Microstructure Dataset Research Articles

Multi-plane denoising diffusion-based dimensionality expansion for 2D-to-3D reconstruction of microstructures with harmonized sampling

Acquiring reliable microstructure datasets is a pivotal step toward the systematic design of materials with the aid of integrated computational materials engineering (ICME) approaches. However, obtaining three-dimensional (3D) microstructure datasets is often challenging due to high experimental costs or technical limitations, while acquiring two-dimensional (2D) micrographs is comparatively easier. To deal with this issue, this study proposes a novel framework called ‘Micro3Diff’ for 2D-to-3D reconstruction of microstructures using diffusion-based generative models (DGMs). Specifically, this approach solely requires pre-trained DGMs for the generation of 2D samples, and dimensionality expansion (2D-to-3D) takes place only during the generation process (i.e., reverse diffusion process). The proposed framework incorporates a concept referred to as ‘multi-plane denoising diffusion’, which transforms noisy samples (i.e., latent variables) from different planes into the data structure while maintaining spatial connectivity in 3D space. Furthermore, a harmonized sampling process is developed to address possible deviations from the reverse Markov chain of DGMs during the dimensionality expansion. Combined, we demonstrate the feasibility of Micro3Diff in reconstructing 3D samples with connected slices that maintain morphologically equivalence to the original 2D images. To validate the performance of Micro3Diff, various types of microstructures (synthetic or experimentally observed) are reconstructed, and the quality of the generated samples is assessed both qualitatively and quantitatively. The successful reconstruction outcomes inspire the potential utilization of Micro3Diff in upcoming ICME applications while achieving a breakthrough in comprehending and manipulating the latent space of DGMs.

ResUNet involved generative adversarial network-based topology optimization for design of 2D microstructure with extreme material properties

Topology optimization is one of the most common methods for design of material distribution in mechanical metamaterials, but resulting in expensive computational cost due to iterative simulation of finite element method. In this work, a novel deep learning-based topology optimization method is proposed to design mechanical microstructure efficiently for metamaterials with extreme material properties, such as maximum bulk modulus, maximum shear modulus, or negative Poisson’s ratio. Large numbers of microstructures with various configurations are first simulated by modified solid isotropic material with penalization (SIMP), to construct the microstructure data set. Subsequently, the ResUNet involved generative and adversarial network (ResUNet-GAN) is developed for high-dimensional mapping between optimization parameters and corresponding microstructures to improve the design accuracy of ResUNet. By given optimization parameters, the well-trained ResUNet-GAN is successfully applied to the microstructure design of metamaterials with different optimization objectives under proper configurations. According to the simulation results, the proposed ResUNet-GAN-based topology optimization not only significantly reduces the computational duration for the optimization process, but also improves the structure precise and mechanical performance.

Active learning for regression of structure–property mapping: the importance of sampling and representation

We develop an active workflow for calibrating microstructure–property relationships when a large dataset of microstructures is available, but the cost associated with evaluating the properties associated is high.

Performance-based design of 2D gas diffusion layer microstructure using denoising diffusion probabilistic model

This paper proposes a performance-based microstructure design methodology specifically tailored for gas diffusion layers (GDLs). The generative machine learning denoising diffusion probabilistic model (DDPM) is trained and used for performance-based microstructure design. This study demonstrates significant progress in performance-based design by incorporating DDPM into the microstructure design process, offering a promising approach for GDL microstructure design. This methodology provides the advantage of generating 2D microstructures with desired permeability and volume fractions. Moreover, it is not limited to a specific performance criterion, making it adaptable to target other metrics. To train the DDPM, a 2D GDL microstructure dataset is constructed using the Lattice Boltzmann Method (LBM) for permeability estimation. Subsequently, we employ the DDPM with U-net architecture, which leverages positional encoding to learn the microstructure’s volume fraction and permeability effectively. The input label pair of permeability and volume fraction is generated considering the inherent relationship between these two parameters to ensure the generation of meaningful microstructures. This relationship is supposed to ensure that the resulting microstructures align with realistic and physically meaningful characteristics. The simulated performance results obtained from the generated microstructures using the proposed methodology demonstrate a strong consistency with the targeted performance objectives.

GRAF: Gap region aware framework for Al-Si alloy microscopic image segmentation

The shape of the primary silicon in Al-Si alloys is one of the main factors determining the properties of the alloy, which makes the microscopic image of Al-Si alloys become a crucial reference material in the study of the alloy. Accurate segmentation of silicon particles in Al-Si alloy micrographs is a necessary prerequisite for their quantitative analysis. The traditional manual annotation method requires high time and labor costs and will be affected by subjective factors of the annotator. Although automatic image segmentation methods can avoid these problems, there are silicon particles of different shapes and sizes in the Al-Si alloy microscopic image, and it is hard to separate adjacent silicon particles. These characteristics bring the automatic segmentation method severe challenge. Therefore, to address the issue of deviation in the annotation range when there is agglomeration of primary silicon particles in the microstructure images of Al-Si alloys, We propose a Residual Position-Aware Attention Network (RPAA-Net) for the segmentation of primary silicon particles. The RPAA-Net method enhances segmentation accuracy and robustness by incorporating a residual position-aware attention mechanism, enabling the network to better distinguish silicon particles from the surrounding non-silicon regions. To address the challenge of separating adjacent silicon particles in the image, we introduce a novel Gap Region Weighting Strategy (GRWS). GRWS enhances the model's focus on the gap regions between adjacent objects by applying additional weights during training. By combining RPAA-Net with GRWS, we construct a Gap Region Awareness Framework (GRAF) and experiment with different weights. We find that the weight with the most significant impact is 10, leading to the framework being named GRAF-10. Finally, we apply GRAF-10 to the Aluminum-Silicon Alloy Microstructure (ASAM) dataset. The results show that GRAF-10 outperforms the current state-of-the-art methods, improving the object-level Dice index(Dobj) by 1.56%. Additionally, it reduces the Merge Error (ME) metric by 6.74 and the Variation of Information (VI) metric by 5.43, effectively segmenting aluminum–silicon alloy microstructure images.

A simulation-driven supervised learning framework to estimate brain microstructure using diffusion MRI

We propose a framework to train supervised learning models on synthetic data to estimate brain microstructure parameters using diffusion magnetic resonance imaging (dMRI). Although further validation is necessary, the proposed framework aims to seamlessly incorporate realistic simulations into dMRI microstructure estimation.Synthetic data were generated from over 1,000 neuron meshes converted from digital neuronal reconstructions and linked to their neuroanatomical parameters (such as soma volume and neurite length) using an optimized diffusion MRI simulator that produces intracellular dMRI signals from the solution of the Bloch–Torrey partial differential equation. By combining random subsets of simulated neuron signals with a free diffusion compartment signal, we constructed a synthetic dataset containing dMRI signals and 40 tissue microstructure parameters of 1.45 million artificial brain voxels.To implement supervised learning models we chose multilayer perceptrons (MLPs) and trained them on a subset of the synthetic dataset to estimate some microstructure parameters, namely, the volume fractions of soma, neurites, and the free diffusion compartment, as well as the area fractions of soma and neurites. The trained MLPs perform satisfactorily on the synthetic test sets and give promising in-vivo parameter maps on the MGH Connectome Diffusion Microstructure Dataset (CDMD). Most importantly, the estimated volume fractions showed low dependence on the diffusion time, the diffusion time independence of the estimated parameters being a desired property of quantitative microstructure imaging.The synthetic dataset we generated will be valuable for the validation of models that map between the dMRI signals and microstructure parameters. The surface meshes and microstructures parameters of the aforementioned neurons have been made publicly available.

A deep adversarial approach for the generation of synthetic titanium alloy microstructures with limited training data

Microstructures play a central role in determining the mechanical and functional properties of a material. An important aspect in computational materials science is to reliably predict the key microstructural features, and to utilise them in bridging the processing and properties of new materials. The existing microstructure characterization and reconstruction (MCR) techniques have inherent limitations in terms of the lack of design variables and information loss due to various assumptions. In previous studies, Generative Adversarial Network (GAN) models were trained using more than 10,000 image datasets, however without performance analysis using quantitative morphometric and statistical measures. In this perspective, the present work demonstrates the capability of GAN architectures to learn the mapping between random latent vectors and synthetic microstructural images, even in a limited data regime (1225 images). Three different architectures Deep Convolutional GAN (DCGAN) ,Wasserstein GAN- Gradient Penalty (WGAN-GP), StyleGAN2- Adaptive Discriminator Augmentation (ADA) were explored, together with comprehensive statistical and morphological analysis, while training on a publicly accessible Ti-6Al-4V (Ti64) alloy microstructure dataset. The StyleGAN2-ADA outperforms the other two GAN models to generate realistic synthetic microstructures of higher resolution, with good qualitative similarity to original images. The analysis of performance metrics, like Frechet Inception Distance (FID), Kernel Inception Distance (KID), and Inception Score (IS) scores, reveal that the generated image distribution is statistically close to the original distribution of microstructural features. The morphometric parameters, including α/β phase fractions, local α/β boundary thickness, and orientation of lamellar morphology, were also used to compare original and synthetic images quantitatively. More importantly, two-point correlation and t-stochastic neighbour embedding (t-SNE) illustrate the statistical similarity between the original and synthetic microstructures. Taken together, the present work establishes the capability of generative models like GAN in generating representative microstructures of Titanium alloy in a statistically reliable manner. Such an approach, when adopted, will accelerate the field of microstructure fingerprinting.

Numerical microstructural optimization for the hydrogen electrode of solid oxide cells

AbstractA multiscale model has been used to optimize the microstructure of a classical hydrogen electrode made of nickel and yttria‐stabilized zirconia (Ni‐8YSZ). For this purpose, a 3D reconstruction of a reference electrode has been obtained by X‐ray nano‐holotomography. Then, a large dataset of synthetic microstructures has been generated around this reference with the truncated Gaussian random field method, varying the ratio Ni/8YSZ and the Ni particle size. All the synthetic microstructures have been introduced in a multiscale modeling approach to analyze the impact of the microstructure on the electrode and cell responses. The local electrode polarization resistance in the hydrogen electrode, as well as the complete cell impedance spectra, have been computed for the different microstructures. A significant performance improvement was found when decreasing the Ni particle size distribution. Moreover, an optimum has been identified in terms of electrode composition allowing the minimization of the cell polarization resistance. The same methodology has been also applied to assess the relevance of graded electrodes. All these results allow a better understanding of the precise role of microstructure on cell performances and provide useful guidance for cell manufacturing.

Application of Deep Learning Image Segmentation to Synchrotron Radiation µCT Bone Microstructure Datasets.

Application of Deep Learning Image Segmentation to Synchrotron Radiation µCT Bone Microstructure Datasets.

Diffusion MRI data analysis assisted by deep learning synthesized anatomical images (DeepAnat).

Diffusion MRI is a useful neuroimaging tool for non-invasive mapping of human brain microstructure and structural connections. The analysis of diffusion MRI data often requires brain segmentation, including volumetric segmentation and cerebral cortical surfaces, from additional high-resolution T1-weighted (T1w) anatomical MRI data, which may be unacquired, corrupted by subject motion or hardware failure, or cannot be accurately co-registered to the diffusion data that are not corrected for susceptibility-induced geometric distortion. To address these challenges, this study proposes to synthesize high-quality T1w anatomical images directly from diffusion data using convolutional neural networks (CNNs) (entitled "DeepAnat"), including a U-Net and a hybrid generative adversarial network (GAN), and perform brain segmentation on synthesized T1w images or assist the co-registration using synthesized T1w images. The quantitative and systematic evaluations using data of 60 young subjects provided by the Human Connectome Project (HCP) show that the synthesized T1w images and results for brain segmentation and comprehensive diffusion analysis tasks are highly similar to those from native T1w data. The brain segmentation accuracy is slightly higher for the U-Net than the GAN. The efficacy of DeepAnat is further validated on a larger dataset of 300 more elderly subjects provided by the UK Biobank. Moreover, the U-Nets trained and validated on the HCP and UK Biobank data are shown to be highly generalizable to the diffusion data from Massachusetts General Hospital Connectome Diffusion Microstructure Dataset (MGH CDMD) acquired with different hardware systems and imaging protocols and therefore can be used directly without retraining or with fine-tuning for further improved performance. Finally, it is quantitatively demonstrated that the alignment between native T1w images and diffusion images uncorrected for geometric distortion assisted by synthesized T1w images substantially improves upon that by directly co-registering the diffusion and T1w images using the data of 20 subjects from MGH CDMD. In summary, our study demonstrates the benefits and practical feasibility of DeepAnat for assisting various diffusion MRI data analyses and supports its use in neuroscientific applications.

Local–Global Decompositions for Conditional Microstructure Generation

Conditional microstructure generation tools offer an important, inexpensive pathway to constructing statistically diverse datasets for Integrated Computational Materials Engineering and Materials Informatics efforts. To provide this utility in practice, an ideal generative framework must be able to efficiently, systematically, and robustly generate microstructures corresponding to selected spatial statistics (e.g., 1- and 2-point statistics) while also producing realistic local features (e.g., shapes and sizes of individual phase constituents). Because of the austerity of these requirements, generative frameworks often target either statistical conditioning or visual realism, but not both. In this paper, we propose to bridge these two approaches by approximating a microstructure’s generating process (i.e., its stochastic microstructure function) using a two layer semi-directed probabilistic graphical model. The first layer – a Gaussian Random Field (GRF) – provides direct control of the 1- and 2-point statistics. The second layer – a Score Based Generative Deep Learning model – postprocesses GRF predictions to refine local features while preserving global patterning. To understand and evaluate our proposed framework, we apply it to generate statistically equivalent N-phase microstructures from experimental references, including a 2-Phase Nickel-based Super Alloy and a 3-phase α−β Titanium alloy. Through these two case studies, we demonstrate that our framework successfully matches both lower-order (1- and 2-point statistics) and several salient higher-order statistics. Additionally, we briefly explore the capacity of these models to extrapolate outside of their training data by varying the input 2-point statistics. We discuss the value of this ability towards systematically generating diverse microstructure datasets.

Spatiotemporal prediction of microstructure evolution with predictive recurrent neural network

Prediction of microstructure evolution during material processing is essential to control the material properties. Simulation tools for microstructure evolution prediction based on physical concepts are computationally expensive and time-consuming. Therefore, they are not practical when either there is an urgent need for microstructure morphology during the process or there is a need to generate big microstructure datasets. Essentially, microstructure evolution prediction is a spatiotemporal sequence prediction problem, where the prediction of material microstructure is difficult due to different process histories and chemistry. We propose a Predictive Recurrent Neural Network (PredRNN) model for the microstructure prediction, which extends the inner-layer transition function of memory states in LSTMs to spatiotemporal memory flow. As a case study, we used a dataset from spinodal decomposition simulation of FeCrCo alloy created by the phase-field method for training and predicting future microstructures by previous observations. The results show that the trained network predicts quantitatively accurate microstructure morphologies while it is several orders of magnitude faster than the phase field method.

A deep learning model for automatic analysis of cavities in irradiated materials

Transmission electron microscopy (TEM) is a commonly used technique in materials science for defect investigation. Quantitative analysis of defects is important for understanding the properties of a material, but manual analysis of TEM micrographs can be time-consuming and prone to error, especially when the defects have irregular shapes rather than spherical shapes. Many existing methods or deep learning models do not handle a wide range of sizes for the same object type within a single image. In this work, we present a framework that enables users to train an instance segmentation model called Mask R- CNN on any microstructure dataset, perform multi-detection on the same image at different scales, and obtain properties (e.g., size, area) of the objects based on the desired shape (e.g., circle, ellipse, rectangle). Additionally, we have developed a parallel detection module that uses multiple GPUs to increase the efficiency of the object detection process. We demonstrate the capabilities of our framework using a set of TEM images of cavities with different shapes, size distributions, and background contrasts. Finally, we show that the performance of our model in terms of density, size, and swelling of the cavities is comparable to the human average and that our model achieves the highest recall value compared to existing methods due to the use of image multi-rescaling.

Design of Refractory Alloys for Desired Thermal Conductivity via AI-Assisted In-Silico Microstructure Realization.

A computational methodology based on supervised machine learning (ML) is described for characterizing and designing anisotropic refractory composite alloys with desired thermal conductivities (TCs). The structural design variables are parameters of our fast computational microstructure generator, which were linked to the physical properties. Based on the Sobol sequence, a sufficiently large dataset of artificial microstructures with a fixed volume fraction (VF) was created. The TCs were calculated using our previously developed fast Fourier transform (FFT) homogenization approach. The resulting dataset was used to train our optimal autoencoder, establishing the intricate links between the material's structure and properties. Specifically, the trained ML model's inverse design of tungsten-30% (VF) copper with desired TCs was investigated. According to our case studies, our computational model accurately predicts TCs based on two perpendicular cut-section images of the experimental microstructures. The approach can be expanded to the robust inverse design of other material systems based on the target TCs.

Hybrid Data-Driven Deep Learning Framework for Material Mechanical Properties Prediction with the Focus on Dual-Phase Steel Microstructures

A comprehensive approach to understand the mechanical behavior of materials involves costly and time-consuming experiments. Recent advances in machine learning and in the field of computational material science could significantly reduce the need for experiments by enabling the prediction of a material's mechanical behavior. In this paper, a reliable data pipeline consisting of experimentally validated phase field simulations and finite element analysis was created to generate a dataset of dual-phase steel microstructures and mechanical behaviors under different heat treatment conditions. Afterwards, a deep learning-based method was presented, which was the hybridization of two well-known transfer-learning approaches, ResNet50 and VGG16. Hyper parameter optimization (HPO) and fine-tuning were also implemented to train and boost both methods for the hybrid network. By fusing the hybrid model and the feature extractor, the dual-phase steels' yield stress, ultimate stress, and fracture strain under new treatment conditions were predicted with an error of less than 1%.

MicroLib: A library of 3D microstructures generated from 2D micrographs using SliceGAN

3D microstructural datasets are commonly used to define the geometrical domains used in finite element modelling. This has proven a useful tool for understanding how complex material systems behave under applied stresses, temperatures and chemical conditions. However, 3D imaging of materials is challenging for a number of reasons, including limited field of view, low resolution and difficult sample preparation. Recently, a machine learning method, SliceGAN, was developed to statistically generate 3D microstructural datasets of arbitrary size using a single 2D input slice as training data. In this paper, we present the results from applying SliceGAN to 87 different microstructures, ranging from biological materials to high-strength steels. To demonstrate the accuracy of the synthetic volumes created by SliceGAN, we compare three microstructural properties between the 2D training data and 3D generations, which show good agreement. This new microstructure library both provides valuable 3D microstructures that can be used in models, and also demonstrates the broad applicability of the SliceGAN algorithm.

Adjustable mechanical properties design of microstructure by using generative and adversarial network with gradient penalty

An intelligent microstructural design method based on deep learning is proposed considering performance indicators that contains boundary information and homogenized elastic modules. Microstructure dataset is established by random boundary method and homogenization method. Random boundary method is proposed to design microstructures under given boundary information, and homogenization method is utilized to acquire homogenized elastic modules. A generative and adversarial network with gradient penalty is developed to establish the high-dimensional mapping between performance indicators and microstructure. The Wasserstein distance is imported to overcome mode collapse. Numerical simulation shows that the pre-trained network successfully achieved corresponding microstructure design by given performance indicators.

Variability of the diapycnal mixing coefficient in coastal oceans investigated with direct microstructure measurements

Mass and heat fluxes in the ocean are important for understanding global ocean dynamics and ecosystems. Estimates of the diapycnal diffusivity (Kρ) are required for quantifying these fluxes. In this regard, one of the key parameters that is required to estimate the diapycnal eddy diffusivity is the “mixing coefficient” (Γ). The diapycnal diffusivity is estimated from a combination of the rate of dissipation of turbulent kinetic energy ε, the buoyancy frequency N (a measure of background density stratification) and Γ. This study investigates how the mixing coefficient (Γ) may be inferred from field measurable parameters using in-situ direct microstructure measurements in coastal oceans. Four microstructure data sets were analyzed to investigate the variability of Γ and associated parameters. While Γ is found to vary widely within a range of O(10−3−101), it can be parameterized using a ratio of relevant turbulent length scales: the Ellison scale (LE, which is approximately equivalent to the Thorpe scale) and the Ozmidov scale (LO). When LE/LO is less than unity, the results show that Γ is proportional to (LE/LO)4/3, consistent with previous observations. On the other hand, when LE/LO exceeds unity, Γ is approximately a constant with no discernable dependence on LE/LO, consistent with a recent theoretical and numerical study.

Data-driven learning of 3-point correlation functions as microstructure representations

This paper considers the open challenge of identifying complete, concise, and explainable quantitative microstructure representations for disordered heterogeneous material systems. Completeness and conciseness have been achieved through existing data-driven methods, e.g., deep generative models, which, however, do not provide mathematically explainable latent representations. This study investigates representations composed of three-point correlation functions, which are a special type of spatial convolutions. We show that a variety of microstructures can be characterized by a concise subset of three-point correlations (100-fold smaller than the full set), and the identification of such subsets can be achieved by Bayesian optimization on a small microstructure dataset. The proposed representation can directly be used to compute material properties by leveraging the effective medium theory, allowing the construction of predictive structure-property models with significantly less data than needed by purely data-driven methods and with a computational cost 100-fold lower than the physics-based model.

3D optical flow for large CT data of materials microstructures

AbstractWe compute three‐dimensional displacement vector fields to estimate the deformation of microstructural data sets in mechanical tests. For this, we extend the well‐known optical flow by Brox et al. to three dimensions, with special focus on the discretization of nonlinear terms. We evaluate our method first by synthetically deforming foams and comparing against this ground truth and second with data sets of samples that underwent real mechanical tests. Our results are compared to those from state‐of‐the‐art algorithms in materials science and medical image registration. By a thorough evaluation, we show that our proposed method is able to resolve the displacement best among all chosen comparison methods.