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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Chemical crystallography by serial femtosecond X-ray diffraction

Abstract Inorganic–organic hybrid materials represent a large share of newly reported structures, owing to their simple synthetic routes and customizable properties 1 . This proliferation has led to a characterization bottleneck: many hybrid materials are obligate microcrystals with low symmetry and severe radiation sensitivity, interfering with the standard techniques of single-crystal X-ray diffraction 2,3 and electron microdiffraction 4–11 . Here we demonstrate small-molecule serial femtosecond X-ray crystallography (smSFX) for the determination of material crystal structures from microcrystals. We subjected microcrystalline suspensions to X-ray free-electron laser radiation 12,13 and obtained thousands of randomly oriented diffraction patterns. We determined unit cells by aggregating spot-finding results into high-resolution powder diffractograms. After indexing the sparse serial patterns by a graph theory approach 14 , the resulting datasets can be solved and refined using standard tools for single-crystal diffraction data 15–17 . We describe the ab initio structure solutions of mithrene (AgSePh) 18–20 , thiorene (AgSPh) and tethrene (AgTePh), of which the latter two were previously unknown structures. In thiorene, we identify a geometric change in the silver–silver bonding network that is linked to its divergent optoelectronic properties 20 . We demonstrate that smSFX can be applied as a general technique for structure determination of beam-sensitive microcrystalline materials at near-ambient temperature and pressure.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Model-Form Epistemic Uncertainty Quantification for Modeling with Differential Equations: Application to Epidemiology

Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. Here in this work we investigate this limitation through the lens of Neural Tangent Kernel (NTK) theory and elucidate how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK. Using this observation, we construct novel architectures that employ spatio-temporal and multi-scale random Fourier features, and justify how such coordinate embedding layers can lead to robust and accurate PINN models. Numerical examples are presented for several challenging cases where conventional PINN models fail, including wave propagation and reaction–diffusion dynamics, illustrating how the proposed methods can be used to effectively tackle both forward and inverse problems involving partial differential equations with multi-scale behavior.

42 ENGINEERING↗
DOE OSTI2024

FuseIM: Fusing Probabilistic Traversals for Influence Maximization on Exascale Systems

Probabilistic breadth-first traversals (BPTs) are used in many network science and graph machine learning applications. In this paper, we are motivated by the application of BPTs in stochastic diffusion-based graph problems such as influence maximization. These applications heavily rely on BPTs to implement a Monte-Carlo sampling step for their approximations. Given the large sampling complexity, stochasticity of the diffusion process, and the inherent irregularity in real-world graph topologies, efficiently parallelizing these BPTs remains significantly challenging. In this paper, we present a new algorithm to fuse massive number of concurrently executing BPTs with random starts on the input graph. Our algorithm is designed to fuse BPTs by combining separate traversals into a unified frontier on distributed multi-GPU systems. To show the general applicability of the fused BPT technique, we have incorporated it into two state-of-the-art influence maximization parallel implementations (gIM and Ripples). Our experiments on up to 4K nodes of the OLCF Frontier supercomputer (32,768 GPUs and 196K CPU cores) show strong scaling behavior, and that fused BPTs can improve the performance of these implementations up to 34x (for gIM) and ~360x (for Ripples).

Neff, Reece W.↗
DOE OSTI2024

Dataset for scientific paper "Simulated plant‑mediated oxygen input has strong impacts on fine‑scale porewater biogeochemistry and weak impacts on integrated methane fluxes in coastal wetlands", a modeling study based on field observation at the tidal salt marshes of the Parker River Estuary, Massachusetts, United States

This dataset is the raw and processed data for the paper "Simulated plant ‑ mediated oxygen input has strong impacts on fine ‑ scale porewater biogeochemistry and weak impacts on integrated methane fluxes in coastal wetlands". This study investigated how plant-mediated oxygen input affects subsurface biogeochemical reactions of organic carbon degradation and the resulting methane emissions of coastal wetlands by model simulation. We used the subsurface geochemical simulator PFLOTRAN for the modeling, which produced the simulated changes in porewater chemical substances and methane emissions over 10 days under different scenarios of plant-mediated oxygen input.Specifically, this dataset contains: 1) the input files for PFLOTRAN of all simulation runs conducted in this study. Those files are with an extension of ".in", containing information of the biogeochemical reaction network (stoichiometry, reaction rate, Monod constants, etc), fluid flow rate and oxygen concentration in the fluid which together simulated the plant-mediated oxygen input, the configuration of artificial reactions that simulated the methane fluxes, etc. The PFLOTRAN input files are text files, which can be opened by NotePad, but running these input files will require proper installation of PFLOTRAN (instruction: https://documentation.pflotran.org/user_guide/how_to/installation/installation.html). 2) the raw and processed model output from PFLOTRAN of all simulation runs, and 3) the python scripts used to process the raw model output, including random allocation of root cells, converting raw data into organized formats, calculating the methane fluxes based on the model output, data visualization, etc. The raw and processed model output from PFLOTRAN are in .spydata format, which can be viewed with Python. and 3) the python scripts for data processing and analysis are programming scripts, which can be opened with Python.This modeling work, in particular the model parameterization of root density and initial conditions of porewater concentrations of biogeochemical substances, was based on field measurements at the salt marsh of the Upper Parker River Estuary, Massachusetts, United States.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Emergency Voltage Regulation in Power Systems via Ripple-Type Control: Preprint

With increasing penetration of volatile renewable generation and cyber-physical disruptions, ensuring safe operation of bulk power systems has become unprecedentedly challenging. Since communication and computational costs restrict centralized system dispatch to be called upon every few minutes; and purely local schemes are shown to be insufficient, distributed controls have been advocated for handling unanticipated system conditions in real time. However, the applicability of distributed control schemes is fundamentally limited by their need for widespread communication and model cognizance. In this con-text, we put forth a hybrid low-communication saturation-driven protocol for the coordination of control agents that are distributed over a physical system and are allowed to communicate with peers over a ‘hotline’ communication network. Under this protocol, when agents observe a constraint violation based on local measurements, they respond locally until their control resources saturate, in which case they send a beacon for assistance to peer agents. The scheme ensures that minor violations are efficiently mitigated via fast local controls, while severe violations may be handled by a collaboration of a relatively small set of agents. We evaluate the performance of this scheme via extensive numerical tests on the IEEE 14-bus test feeder, where agents act upon noisy measurements under diverse scenarios of random load variations and severe low/high voltage events.

distributed control↗
DOE OSTI2022

Accuracy of predictions made by machine learned models for biocrude yields obtained from hydrothermal liquefaction of organic wastes

Hydrothermal liquefaction (HTL) has potential for converting abundant wet organic wastes into renewable fuels. Because HTL consists of a complex reaction network, deterministic, physics-based prediction of its biocrude yield is prohibitively difficult. Data-driven methods provide an alternative to the physics-based approach; however, rigorous testing must be performed to ensure the accuracy of predictions made by data-driven methods. To this end, a data set was assembled consisting of 570 data points appearing in the open literature. The data set was divided into training, validation, and test sub-sets and used for evaluating different machine learning regression approaches to predict biocrude yield. Among the tested algorithms, Random Forest and eXtreme Gradient Boosting (XGBoost) predicted biocrude yields in a test set that had not been used for training with the greatest accuracy, with root mean square errors (RMSE) of 8.34 and 8.57, respectively. Further refinement of the Random Forest model reduced its RMSE to 8.07. In comparison, predictions of a series of literature models resulted in RMSE ranging from 9.16 in the most accurate case to 27.6 in the least accurate; most literature models yielded RMSE values > 10. Using biocrude yield predictions from the most accurate Random Forest model and a probabilistic economic analysis found that the model accuracy is sufficient to prioritize allocation of resources based on projected minimum fuel selling price. In our report the models and analysis represent a major advance in the ability to use readily available data to predict biocrude yields on new feedstocks that have not previously been studied.

42 ENGINEERING↗
DOE OSTI2020

Modeling Nanoconfinement Effects Using Active Learning

Predicting the spatial configuration of gas in nanopores of is relevant in applications such as fluid flow forecasting and hydrocarbon reserves estimation. For example, shale reservoirs have suffered from computationally intractable multiscale problems, since fluid properties such as viscosity, density, and adsorption must be calculated by using expensive molecular dynamics (MD) simulations within each nanopore, whereas flow through these connected nanopores must be simulated at the micrometer scale. We utilize machine learning techniques to quickly and accurately model nanoscale confinement effects as an important step toward bridging the nano and micro scales. Our workflow is based on building and training physics-based deep-neural-networks models by learning from a database of MD calculations. The model accounts for the adsorption phenomenon by predicting the statistical distribution of gas inside nanopores. Because large databases of MD calculations are expensive to create, we investigate active learning (AL) as a data set construction strategy. In this workflow, new data are selected based on the model uncertainty via the query-by-committee approach. We show that our workflow obtains accurate models that generalize to real scanning electron microscopy geometries with 1/10th of the number of MD calculations required vs random data set generation. Our method enables the possibility of modeling nanoconfinement effects at the mesoscale, where complex connected sets of nanopores affect flow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Randomized probe imaging through deep k-learning

Randomized probe imaging (RPI) is a single-frame diffractive imaging method that uses highly randomized light to reconstruct the spatial features of a scattering object. The reconstruction process, known as phase retrieval, aims to recover a unique solution for the object without measuring the far-field phase information. Typically, reconstruction is done via time-consuming iterative algorithms. In this work, we propose a fast and efficient deep learning based method to reconstruct phase objects from RPI data. The method, which we call deep k-learning, applies the physical propagation operator to generate an approximation of the object as an input to the neural network. This way, the network no longer needs to parametrize the far-field diffraction physics, dramatically improving the results. Deep k-learning is shown to be computationally efficient and robust to Poisson noise. The advantages provided by our method may enable the analysis of far larger datasets in photon starved conditions, with important applications to the study of dynamic phenomena in physical science and biological engineering.

Guo, Zhen (ORCID:0000000213473451)↗
DOE OSTI2022

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale

The numerical simulation of quantum circuits is an indispensable tool for development, verification, and validation of hybrid quantum-classical algorithms intended for near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. Here, we present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) that serves as the quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the scalable tensor network processing library ExaTN (Exascale Tensor Networks). It provides multiple configurable quantum circuit simulators that perform either an exact quantum circuit simulation via the full tensor network contraction or an approximate simulation via a suitably chosen tensor factorization scheme. Upon necessity, stochastic noise modeling from real quantum processors is incorporated into the simulations by modeling quantum channels with Kraus tensors. By combining the portable XACC quantum programming frontend and the scalable ExaTN numerical processing backend, we introduce an end-to-end virtual quantum development environment that can scale from laptops to future exascale platforms. We report initial benchmarks of our framework, which include a demonstration of the distributed execution, incorporation of quantum decoherence models, and simulation of the random quantum circuits used for the certification of quantum supremacy on Google’s Sycamore superconducting architecture.

Nguyen, Thien↗
DOE OSTI2022

Design of functional materials based on new principles of disorder. Final Report

Disorder is present to some extent in every material. The disorder can be sparse and localized – individual defects – or globally such as in a glass. Normally disorder is considered to be detrimental to function. However, this is not necessarily always the case. This project addressed the question: How does disorder provide new potentialities for the behavior of a material that would be absent in a crystalline material of the same composition? We have discovered a new principle for disordered matter: Independence of bond-level response. This work has introduced the possibility of creating new classes of mechanical meta-materials with applications everywhere from microscopic biological molecules (allostery) to large scale architectural disordered networks. During the course of this grant, we have subsequently elaborated on these novel ideas about bond-level independence of properties in disordered materials. In particular, this study has required that we understand the limits of disorder. That is, if crystals are perfect order, is there another diametrically opposed pole which is the most disordered state? We have shown that, in a well-defined way, jamming is one extreme disordered pole of rigid matter. Jamming is a far-from-equilibrium way of creating a rigid solid by rapidly quenching a random distribution of particles to a mechanically stable system at zero temperature. To understand the jammed state of matter, we have elucidated the low-frequency excitation of these systems. This has allowed a new way of understanding materials that cannot be easily classified as crystals or glasses. These ideas can be extended to address the mechanical properties of polycrystalline matter. Memory formation in matter can take inspiration from memory that occurs in a biological context. The issue of memory formation raises another set of questions at the heart of how the energy landscape is organized and how it can be manipulated to store information in a solid. This project has explored how to understand the degree to which multiple memories can be stored in a single system and has created a holistic understanding of how inputs can be used to create a desired response.

36 MATERIALS SCIENCE↗
DOE OSTI2022

High-fidelity retrieval from instantaneous line-of-sight returns of nacelle-mounted lidar including supervised machine learning

Abstract. Wind turbine applications that leverage nacelle-mounted Doppler lidar are hampered by several sources of uncertainty in the lidar measurement, affecting both bias and random errors. Two problems encountered especially for nacelle-mounted lidar are solid interference due to intersection of the line of sight with solid objects behind, within, or in front of the measurement volume and spectral noise due primarily to limited photon capture. These two uncertainties, especially that due to solid interference, can be reduced with high-fidelity retrieval techniques (i.e., including both quality assurance/quality control and subsequent parameter estimation). Our work compares three such techniques, including conventional thresholding, advanced filtering, and a novel application of supervised machine learning with ensemble neural networks, based on their ability to reduce uncertainty introduced by the two observed nonideal spectral features while keeping data availability high. The approach leverages data from a field experiment involving a continuous-wave (CW) SpinnerLidar from the Technical University of Denmark (DTU) that provided scans of a wide range of flows both unwaked and waked by a field turbine. Independent measurements from an adjacent meteorological tower within the sampling volume permit experimental validation of the instantaneous velocity uncertainty remaining after retrieval that stems from solid interference and strong spectral noise, which is a validation that has not been performed previously. All three methods perform similarly for non-interfered returns, but the advanced filtering and machine learning techniques perform better when solid interference is present, which allows them to produce overall standard deviations of error between 0.2 and 0.3 m s−1, or a 1 %–22 % improvement versus the conventional thresholding technique, over the rotor height for the unwaked cases. Between the two improved techniques, the advanced filtering produces 3.5 % higher overall data availability, while the machine learning offers a faster runtime (i.e., ∼ 1 s to evaluate) that is therefore more commensurate with the requirements of real-time turbine control. The retrieval techniques are described in terms of application to CW lidar, though they are also relevant to pulsed lidar. Previous work by the authors (Brown and Herges, 2020) explored a novel attempt to quantify uncertainty in the output of a high-fidelity lidar retrieval technique using simulated lidar returns; this article provides true uncertainty quantification versus independent measurement and does so for three techniques rather than one.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

How does ion temperature gradient turbulence depend on magnetic geometry? Insights from data and machine learning

Magnetic geometry has a significant effect on the level of turbulent transport in fusion plasmas. Here, we model and analyse this dependence using multiple machine learning methods and a dataset of >200 000 nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence in diverse non-axisymmetric geometries. The dataset is generated using a large collection of both optimised and randomly generated stellarator equilibria. At fixed gradients and other input parameters, the turbulent heat flux varies between geometries by several orders of magnitude. Trends are apparent among the configurations with particularly high or particularly low heat flux. Regression and classification techniques from machine learning are then applied to extract patterns in the dataset. Due to a symmetry of the gyrokinetic equation, the heat flux and regressions thereof should be invariant to translations of the raw features in the parallel coordinate, similar to translation invariance in computer vision applications. Multiple regression models including convolutional neural networks (CNNs) and decision trees can achieve reasonable predictive power for the heat flux in held-out test configurations, with highest accuracy for the CNNs. Using Spearman correlation, sequential feature selection and Shapley values to measure feature importance, it is consistently found that the most important geometric lever on the heat flux is the flux surface compression in regions of bad curvature. The second most important geometric feature relates to the magnitude of geodesic curvature. These two features align remarkably with surrogates that have been proposed based on theory, while the methods here allow a natural extension to more features for increased accuracy. The dataset, released with this publication, may also be used to test other proposed surrogates, and we find that many previously published proxies do correlate well with both the heat flux and stability boundary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Rapid Identification of X-ray Diffraction Patterns Based on Very Limited Data by Interpretable Convolutional Neural Networks

Large volumes of data from material characterizations call for rapid and automatic data analysis to accelerate materials discovery. Herein, we report a convolutional neural network (CNN) that was trained based on theoretical data and very limited experimental data for fast identification of experimental X-ray diffraction (XRD) patterns of metal–organic frameworks (MOFs). To augment the data for training the model, noise was extracted from experimental data and shuffled; then it was merged with the main peaks that were extracted from theoretical spectra to synthesize new spectra. For the first time, one-to-one material identification was achieved. Theoretical MOFs patterns (1012) were augmented to a whole data set of 72 864 samples. It was then randomly shuffled and split into training (58 292 samples) and validation (14 572 samples) data sets at a ratio of 4:1. For the task of discriminating, the optimized model showed the highest identification accuracy of 96.7% for the top 5 ranking on a test data set of 30 hold-out samples. Neighborhood component analysis (NCA) on the experimental XRD samples shows that the samples from the same material are clustered in groups in the NCA map. Analysis on the class activation maps of the last CNN layer further discloses the mechanism by which the CNN model successfully identifies individual MOFs from the XRD patterns. Furthermore, this CNN model trained by the data augmentation technique would not only open numerous potential applications for identifying XRD patterns for different materials, but also pave avenues to autonomously analyze data by other characterization tools such as FTIR, Raman, and NMR spectroscopies.

36 MATERIALS SCIENCE↗
DOE OSTI2024

SPARTAN (Scalable Probabilistic Application Reconfigurable Tensor Autonomous Network)

The technical founder of Ludwig Computing Inc has been competitively selected for support by Cyclotron Road, a U.S. Department of Energy (DOE) Advanced Manufacturing Office (AMO) Lab-Embedded Entrepreneurship Program (LEEP) through an approved merit review process. Ludwig Computing Inc, supported by the U.S. Department of Energy's Advanced Manufacturing Office through the Cyclotron Road program, has investigated the advantages of probabilistic computing for real-world compute-intensive applications. This research adds to the understanding of alternative computing paradigms by exploring a unique hardware-software co-design that integrates quantum computing methods with nature-inspired problem-solving techniques. The project's focus on areas such as combinatorial optimization, graph analytics, and machine learning demonstrates the potential for significant advancements in computational efficiency and performance. By harnessing natural randomness to streamline large circuits into fewer devices, Ludwig's approach enables massive parallelism, potentially offering higher throughput, speed, and energy efficiency compared to conventional hardware solutions. This work benefits the public by paving the way for more efficient computing solutions that could address complex real-world problems while potentially reducing energy consumption in data-intensive industries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Permanently Magnetized Insulating Thin-Film Devices by Reduction

A reduction-based manufacturing process for creating technologically important multilayer structures from lattice-matched ferromagnetic insulators and ferromagnetic conductors is reported. The process is demonstrated by growing a permanently magnetized double-layer structure, consisting of lattice-matched conducting (Ni,Co) and insulating (Ni 0.4 Co 0.6 ) 3 O 3 layers, through a single deposition cycle. The orientation of the metal cation network is preserved after reduction. Close-packing displacements of Ni and Co take place in such a manner that the in-plane hexagonal arrangement is preserved. This is critical for ensuring high-quality interfaces joining the layers. At room temperature the hysteresis loop is centered. At low temperature the oxide layer becomes ferrimagnetically ordered, accompanied by a shift of the hysteresis loop along the magnetic field axis. The shift is assigned to exchange bias phenomenon. Biaxial compressive strain is responsible for the required ferrimagnetic ordering. Finally, spin valves and closely related magnetoresistance random access memory and spin-transfer-torque magnetic random access memory devices are addressed as potential applications.

42 ENGINEERING↗
DOE OSTI2024

Upscaling Soil Organic Carbon Measurements at the Continental Scale Using Multivariate Clustering Analysis and Machine Learning

Abstract Estimates of soil organic carbon (SOC) stocks are essential for many environmental applications. However, significant inconsistencies exist in SOC stock estimates for the U.S. across current SOC maps. We propose a framework that combines unsupervised multivariate geographic clustering (MGC) and supervised Random Forests regression, improving SOC maps by capturing heterogeneous relationships with SOC drivers. We first used MGC to divide the U.S. into 20 SOC regions based on the similarity of covariates (soil biogeochemical, bioclimatic, biological, and physiographic variables). Subsequently, separate Random Forests models were trained for each SOC region, utilizing environmental covariates and SOC observations. Our estimated SOC stocks for the U.S. (52.6 ± 3.2 Pg for 0–30 cm and 108.3 ± 8.2 Pg for 0–100 cm depth) were within the range estimated by existing products like Harmonized World Soil Database, HWSD (46.7 Pg for 0–30 cm and 90.7 Pg for 0–100 cm depth) and SoilGrids 2.0 (45.7 Pg for 0–30 cm and 133.0 Pg for 0–100 cm depth). However, independent validation with soil profile data from the National Ecological Observatory Network showed that our approach ( R 2 = 0.51) outperformed the estimates obtained from Harmonized World Soil Database ( R 2 = 0.23) and SoilGrids 2.0 ( R 2 = 0.39) for the topsoil (0–30 cm). Uncertainty analysis (e.g., low representativeness and high coefficients of variation) identified regions requiring more measurements, such as Alaska and the deserts of the U.S. Southwest. Our approach effectively captures the heterogeneous relationships between widely available predictors and the current SOC baseline across regions, offering reliable SOC estimates at 1 km resolution for benchmarking Earth system models.

58 GEOSCIENCES↗
DOE OSTI2024

Comparative Assessment of U-Net-Based Deep Learning Models for Segmenting Microfractures and Pore Spaces in Digital Rocks

Segmentation of high-resolution X-ray microcomputed tomography (µCT) images is crucial in digital rock physics (DRP), affecting the characterization and analysis of microscale phenomena in the porous media. The complexity of geological structures and nonideal scanning conditions pose significant challenges to conventional image segmentation approaches. Motivated by the recent increasing popularity of deep learning (DL) techniques in image processing, this work undertakes a comparative study of DL models, specifically U-Net and its variants, for segmenting multiple targets with distinguished features in digital rocks, including discrete fracture networks (DFNs), pore spaces, and solid rock. Particularly, DFNs have a smaller volumetric fraction over others, bringing in a substantial challenge of imbalanced segmentation. The primary focus is to evaluate the architecture and feature enhancement strategies of various DL models, including U-Net, attention U-Net, residual U-Net, U-Net++, and residual U-Net++. The models were designed as 2.5D, utilizing a central 2D image and its two adjacent upper and lower 2D images as input to provide a pseudo-3D context. In addition, because the ground truth of segmentation was unknown for real-world digital rocks, we created a benchmark data set following the inverse operations of segmentation. The data synthesis started from the label images (i.e., solid rock, pore spaces, and DFNs), followed by simulating partial volume blurring, adding random background noise, and introducing ring artifacts to mimic real raw X-ray µCT images. The data set, which included various rock types (i.e., sandstone and artificial data), scanning resolution, and magnitudes of noise and artifacts, was divided into training and testing data sets with a 90% and 10% ratio, respectively. Moreover, in addition to the conventional pixel-wise evaluation metrics, the physics-based metric of the lattice-Boltzmann method (LBM) simulated permeability provided more comprehensive assessments. The results demonstrated that the residual connections, nested architectures, and redesigned skip connections contribute to the model performance and give the residual U-Net++ the highest accuracy. The improvements were mainly on the boundaries and small targets, especially the DFNs, which dominate the interconnectivity and therefore affect the permeability greatly. This study also rigorously evaluated the efficiency and generalization of each model, demonstrating that the sophisticated architectures achieved excellent practicability and maintained robust performance on completely unseen data, ensuring their suitability for diverse and challenging DRP applications.

58 GEOSCIENCES↗