卷積神經(jīng)網(wǎng)絡(luò)機(jī)器學(xué)習(xí)外文文獻(xiàn)翻譯中英文2020

1、 卷積神經(jīng)網(wǎng)絡(luò)機(jī)器學(xué)習(xí)相關(guān)外文翻譯中英文 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.中文基于卷積神經(jīng)網(wǎng)絡(luò)的復(fù)合材料微結(jié)構(gòu)應(yīng)力-應(yīng)變曲線預(yù)測(cè)查爾斯，吉姆，瑞恩

49、，格瑞斯摘要應(yīng)力-應(yīng)變曲線是材料機(jī)械性能的重要代表，從中可以定義重要的性能，例如彈性模量，強(qiáng)度和韌性。但是，從數(shù)值方法（例如有限元方法（FEM）生成應(yīng)力-應(yīng)變曲線的計(jì)算量很大，尤其是在考慮材料的整個(gè)失效路徑時(shí)。結(jié)果，難以對(duì)具有較大設(shè)計(jì)空間的材料進(jìn)行高通量計(jì)算設(shè)計(jì)，尤其是在考慮超出彈性極限的機(jī)械響應(yīng)時(shí)。在這項(xiàng)工作中，主成分分析（PCA）和卷積神經(jīng)網(wǎng)絡(luò)（CNN）的組合被用于預(yù)測(cè)在整個(gè)失效路徑上評(píng)估的二元復(fù)合材料的整體應(yīng)力 -應(yīng)變行為，這是由于經(jīng)驗(yàn)?zāi)Ｐ偷耐茢嗨俣蕊@著加快的緣故。我們展示了 PCA 通過可視化 PCA 的本征基礎(chǔ)將應(yīng)力-應(yīng)變曲線轉(zhuǎn)換為有效的潛在空間。盡管只有可能的微觀結(jié)構(gòu)配置的 10-

50、27的數(shù)據(jù)集，但在基于派生的材料描述符（例如模量，強(qiáng)度）測(cè)量模型性能時(shí)，預(yù)測(cè)的平均絕對(duì)誤差小于數(shù)據(jù)集中值范圍的 10和韌性。我們的研究表明使用機(jī)器學(xué)習(xí)11 來加速材料設(shè)計(jì)，表征和優(yōu)化的潛力。關(guān)鍵詞：機(jī)器學(xué)習(xí)，卷積神經(jīng)網(wǎng)絡(luò)，力學(xué)性能，微觀結(jié)構(gòu)，計(jì)算力學(xué)引言理解材料的結(jié)構(gòu)與性能之間的關(guān)系是材料科學(xué)中的一個(gè)重要問題，在設(shè)計(jì)下一代材料方面有重要的應(yīng)用。一個(gè)主要的動(dòng)機(jī)示例是設(shè)計(jì)用于承重應(yīng)用的復(fù)合材料微結(jié)構(gòu)，因?yàn)閺?fù)合材料可提供有利的高比強(qiáng)度和比韌性。增材制造的最新進(jìn)展促進(jìn)了復(fù)雜復(fù)合結(jié)構(gòu)的制造，結(jié)果，通過 3D 打印方法制造并測(cè)試了各種復(fù)雜設(shè)計(jì)。盡管更先進(jìn)的制造技術(shù)為先進(jìn)的材料和新穎的功能性開辟了前所未有的

51、機(jī)遇，但要確定具有所需性能的微結(jié)構(gòu)卻是一個(gè)困難的優(yōu)化問題。確定最佳組合設(shè)計(jì)的一種方法是構(gòu)建分析理論。對(duì)于常規(guī)的顆粒/纖維增強(qiáng)復(fù)合材料，已開發(fā)出多種均質(zhì)化理論來預(yù)測(cè)復(fù)合材料的機(jī)械性能隨增強(qiáng)材料的體積分?jǐn)?shù)，縱橫比和取向分布的變化。由于許多通過自組裝過程合成的天然復(fù)合材料具有相對(duì)周期性和規(guī)則的結(jié)構(gòu)，因此，如果了解代表性單位晶格的載荷傳遞機(jī)理和自相似分層結(jié)構(gòu)的作用，則可以預(yù)測(cè)其機(jī)械性能。但是，在存在缺陷的情況下，分析理論的應(yīng)用范圍僅限于定量預(yù)測(cè)超出彈性極限的復(fù)合材料性能，因?yàn)榇祟惱碚撘蕾囉诖眢w積元素（RVE）的概念，即材料性能的統(tǒng)計(jì)表示，而強(qiáng)度和強(qiáng)度失敗取決于整個(gè)樣本域中最弱的缺陷?；谟邢拊椒ǎ?/p>

52、FEM）的數(shù)值建?？梢匝a(bǔ)充用于預(yù)測(cè)非彈性屬性（例如強(qiáng)度和韌性模量，以下簡稱韌性）的分析方法，這些方法只能從完整的應(yīng)力 -應(yīng)12 變曲線獲得。但是，由于需要非常細(xì)的網(wǎng)格來適應(yīng)裂紋尖端附近的高度集中的應(yīng)力場(chǎng)，因此能夠模擬曲線裂紋的萌生和擴(kuò)展的數(shù)值模式（例如裂紋相場(chǎng)模型）在計(jì)算上是昂貴且費(fèi)時(shí)的。擴(kuò)散裂紋表面附近損傷參數(shù)的變化。同時(shí)，分析模型需要大量的人力和領(lǐng)域?qū)I(yè)知識(shí)，并且不能推廣到類似的領(lǐng)域問題。為了在現(xiàn)實(shí)的時(shí)間內(nèi)在大型設(shè)計(jì)空間中識(shí)別出高性能的復(fù)合材料，我們需要能夠快速描述復(fù)雜系統(tǒng)的機(jī)械性能并易于推廣到類似系統(tǒng)的模型。機(jī)器學(xué)習(xí)提供了極快的推理時(shí)間的優(yōu)勢(shì)，并且僅需訓(xùn)練數(shù)據(jù)即可學(xué)習(xí)輸入和輸出之間的關(guān)系

53、，例如復(fù)合微結(jié)構(gòu)及其機(jī)械性能。機(jī)器學(xué)習(xí)已被應(yīng)用來加速幾個(gè)不同物理系統(tǒng)的優(yōu)化，包括石墨烯 kirigami 切割，微調(diào)自旋 qubit 參數(shù)和探針顯微鏡微調(diào)。這樣的模型不需要大量的人工干預(yù)或知識(shí)，不需要相對(duì)于輸入設(shè)計(jì)空間有效地學(xué)習(xí)關(guān)系，并且可以推廣到不同的系統(tǒng)。在本文中，我們結(jié)合主成分分析（PCA）和卷積神經(jīng)網(wǎng)絡(luò)（CNN）來預(yù)測(cè)超出彈性極限的復(fù)合材料破壞的整個(gè)應(yīng)力 -應(yīng)變曲線。選擇應(yīng)力-應(yīng)變曲線作為模型的目標(biāo)，因?yàn)殍b于它們的高維數(shù)，它們很難預(yù)測(cè)。另外，應(yīng)力-應(yīng)變曲線用于導(dǎo)出重要的材料描述，如模量，強(qiáng)度和韌性。從這個(gè)意義上講，預(yù)測(cè)應(yīng)力 -應(yīng)變曲線是比定標(biāo)器材料描述符的任何組合更全面的復(fù)合材料性能描

54、述。100,000 個(gè)不同的復(fù)合微結(jié)構(gòu)及其對(duì)應(yīng)的應(yīng)力-應(yīng)變曲線的數(shù)據(jù)集用于訓(xùn)練和評(píng)估模型性能。由于應(yīng)力 -應(yīng)變數(shù)據(jù)集的高維性，因此使用了多種降維方法，包括PCA，該方法將領(lǐng)域理解和傳統(tǒng)機(jī)器學(xué)習(xí)相結(jié)合，從而簡化了問題，13 而又不損失模型的一般性。我們將首先描述建模方法和用于生成數(shù)據(jù)的有限元方法（FEM）的參數(shù)。然后呈現(xiàn)學(xué)習(xí)到的 PCA 潛在空間的可視化以及模型性能結(jié)果。CNN 的實(shí)施和培訓(xùn)卷積神經(jīng)網(wǎng)絡(luò)經(jīng)過訓(xùn)練可以預(yù)測(cè)應(yīng)力向量的這種較低維表示。CNN 的輸入是代表復(fù)合設(shè)計(jì)的二進(jìn)制矩陣，其中 0 對(duì)應(yīng)于軟塊，而 1對(duì)應(yīng)于硬塊。 PCA 是使用默認(rèn)的超參數(shù)通過開源 Python 軟件包scikit-

55、learn 實(shí)現(xiàn)的。 CNN 是使用 Keras 與 TensorFlow 后端實(shí)現(xiàn)的。所有實(shí)驗(yàn)的批次大小均設(shè)置為 16，歷時(shí)數(shù)設(shè)置為 30。 Adam 優(yōu)化器用于在反向傳播期間更新 CNN 權(quán)重。使用的火車/測(cè)試拆分比率為 95：5 由于數(shù)據(jù)集相對(duì)較大，因此我們使用比標(biāo)準(zhǔn) 80:20 小的比率進(jìn)行驗(yàn)證。比率為 95：5 且具有100,000 個(gè)實(shí)例的數(shù)據(jù)集，測(cè)試集大小仍然具有足夠的數(shù)據(jù)點(diǎn)（大約幾千個(gè)），以便將其結(jié)果推廣。將目標(biāo) PCA 表示的每一列標(biāo)準(zhǔn)化為平均值為 0，標(biāo)準(zhǔn)差為 1，以防止訓(xùn)練不穩(wěn)定。有限元方法數(shù)據(jù)生成FEM 用于生成 CNN 模型的訓(xùn)練數(shù)據(jù)。盡管最初獲得的訓(xùn)練數(shù)據(jù)是計(jì)算密集

56、型的，但訓(xùn)練 CNN 模型所需的時(shí)間要少得多，并且可以對(duì)成千上萬個(gè)新的，隨機(jī)生成的復(fù)合物進(jìn)行高吞吐量推斷的時(shí)間更少。裂紋相場(chǎng)求解器基于用于彈性固體準(zhǔn)靜態(tài)斷裂的混合公式，并在帶有用戶元素子例程（UEL）的商業(yè) FEM 軟件 ABAQUS 中實(shí)現(xiàn)。14 可視化 PCA為了更好地理解 PCA 在有效捕獲應(yīng)力-應(yīng)變曲線中包含的信息中所起的作用，應(yīng)力-應(yīng)變曲線的主成分表示形式分為 3 維。具體來說，我們采用前三個(gè)主要成分，它們具有 85的累積解釋方差，并在此基礎(chǔ)上繪制應(yīng)力-應(yīng)變曲線，并提供幾個(gè)不同的角度來查看 3D 繪圖。每個(gè)點(diǎn)代表 PCA 潛在空間中的應(yīng)力-應(yīng)變曲線，并根據(jù)關(guān)聯(lián)的模量值進(jìn)行著色。似乎 PCA 能夠基于模量值在潛在空間中展開曲線，這表明這是 CNN 進(jìn)行預(yù)測(cè)的有用潛在空間。CNN