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At least 343 records · Page 19

Enabling accurate chemical modeling of shocked energetic materials using a machine learning interatomic potential

Understanding the complex chemistry of organic materials under dynamic compression is important for many applications, but it is challenging due to the large number of reactions occurring at various time scales. Here, in this study, we develop a machine learning potential based on Chebyshev polynomials to study the insensitive energetic material 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) under detonation. We discuss a strategy for constructing diverse training data needed to capture the complex chemistry of TATB. Our potential demonstrates strong transferability across a wide range of thermodynamic conditions and other explosives, enabling accurate and reliable chemical modeling of organic materials under extreme conditions. The efficiency of our approach allows for simulations over several nanoseconds and for large system sizes, providing detailed insights into the chemistry of shocked TATB. The model accurately reproduces experimental Hugoniot equation of state data, and our simulations reveal the rapid formation of nitrogen-rich carbon clusters following shock. The methods and datasets developed here offer a robust framework for accurate chemical modeling of other shocked organic energetic materials.

Chemistry↗

Performance Improvement of LTS Undulators for Synchrotron Light Sources

The joint expertise of ANL and FNAL has led to the production of $\text{Nb}_{3}\text{Sn}$ undulator magnets in operation in the ANL Advanced Photon Source (APS). These magnets showed performance reproducibility close to the short sample limit, and a design field increase of 20% at 820 A. However, the long training did not allow obtaining the expected 50% increase of the on-axis magnetic field with respect to the ∼1 T produced at 450 A current in the ANL NbTi undulator. To address this, 10-pole long undulator prototypes were fabricated, and CTD-101K was replaced as impregnation material with TELENE, an organic olefin-based thermosetting dicyclopentadiene resin produced by RIMTEC Corporation, Japan. Training and magnet retraining after a thermal cycle were nearly eliminated, with only a couple of quenches needed before reaching short sample limit at over 1,100 A. TELENE will enable operation of $\text{Nb}_{3}\text{Sn}$ undulators much closer to their short sample limit, expanding the energy range and brightness intensity of light sources. TELENE is Co-60 gamma radiation resistant up to 7–8 MGy, and therefore already applicable to impregnate planar, helical and universal devices operating in lower radiation environments than high energy colliders.

43 PARTICLE ACCELERATORS↗

Simultaneously improving accuracy and computational cost under parametric constraints in materials property prediction tasks

Abstract Modern data mining techniques using machine learning (ML) and deep learning (DL) algorithms have been shown to excel in the regression-based task of materials property prediction using various materials representations. In an attempt to improve the predictive performance of the deep neural network model, researchers have tried to add more layers as well as develop new architectural components to create sophisticated and deep neural network models that can aid in the training process and improve the predictive ability of the final model. However, usually, these modifications require a lot of computational resources, thereby further increasing the already large model training time, which is often not feasible, thereby limiting usage for most researchers. In this paper, we study and propose a deep neural network framework for regression-based problems comprising of fully connected layers that can work with any numerical vector-based materials representations as model input. We present a novel deep regression neural network, iBRNet, with branched skip connections and multiple schedulers, which can reduce the number of parameters used to construct the model, improve the accuracy, and decrease the training time of the predictive model. We perform the model training using composition-based numerical vectors representing the elemental fractions of the respective materials and compare their performance against other traditional ML and several known DL architectures. Using multiple datasets with varying data sizes for training and testing, We show that the proposed iBRNet models outperform the state-of-the-art ML and DL models for all data sizes. We also show that the branched structure and usage of multiple schedulers lead to fewer parameters and faster model training time with better convergence than other neural networks. Scientific contribution: The combination of multiple callback functions in deep neural networks minimizes training time and maximizes accuracy in a controlled computational environment with parametric constraints for the task of materials property prediction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Adaptive hyperparameter updating for training restricted Boltzmann machines on quantum annealers

Restricted Boltzmann Machines (RBMs) have been proposed for developing neural networks for a variety of unsupervised machine learning applications such as image recognition, drug discovery, and materials design. The Boltzmann probability distribution is used as a model to identify network parameters by optimizing the likelihood of predicting an output given hidden states trained on available data. Training such networks often requires sampling over a large probability space that must be approximated during gradient based optimization. Quantum annealing has been proposed as a means to search this space more efficiently which has been experimentally investigated on D-Wave hardware. D-Wave implementation requires selection of an effective inverse temperature or hyperparameter (β) within the Boltzmann distribution which can strongly influence optimization. Here, we show how this parameter can be estimated as a hyperparameter applied to D-Wave hardware during neural network training by maximizing the likelihood or minimizing the Shannon entropy. We find both methods improve training RBMs based upon D-Wave hardware experimental validation on an image recognition problem. Neural network image reconstruction errors are evaluated using Bayesian uncertainty analysis which illustrate more than an order magnitude lower image reconstruction error using the maximum likelihood over manually optimizing the hyperparameter. The maximum likelihood method is also shown to out-perform minimizing the Shannon entropy for image reconstruction.

97 MATHEMATICS AND COMPUTING↗

AGR-5/6/7 Test Train Disassembly & Tools Phases I & II

This document provides the process for qualification of the AGR-5/6/7 Test Train Disassembly equipment for remote operation in the HFEF Main Cell. The test train is composed of five welded stainless steel capsules that are expected to be transported in two sections. The first section will be Capsules 1 and 2. The second section will include Capsules 3, 4 and 5. The capsules range in length from about 9 inches to about 12 inches. Inside the capsules is a graphite holder that contains multiple fueled AGR compacts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Advanced data science toolkit for non-data scientists – A user guide

Emerging modern data analytics attracts much attention in materials research and shows great potential for enabling data-driven design. Data populated from the high-throughput CALPHAD approach enables researchers to better understand underlying mechanisms and to facilitate novel hypotheses generation, but the increasing volume of data makes the analysis extremely challenging. Here in this paper, we introduce an easy-to-use, versatile, and open-source data analytics frontend, ASCENDS (Advanced data SCiENce toolkit for Non-Data Scientists), designed with the intent of accelerating data-driven materials research and development. The toolkit is also of value beyond materials science as it can analyze the correlation between input features and target values, train machine learning models, and make predictions from the trained surrogate models of any scientific dataset. Various algorithms implemented in ASCENDS allow users performing quantified correlation analyses and supervised machine learning to explore any datasets of interest without extensive computing and data science background. The detailed usage of ASCENDS is introduced with an example of experimental high-temperature alloy data.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Generalizing synthetic data-trained acoustic predictive models to real-world measurements

Acoustic Resonance Spectroscopy (ARS) is highly sensitive to structural properties such as material, geometry, and environmental conditions; as a consequence, it can noninvasively measure internal properties that are unobservable by most other methods. Because of its sensing capabilities and low implementation cost and complexity, ARS has potential as a paradigm shift in noninvasive sensing, characterization, and monitoring applications. However, extracting specific properties from ARS measurements, comprising the vibration spectrum of a test object, is challenging due to the sensitivity of the spectra to other structural changes not being measured, e.g. manufacturing tolerances, component coupling, environmental variation, etc. Neural Networks are promising tools for identifying trends in ARS measurements, but their training typically requires large datasets, which are often impractical to obtain for real-world systems. Synthetic data can be simulated efficiently, but discrepancies between synthetic and real-world data frequently lead to poor generalization when testing on the real-world data. We propose a novel ARS model training framework that enables networks trained exclusively on synthetic ARS data to generalize effectively to real-world measurements. Our approach leverages the Correlation Alignment (CORAL) technique to enforce the extraction of features common to both synthetic and real-world domains. As a case study, we demonstrate noninvasive ARS-based pressure measurements in sealed systems. Finite element method (FEM) simulations were used to generate synthetic training data across diverse vessel configurations and pressure conditions, and model performance was then tested on real-world measurements. We demonstrate that robust machine learning models for ARS can be developed without large real-world datasets, significantly broadening the applicability of ARS for noninvasive sensing. Moreover, the approach is extensible to other sensing modalities where synthetic data are abundant but real-world data are limited.

36 MATERIALS SCIENCE↗

Data Readiness for Scientific AI at Scale

This paper examines how Data Readiness for AI (DRAI) principles apply to leadership-scale scientific datasets used to train foundation models. We analyze archetypal workflows across four representative domains—climate, nuclear fusion, bio/health, and materials—to identify common preprocessing patterns and domain-specific constraints. We introduce a two-dimensional readiness framework that combines canonical preprocessing patterns with a five-level operational readiness scale, both tailored to high-performance computing (HPC) environments. This framework helps outline key challenges in transforming large-scale scientific data into formats suitable for scalable AI training. Together, these dimensions form a conceptual maturity matrix that characterizes scientific data readiness and guides infrastructure development toward standardized, cross-domain support for scalable and reproducible AI for science.

Brewer, Wes [ORNL] (ORCID:0000000236393956)↗

Probing Coherent States of Light and Matter in Two-Dimensional Semiconductors. Final Report

The ability to enhance light-matter interactions in engineered optical environments is well-established in micro- and nano-photonics. New classes of materials bring new rich correlations between spin, momentum, and light polarization that can be exploited in these photonic systems for information processing and low-power electronics. Interfacing these novel material features with strong optical interactions suggests the compelling capability to create hybrid light-matter systems harnessing low-energy and protected material properties such as spin. The long-term objective of this program was to investigate the interplay between pseudospin in 2D materials and light, revealing new coherent phenomena. The materials studied are the monolayer transition metal dichalcogenides (TMDs), which support polarization-sensitive optical transitions when isolated to a single sub-nanometer crystal layer in thickness. In particular, monolayer TMD semiconductors such as MoS 2 exhibit degenerate valleys in momentum space with distinct spin character. These valleys can be separately addressed by circularly polarized light, providing a tool for manipulation. Integrating this valley pseudospin of excitons in monolayer TMDs with engineered strong optical excitations to create novel coherent phenomena was a key long-term goal of this research. The scope of this research primarily focused on studying light-matter interactions of valley-sensitive excitations in monolayer TMDs. The scope also included the integration of monolayer materials that support valley-polarized emission into photonic devices. This approach extends prior work on exciton-polaritons in 2D materials toward a platform with far more control and improved light input and output characteristics to aid scalability of these polarization-sensitive phenomena to many-body, long-range optical networks. During the course of the five-year Early Career program, the approaches led to successful progress on each proposed aim. Initial successful work seeded additional research that developed from the main themes, while this program focus evolved toward coherent manipulation of valley polaritons and integration with photonics. Both of these advanced topics set the stage for new capabilities in future innovative research. The results of this project provide advances in materials and methods relevant for new visions of opto-electronics and photonics that can improve information processing in an era of increased focus on quantum and coherent phenomena. The research has also contributed to the training of two postdoctoral scholars and five graduate students.

2D Materials↗

Microstructural and rheological training and memory of nanocolloidal soft glasses under cyclic shear

An intrinsic feature of disordered and out-of-equilibrium materials, such as glasses, is the dependence of their properties on their history. An important example is rheological memory, in which disordered solids obtain properties based on their deformation history. Here, in this study, we employ x-ray photon correlation spectroscopy with in situ rheometry to characterize memory formation in a nanocolloidal soft glass due to cyclic shear. During a cycle, particles undergo irreversible displacements composed of a combination of shear-induced diffusion and heterogeneous, residual strain fields. At lower shear amplitudes, the displacements resemble a random walk in which the directions in each cycle are independent of those in preceding cycles, while at high amplitude, the irreversible displacements in consecutive cycles become correlated. The magnitudes of the displacements decrease with each cycle before reaching a steady state where the microstructure has been trained to achieve enhanced reversibility even at shear amplitudes well above yielding and despite the presence of thermal fluctuations. At amplitudes below and near yielding, these decreases are monotonic, while well above yielding, they are nonmonotonic, suggesting evidence of shear banding. Accompanying this microstructural training are corresponding decreases in the dissipation during each cycle and the magnitude of the residual stress toward steady-state values. Memory of the training is revealed by measurements in which the amplitude of the shear is changed after steady state is reached. The magnitude of the particle displacements, as well as the dissipation and the change in residual stress, vary nonmonotonically with the new shear amplitude, having minima near the training amplitude, thereby revealing correlated microscopic and macroscopic signatures of memory.

Chen, Yihao [Johns Hopkins Univ., Baltimore, MD (U↗

Machine-Guided Design of Oxidation-Resistant Superconductors for Quantum Information Applications

Decoherence in superconducting qubits has long been attributed to two-level systems arising from the surfaces and interfaces present in real devices. A recent significant step in reducing decoherence was the replacement of superconducting niobium by superconducting tantalum, resulting in a tripling of transmon qubit lifetimes (T1). The identity, thickness, and quality of the native surface oxide, is thought to play a major role, as tantalum only has one oxide whereas niobium has several. Here we report the development of a thermodynamic metric to rank materials based on their potential to form a well-defined, thin, surface oxide. We first computed this metric for known binary and ternary metal alloys using data available from the Materials Project and experimentally validated the strengths and limits of this metric through the preparation and controlled oxidation of eight known metal alloys. Then we trained a convolutional neural network to predict the value of this metric from atomic composition and atomic properties. This allowed us to compute the metric for materials that are not present in the Materials Project, including a large selection of known superconductors, and, when combined with Tc, allowed us to identify new candidate superconductors for quantum information science and engineering (QISE) applications. We tested the oxidation resistance of a pair of these predictions experimentally. Our results are expected to lay the foundation for the tailored and rapid selection of improved superconductors for QISE.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Automated Grain Boundary (GB) Segmentation and Microstructural Analysis in 347H Stainless Steel Using Deep Learning and Multimodal Microscopy

Austenitic 347H stainless steel offers superior mechanical properties and corrosion resistance required for extreme operating conditions such as high temperature. The change in microstructure due to composition and process variations is expected to impact material properties. Identifying microstructural features such as grain boundaries thus becomes an important task in the process-microstructure-properties loop. Applying convolutional neural network (CNN)-based deep learning models is a powerful technique to detect features from material micrographs in an automated manner. In contrast to microstructural classification, supervised CNN models for segmentation tasks require pixel-wise annotation labels. However, manual labeling of the images for the segmentation task poses a major bottleneck for generating training data and labels in a reliable and reproducible way within a reasonable timeframe. Microstructural characterization especially needs to be expedited for faster material discovery by changing alloy compositions. Here, in this study, we attempt to overcome such limitations by utilizing multimodal microscopy to generate labels directly instead of manual labeling. We combine scanning electron microscopy images of 347H stainless steel as training data and electron backscatter diffraction micrographs as pixel-wise labels for grain boundary detection as a semantic segmentation task. The viability of our method is evaluated by considering a set of deep CNN architectures. We demonstrate that despite producing instrumentation drift during data collection between two modes of microscopy, this method performs comparably to similar segmentation tasks that used manual labeling. Additionally, we find that naïve pixel-wise segmentation results in small gaps and missing boundaries in the predicted grain boundary map. By incorporating topological information during model training, the connectivity of the grain boundary network and segmentation performance is improved. Finally, our approach is validated by accurate computation on downstream tasks of predicting the underlying grain morphology distributions which are the ultimate quantities of interest for microstructural characterization.

36 MATERIALS SCIENCE↗

Constrained GAN-Generated X-Ray CT Data For Self-Supervised And Foundation-Model Segmentation Of Concrete Microstructures

Three-dimensional characterization of materials using X-ray computed tomography (XCT) is challenging due to the complexity of internal structures, noise, and variations in resolution. Traditional computer vision models often struggle to accurately segment these images, particularly in domain-specific applications like materials science. While supervised deep learning approaches have been developed to address the limitations of conventional algorithms, they typically require large amounts of labeled training data and often fail to generalize across different datasets. Self-supervised, few-and zero-shot learning methods have gained prominence in natural image processing and segmentation tasks, but their application to scientific imaging remains limited due to the unique structural complexity, noise, and textural artifacts present in materials science data. In this work, we investigate how domain adaptation, leveraging physics-based and GAN-generated synthetic data, impacts segmentation performance. We introduce a modified Contrastive Unpaired Translation (CUT) model designed to generate realistic labeled data, which can be used for training, pre-training, and fine-tuning segmentation models for real XCT microstructure data. We evaluate the performance of two segmentation approaches: a self-supervised network (SSL-ALPNet) and a foundation model (Segment Anything Model), assessing their improvements when pre-trained and/or fine-tuned on the synthesized data. Our results demonstrate that leveraging synthetic data significantly enhances segmentation performance, particularly in challenging materials science applications.

Ziabari, Amir [ORNL] (ORCID:000000034776457X)↗

Machine learned interatomic potential for dispersion strengthened plasma facing components

Tungsten (W) is a material of choice for the divertor material due to its high melting temperature, thermal conductivity, and sputtering threshold. However, W has a very high brittle-to-ductile transition temperature, and at fusion reactor temperatures (≥1000 K), it may undergo recrystallization and grain growth. Dispersion-strengthening W with zirconium carbide (ZrC) can improve ductility and limit grain growth, but much of the effects of the dispersoids on microstructural evolution and thermomechanical properties at high temperatures are still unknown. We present a machine learned Spectral Neighbor Analysis Potential for W–ZrC that can now be used to study these materials. In order to construct a potential suitable for large-scale atomistic simulations at fusion reactor temperatures, it is necessary to train on ab initio data generated for a diverse set of structures, chemical environments, and temperatures. Further accuracy and stability tests of the potential were achieved using objective functions for both material properties and high temperature stability. Additionally, validation of lattice parameters, surface energies, bulk moduli, and thermal expansion is confirmed on the optimized potential. Tensile tests of W/ZrC bicrystals show that although the W(110)–ZrC(111) C-terminated bicrystal has the highest ultimate tensile strength (UTS) at room temperature, observed strength decreases with increasing temperature. At 2500 K, the terminating C layer diffuses into the W, resulting in a weaker W–Zr interface. Meanwhile, the W(110)–ZrC(111) Zr-terminated bicrystal has the highest UTS at 2500 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Attention-based functional-group coarse-graining: a deep learning framework for molecular prediction and design

Machine learning (ML) offers considerable promise for the design of new molecules and materials. In real-world applications, the design problem is often domain-specific, and suffers from insufficient data, particularly labeled data, for ML training. In this study, we report a data-efficient, deep-learning framework for molecular discovery that integrates a coarse-grained functional-group representation with a self-attention mechanism to capture intricate chemical interactions. Our approach exploits group-contribution concepts to create a graph-based intermediate representation of molecules, serving as a low-dimensional embedding that substantially reduces the data demands typically required for training. Using a self-attention mechanism to learn the subtle but highly relevant chemical context of functional groups, the method proposed here consistently outperforms existing approaches for predictions of multiple thermophysical properties. In a case study focused on adhesive polymer monomers, we train on a limited dataset comprising only 6,000 unlabeled and 600 labeled monomers. The resulting chemistry prediction model achieves over 92% accuracy in forecasting properties directly from SMILES strings, exceeding the performance of current state-of-the-art techniques. Furthermore, the latent molecular embedding is invertible, enabling the design pipeline to automatically generate new monomers from the learned chemical subspace. We illustrate this functionality by targeting several properties, including high and low glass transition temperatures (Tg), and demonstrate that our model can identify new candidates with values that surpass those in the training set. The ease with which the proposed framework navigates both chemical diversity and data scarcity offers a promising route to accelerate and broaden the search for functional materials.

Han, Ming [Univ. of Chicago, IL (United States)]↗

Computer vision models and advanced TEM imaging for microstructures of irradiated AM316 stainless steels

Advancements were made in automating microscopy-based material characterization, particularly in studying irradiation effects on additively manufactured (AM) materials using machine learning (ML) and computer vision (CV). These automation efforts address the challenges of analyzing complex microstructures, accelerating the detection of irradiation-induced defects. Two CV models were developed at Argonne National Laboratory (ANL) to enhance transmission electron microscopy (TEM) analysis of irradiated AM 316 stainless steel. The first model focused on the detection of irradiation-induced dislocation loops, which contribute to material hardening and embrittlement. These loops, categorized as faulted or perfect, were automatically detected and classified using a Mask R-CNN model trained on TEM images from both in-situ and ex-situ ion irradiation experiments. The model achieved high accuracy, with precision, recall, and F1 scores of 0.839, 0.734, and 0.776, respectively, demonstrating its effectiveness in analyzing dislocation loops in irradiated AM materials. The second CV model was developed to analyze the size and wall thickness of dislocation cells in laser powder bed fusion (LPBF) 316 stainless steel. Using a U-Net++ architecture with EfficientNet as the encoder, the model was trained on TEM images to segment and measure cell size and wall thickness.

36 MATERIALS SCIENCE↗

Graph neural networks for mechanical property prediction of 2D fiber composites

This work investigates the ability of graph neural networks (GNNs) to homogenize 2D fiber composite microstructures. We use different inhomogeneity and anisotropy indices to motivate and show that the Volume Elements (VEs) used in ML methods should ideally be far from their Representative Volume Element (RVE) size limit and, consequently, are notably anisotropic. Hence, training only the isotropic limit properties may not be acceptable. Another aspect is the need to normalize elastic stiffness values for ML, especially when high elastic contrast ratios are encountered between composite phases or in the material set. We introduce a normalization technique based on the mean-field method (MFM) to handle such high contrast ratios and train for the entire stiffness tensor. We show that the proposed GNN approaches exhibit high accuracy and efficiency compared to traditional methods and convolutional neural networks, utilizing unstructured graphs constructed from microstructure topology. Our model successfully predicts the stiffness tensor, peak strength under bulk damage, and brittle fracture initiation strength across diverse microstructure configurations while maintaining high accuracy even for extreme material contrasts and volume fractions. We also present a method to improve prediction accuracy for small dataset sizes using Voronoi partitioning.

Brittle strength↗

Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials and Components (Final Technical Report)

Metal Additive Manufacturing (AM) is a promising method for cost-efficient fabrication of complex shape structures for applications in harsh environment, such as in a nuclear reactor. However, internal defects (pores) occur in high-strength AM alloys, which are manufactured with Laser Powder Bed Fusion (LPBF) AM method. Pulsed Infrared Thermography (PIT) is an efficient nondestructive evaluation (NDE) method to examine actual structures, because this method offers one-sided non-contact measurements, and fast processing of large sample areas. However, imaging of material defects, particularly defects with sizes at microscopic level, is challenging. In this report, we benchmark the performance of several Unsupervised Learning (UL) algorithms designed to enhance imaging of microscopic defects in metals with PIT. UL aims to learn the latent principal patterns (dictionaries) in PIT data to detect defects with minimal human supervision. Performance of Independent Component Analysis (ICA), Sparse Coding (SC), Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA) was compared using F-score, UL model training time and defects reconstruction time. We obtained the average F-score of 0.75, and a highest F-score of 0.89 for the EFA algorithm. Overall, EFA outperforms other UL algorithms considered in this study. In another approach, we investigate Thermal Tomography (TT), which is a computational method for reconstruction of depth profile of internal material defects from PIT nondestructive evaluation (NDE). TT algorithm obtains depth reconstructions of thermal effusivity, which has been shown to provide visualization of subsurface internals defects in metals. In many applications, one needs to determine the defect shape and orientation from reconstructed effusivity images. Interpretation of TT images is non-trivial because of blurring, which increases with depth due to heat diffusion-based nature of image formation. We have developed a deep learning convolutional neural network (CNN) to classify size and orientation of subsurface material defects in TT images. CNN was trained with TT images produced with computer simulations of 2D metallic structures (thin plates) containing elliptical subsurface voids. Performance of CNN was investigated using test TT images developed with computer simulations of plates containing elliptical defects, and defects with shape imported from scanning electron microscopy (SEM) images. CNN demonstrated the ability to classify radii and angular orientation of elliptical defects in previously unseen test TT images. We have also demonstrated that CNN trained on TT images of elliptical defects is capable of classifying shape and orientation of irregular defects. Training the CNN on irregular defect shapes instead of on elliptical shapes would make the resulting classifications more descriptive of actual defect shapes. However, this requires a much higher volume of SEM images of material defects, which are difficult to obtain because of random occurrence of defects in LPBF. To address this challenge, we developed a generative adversarial network (GAN) to augment the existing dataset of SEM defect images. The GAN model is demonstrated to create novel yet realistic defect shapes that can be used as input for simulated PTT images to train CNN. We also investigate several approaches based on Gaussian Random Circle and Bezier Curves for constructing parametric models of irregular-shape defects.

36 MATERIALS SCIENCE↗