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DOE OSTI2023

Non-Boolean quantum amplitude amplification and quantum mean estimation

This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-Boolean oracles. The action of a non-Boolean oracle $U_\varphi $ on an eigenstate $\mathinner {|{x}\rangle }$ is to apply a state-dependent phase-shift $\varphi (x)$. Unlike Boolean oracles, the eigenvalues $\exp (i\varphi (x))$ of a non-Boolean oracle are not restricted to be $\pm 1$. Two new oracular algorithms based on such non-Boolean oracles are introduced. The first is the non-Boolean amplitude amplification algorithm, which preferentially amplifies the amplitudes of the eigenstates based on the value of $\varphi (x)$. Starting from a given initial superposition state $\mathinner {|{\psi _0}\rangle }$, the basis states with lower values of $\cos (\varphi )$ are amplified at the expense of the basis states with higher values of $\cos (\varphi )$. The second algorithm is the quantum mean estimation algorithm, which uses quantum phase estimation to estimate the expectation $\mathinner {\langle {\psi _0|U_\varphi |\psi _0}\rangle }$, i.e., the expected value of $\exp (i\varphi (x))$ for a random x sampled by making a measurement on $\mathinner {|{\psi _0}\rangle }$. It is shown that the quantum mean estimation algorithm offers a quadratic speedup over the corresponding classical algorithm. Both algorithms are demonstrated using simulations for a toy example. Potential applications of the algorithms are briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Nonparametric, data-based kernel interpolation for particle-tracking simulations and kernel density estimation

Traditional interpolation techniques for particle tracking include binning and convolutional formulas that use pre-determined (i.e., closed-form, parameteric) kernels. In many instances, the particles are introduced as point sources in time and space, so the cloud of particles (either in space or time) is a discrete representation of the Green’s function of an underlying PDE. As such, each particle is a sample from the Green’s function; therefore, each particle should be distributed according to the Green’s function. In short, the kernel of a convolutional interpolation of the particle sample “cloud” should be a replica of the cloud itself. This idea gives rise to an iterative method by which the form of the kernel may be discerned in the process of interpolating the Green’s function. When the Green’s function is a density, this method is broadly applicable to interpolating a kernel density estimate based on random data drawn from a single distribution. We formulate and construct the algorithm and demonstrate its ability to perform kernel density estimation of skewed and/or heavy-tailed data including breakthrough curves.

42 ENGINEERING↗

DOE OSTI2021

A scalable algorithm for the optimization of neural network architectures

In this work, we propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers that is at least as performant as neural networks of the same structure identified by other hyperparameter search algorithms in terms of accuracy and computational cost. Numerical results performed on benchmark datasets show that, for these datasets, our method outperforms state-of-the-art hyperparameter optimization algorithms in terms of attainable predictive performance by the selected neural network architecture, and time-to-solution for the hyperparameter optimization to complete.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Monte Carlo simulations of time-of-flight PET with double-ended readout: calibration, coincidence resolving times and statistical lower bounds

Here, this paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound. One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Another Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set. Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3 × 3 × 30 mm 3 scintillators: Lu 2 SiO 5 :Ce,Ca (LSO), LaBr 3 :Ce, and a hypothetical ultra-fast scintillator. To isolate the factors that depend on the scintillator length and the ability to estimate the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For LSO with 4000 photoelectrons and single photoelectron time jitter of the photodetector J = 0.2 ns (FWHM), the CRT value using the statistically weighted average of corrected trigger times is 0.098 ns FWHM and the statistical lower bound is 0.091 ns FWHM. For LaBr 3 :Ce with 8000 photoelectrons and J = 0.2 ns FWHM, the CRT values are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with 1 ns decay time, 4000 photoelectrons, and J = 0.2 ns FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. Lastly, the examples also show that calibration and correction for depth-dependent variations in pulse height and in annihilation and optical photon transit times are necessary to achieve these CRT values.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Smooth periodic gauge satisfying crystal symmetry and periodicity to study high-harmonic generation in solids

Intense lasers can easily drive nonadiabatic transitions of excited electron wave packets across the Brillouin zones, thus transition dipole moments (TDM) between energy bands of solids should be continuous, satisfying crystal symmetry, and periodic at zone boundaries. While current ab initio algorithms are powerful in calculating band structures of solids, they all introduced random phases into the eigenfunctions at each crystal momentum k. In this work, we show how to choose a “smooth-periodic” gauge where TDMs can be smooth versus k, preserving crystal symmetry, as well as maintaining periodic at boundaries. The symmetry properties of TDMs with respect to k ensure the absence of even-order harmonics from MgO with inversion symmetry, while the TDM in the “smooth-periodic” gauge for broken-symmetry ZnO is responsible for even harmonics that were underestimated in previous simulations. These results reveal the importance of correctly treating the complex TDMs that satisfy crystal symmetry and continuous across zone boundaries in nonlinear laser-solid interactions, which has been elusive in most theories so far.

36 MATERIALS SCIENCE↗

DOE OSTI2023

cTULIP: application of a human-based RNA-seq primary tumor classification tool for cross-species primary tumor classification in canine

The domestic dog, Canis familiaris, is quickly gaining traction as an advantageous model for use in the study of cancer, one of the leading causes of death worldwide. Naturally occurring canine cancers share clinical, histological, and molecular characteristics with the corresponding human diseases. In this study, we take a deep-learning approach to test how similar the gene expression profile of canine glioma and bladder cancer (BLCA) tumors are to the corresponding human tumors. We likewise develop a tool for identifying misclassified or outlier samples in large canine oncological datasets, analogous to that which was developed for human datasets. We test a number of machine learning algorithms and found that a convolutional neural network outperformed logistic regression and random forest approaches. We use a recently developed RNA-seq-based convolutional neural network, TULIP, to test the robustness of a human-data-trained primary tumor classification tool on cross-species primary tumor prediction. Our study ultimately highlights the molecular similarities between canine and human BLCA and glioma tumors, showing that protein-coding one-to-one homologs shared between humans and canines, are sufficient to distinguish between BLCA and gliomas. The results of this study indicate that using protein-coding one-to-one homologs as the features in the input layer of TULIP performs good primary tumor prediction in both humans and canines. Furthermore, our analysis shows that our selected features also contain the majority of features with known clinical relevance in BLCA and gliomas. Our success in using a human-data-trained model for cross-species primary tumor prediction also sheds light on the conservation of oncological pathways in humans and canines, further underscoring the importance of the canine model system in the study of human disease.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Application of Machine Learning and Data Augmentation Algorithms in the Discovery of Metal Hydrides for Hydrogen Storage

The development of efficient and sustainable hydrogen storage materials is a key challenge for realizing hydrogen as a clean and flexible energy carrier. Among various options, metal hydrides offer high volumetric storage density and operational safety, yet their application is limited by thermodynamic, kinetic, and compositional constraints. In this work, we investigate the potential of machine learning (ML) to predict key thermodynamic properties—equilibrium plateau pressure, enthalpy, and entropy of hydride formation—based solely on alloy composition using Magpie-generated descriptors. We significantly expand an existing experimental dataset from ~400 to 806 entries and assess the impact of dataset size and data augmentation, using the PADRE algorithm, on model performance. Models including Support Vector Machines and Gradient Boosted Random Forests were trained and optimized via grid search and cross-validation. Results show a marked improvement in predictive accuracy with increased dataset size, while data augmentation benefits are limited to smaller datasets and do not improve accuracy in underrepresented pressure regimes. Furthermore, clustering and cross-validation analyses highlight the limited generalizability of models across different material classes, though high accuracy is achieved when training and testing within a single hydride family (e.g., AB2). The study demonstrates the viability and limitations of ML for accelerating hydride discovery, emphasizing the importance of dataset diversity and representation for robust property prediction.

augmentation↗

DOE OSTI2023

Method and apparatus for constructing informative outcomes to guide multi-policy decision making

In Multi-Policy Decision-Making (MPDM), many computationally-expensive forward simulations are performed in order to predict the performance of a set of candidate policies. In risk-aware formulations of MPDM, only the worst outcomes affect the decision making process, and efficiently finding these influential outcomes becomes the core challenge. Recently, stochastic gradient optimization algorithms, using a heuristic function, were shown to be significantly superior to random sampling. In this disclosure, it was shown that accurate gradients can be computed-even through a complex forward simulation—using approaches similar to those in dep networks. The proposed approach finds influential outcomes more reliably, and is faster than earlier methods, allowing one to evaluate more policies while simultaneously eliminating the need to design an easily-differentiable heuristic function.

Olson, Edwin↗

DOE OSTI2014

Development and optimization of SPECT gated blood pool cluster analysis for the prediction of CRT outcome

Purpose: Phase analysis of single photon emission computed tomography (SPECT) radionuclide angiography (RNA) has been investigated for its potential to predict the outcome of cardiac resynchronization therapy (CRT). However, phase analysis may be limited in its potential at predicting CRT outcome as valuable information may be lost by assuming that time-activity curves (TAC) follow a simple sinusoidal shape. A new method, cluster analysis, is proposed which directly evaluates the TACs and may lead to a better understanding of dyssynchrony patterns and CRT outcome. Cluster analysis algorithms were developed and optimized to maximize their ability to predict CRT response. Methods: About 49 patients (N = 27 ischemic etiology) received a SPECT RNA scan as well as positron emission tomography (PET) perfusion and viability scans prior to undergoing CRT. A semiautomated algorithm sampled the left ventricle wall to produce 568 TACs from SPECT RNA data. The TACs were then subjected to two different cluster analysis techniques, K-means, and normal average, where several input metrics were also varied to determine the optimal settings for the prediction of CRT outcome. Each TAC was assigned to a cluster group based on the comparison criteria and global and segmental cluster size and scores were used as measures of dyssynchrony and used to predict response to CRT. A repeated random twofold cross-validation technique was used to train and validate the cluster algorithm. Receiver operating characteristic (ROC) analysis was used to calculate the area under the curve (AUC) and compare results to those obtained for SPECT RNA phase analysis and PET scar size analysis methods. Results: Using the normal average cluster analysis approach, the septal wall produced statistically significant results for predicting CRT results in the ischemic population (ROC AUC = 0.73;p < 0.05 vs. equal chance ROC AUC = 0.50) with an optimal operating point of 71% sensitivity and 60% specificity. Cluster analysis results were similar to SPECT RNA phase analysis (ROC AUC = 0.78, p = 0.73 vs cluster AUC; sensitivity/specificity = 59%/89%) and PET scar size analysis (ROC AUC = 0.73, p = 1.0 vs cluster AUC; sensitivity/specificity = 76%/67%). Conclusions: A SPECT RNA cluster analysis algorithm was developed for the prediction of CRT outcome. Cluster analysis results produced results equivalent to those obtained from Fourier and scar analysis.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Benchmarking highly entangled states on a 60-atom analogue quantum simulator

Abstract Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states 1,2 . However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices 2–5 , and it remains unsolved how to estimate the actual entanglement content of experiments 6 . Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement 6 , finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution 2–5 . Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

Science & Technology - Other Topics↗

DOE OSTI2014

Combined iterative reconstruction and image-domain decomposition for dual energy CT using total-variation regularization

Purpose: Dual-energy CT (DECT) is being increasingly used for its capability of material decomposition and energy-selective imaging. A generic problem of DECT, however, is that the decomposition process is unstable in the sense that the relative magnitude of decomposed signals is reduced due to signal cancellation while the image noise is accumulating from the two CT images of independent scans. Direct image decomposition, therefore, leads to severe degradation of signal-to-noise ratio on the resultant images. Existing noise suppression techniques are typically implemented in DECT with the procedures of reconstruction and decomposition performed independently, which do not explore the statistical properties of decomposed images during the reconstruction for noise reduction. In this work, the authors propose an iterative approach that combines the reconstruction and the signal decomposition procedures to minimize the DECT image noise without noticeable loss of resolution. Methods: The proposed algorithm is formulated as an optimization problem, which balances the data fidelity and total variation of decomposed images in one framework, and the decomposition step is carried out iteratively together with reconstruction. The noise in the CT images from the proposed algorithm becomes well correlated even though the noise of the raw projections is independent on the two CT scans. Due to this feature, the proposed algorithm avoids noise accumulation during the decomposition process. The authors evaluate the method performance on noise suppression and spatial resolution using phantom studies and compare the algorithm with conventional denoising approaches as well as combined iterative reconstruction methods with different forms of regularization. Results: On the Catphan©600 phantom, the proposed method outperforms the existing denoising methods on preserving spatial resolution at the same level of noise suppression, i.e., a reduction of noise standard deviation by one order of magnitude. This improvement is mainly attributed to the high noise correlation in the CT images reconstructed by the proposed algorithm. Iterative reconstruction using different regularization, including quadratic orq-generalized Gaussian Markov random field regularization, achieves similar noise suppression from high noise correlation. However, the proposed TV regularization obtains a better edge preserving performance. Studies of electron density measurement also show that our method reduces the average estimation error from 9.5% to 7.1%. On the anthropomorphic head phantom, the proposed method suppresses the noise standard deviation of the decomposed images by a factor of ∼14 without blurring the fine structures in the sinus area. Conclusions: The authors propose a practical method for DECT imaging reconstruction, which combines the image reconstruction and material decomposition into one optimization framework. Compared to the existing approaches, our method achieves a superior performance on DECT imaging with respect to decomposition accuracy, noise reduction, and spatial resolution.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2020

The Future of Computing: Integrating Scientific Computation on Neuromorphic Systems

Neuromorphic computing is known for its integration of algorithms and hardware elements that are inspired by the brain. Conventionally, this nontraditional method of computing is used for many neural or learning inspired applications. Unfortunately, this has resulted in the field of neuromorphic computing being relatively narrow in scope. In this paper we discuss two research areas actively trying to widen the impact of neuromorphic systems. The first is Fugu, a high-level programming interface designed to bridge the gap between general computer scientists and those who specialize in neuromorphic areas. The second aims to map classical scientific computing problems onto these frameworks through the example of random walks. This elucidates a class of scientific applications that are conducive to neuromorphic algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

PCM-Based Durable Write Cache for Fast Disk I/O

Flash based solid-state devices (FSSDs) have been adopted within the memory hierarchy to improve the performance of hard disk drive (HDD) based storage system. However, with the fast development of storage-class memories, new storage technologies with better performance and higher write endurance than FSSDs are emerging, e.g., phase-change memory (PCM). Understanding how to leverage these state-of-the-art storage technologies for modern computing systems is important to solve challenging data intensive computing problems. In this paper, we propose to leverage PCM for a hybrid PCM-HDD storage architecture. We identify the limitations of traditional LRU caching algorithms for PCM-based caches, and develop a novel hash-based write caching scheme called HALO to improve random write performance of hard disks. To address the limited durability of PCM devices and solve the degraded spatial locality in traditional wear-leveling techniques, we further propose novel PCM management algorithms that provide effective wear-leveling while maximizing access parallelism. We have evaluated this PCM-based hybrid storage architecture using applications with a diverse set of I/O access patterns. Our experimental results demonstrate that the HALO caching scheme leads to an average reduction of 36.8% in execution time compared to the LRU caching scheme, and that the SFC wear leveling extends the lifetime of PCM by a factor of 21.6.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2024

Comparison of the spatial statistics of random and defined-sequence photoresist films

The resolution-line edge roughness-sensitivity tradeoff has motivated the exploration of potential improvements using defined sequence polymers and polymer-bound photoacid generators and quenchers. We characterize the internal structures of positive tone photoresist polymer films formed from defined sequence polymers and compare them with random copolymers of the same composition. We model their imaging to connect initially to developable film structures. We use a polymer packing algorithm to simulate films of diverse compositions and locations of photoacid generators and quenchers, using the composition of an ESCAP photoresist. We use a simple extreme ultraviolet exposure-deprotection algorithm to model developable image formation within them. In all cases, the spatial distribution of chemical moieties in the film for defined sequence polymers is nearly indistinguishable from random copolymers. We evaluate several exposure-deprotection scenarios and find that a defined sequence copolymer has a distinctive developable image under certain circumstances. The use of defined sequence polymers within a photoresist layer does not automatically result in improved imaging; however, they do have some characteristics different from random polymers of the same composition. Further study of these characteristics may provide a route to improved control over the nanoscale imaging process.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Automated detection of vessel lumen and stent struts in intravascular optical coherence tomography to evaluate stent apposition and neointimal coverage

Purpose: Intravascular optical coherence tomography (IV-OCT) is a high-resolution imaging method used to visualize the microstructure of arterial walls in vivo. IV-OCT enables the clinician to clearly observe and accurately measure stent apposition and neointimal coverage of coronary stents, which are associated with side effects such as in-stent thrombosis. In this study, the authors present an algorithm for quantifying stent apposition and neointimal coverage by automatically detecting lumen contours and stent struts in IV-OCT images. Methods: The algorithm utilizes OCT intensity images and their first and second gradient images along the axial direction to detect lumen contours and stent strut candidates. These stent strut candidates are classified into true and false stent struts based on their features, using an artificial neural network with one hidden layer and ten nodes. After segmentation, either the protrusion distance (PD) or neointimal thickness (NT) for each strut is measured automatically. In randomly selected image sets covering a large variety of clinical scenarios, the results of the algorithm were compared to those of manual segmentation by IV-OCT readers. Results: Stent strut detection showed a 96.5% positive predictive value and a 92.9% true positive rate. In addition, case-by-case validation also showed comparable accuracy for most cases. High correlation coefficients (R > 0.99) were observed for PD and NT between the algorithmic and the manual results, showing little bias (0.20 and 0.46 μm, respectively) and a narrow range of limits of agreement (36 and 54 μm, respectively). In addition, the algorithm worked well in various clinical scenarios and even in cases with a low level of stent malapposition and neointimal coverage. Conclusions: The presented automatic algorithm enables robust and fast detection of lumen contours and stent struts and provides quantitative measurements of PD and NT. In addition, the algorithm was validated using various clinical cases to demonstrate its reliability. Therefore, this technique can be effectively utilized for clinical trials on stent-related side effects, including in-stent thrombosis and in-stent restenosis.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

Data Fusion for the Development of a Multimodal Freight Transload Facilities Dataset in the U.S.

To withstand the growing demand of commodity volume and its strain on the transportation infrastructure, it is necessary to identify the flow of commodities by route and mode. However, a national multimodal freight routing model does not exist for the U.S. The development of such model requires multiple building blocks, such as virtual representations of roadway, railway, and waterway networks, transload facilities (TFs), and access/egress links. Most of these blocks have a robust database in the U.S., except for the TFs. Here, this paper presents the fusion of dispersed and heterogeneous representations of multimodal TFs into a single, comprehensive, geospatial freight TF dataset. The TF dataset is derived from several sources, including the U.S. Army Corps of Engineers Master Docks Plus, the National Transportation Atlas Database, the Intermodal Association of North America, industry publications, and other public information. First, individual datasets were queried and reconciled. A geocoding/reverse geocoding process was applied to get the best street address and latitude/longitude location for each terminal. Then, duplicate terminals were identified by a fuzzy match algorithm based on terminal name and location, and removed. Validation was performed by visual inspection of random facilities. The main contributions of this work are: a publicly available version of the TF dataset, including facility location and multimodal transfer capability of 9,003 facilities, and an enterprise-version with the same facilities but including commodity handling capabilities. The main purpose of developing the TF dataset is to inform multimodal routing algorithms. The proposed TF dataset allows for credibly modeling the multimodal transfer of commodities within shipment routes.

Commodity Routing↗

DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗

DOE OSTI2013

3D deformation field throughout the interior of materials.

This report contains the one-year feasibility study for our three-year LDRD proposal that is aimed to develop an experimental technique to measure the 3D deformation fields inside a material body. In this feasibility study, we first apply Digital Volume Correlation (DVC) algorithm to pre-existing in-situ Xray Computed Tomography (XCT) image sets with pure rigid body translation. The calculated displacement field has very large random errors and low precision that are unacceptable. Then we enhance these tomography images by setting threshold of the intensity of each slice. DVC algorithm is able to obtain accurate deformation fields from these enhanced image sets and the deformation fields are consistent with the global mechanical loading that is applied to the specimen. Through this study, we prove that the internal markers inside the pre-existing tomography images of aluminum alloy can be enhanced and are suitable for DVC to calculate the deformation field throughout the material body.

Jin, Huiqing↗