比率为 95：5 且具有100,000 个实例的数据集，测试集大小仍然具有足够的数据点（大约几千个），以便将其结果推广。将目标 PCA 表示的每一列标准化为平均值为 0，标准差为 1，以防止训练不稳定。有限元方法数据生成FEM 用于生成 CNN 模型的训练数据。尽管最初获得的训练数据是计算密集

56、型的，但训练 CNN 模型所需的时间要少得多，并且可以对成千上万个新的，随机生成的复合物进行高吞吐量推断的时间更少。裂纹相场求解器基于用于弹性固体准静态断裂的混合公式，并在带有用户元素子例程（UEL）的商业 FEM 软件 ABAQUS 中实现。14 可视化 PCA为了更好地理解 PCA 在有效捕获应力-应变曲线中包含的信息中所起的作用，应力-应变曲线的主成分表示形式分为 3 维。具体来说，我们采用前三个主要成分，它们具有 85的累积解释方差，并在此基础上绘制应力-应变曲线，并提供几个不同的角度来查看 3D 绘图。每个点代表 PCA 潜在空间中的应力-应变曲线，并根据关联的模量值进行着色。似乎 PCA 能够基于模量值在潜在空间中展开曲线，这表明这是 CNN 进行预测的有用潜在空间。CNN