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DOE OSTI2025

Unsupervised Process Anomaly Detection and Identification Using the Leave-One-Variable-Out Approach

Automated anomaly detection and identification can signal equipment issues and pinpoint causes in large-scale industrial systems. For systems with limited failure history, unsupervised machine learning methods can be utilized as they do not require past failures. This study introduces the leave-one-variable-out (LOVO) model, which masks one variable at a time to predict the others, learning underlying process correlations. Detection performance was assessed with synthetic and experimental data, while identification performance used only synthetic data due to its ability to generate labeled anomaly types. For detection using synthetic data, the LOVO model generally outperformed comparative models; while using experimental data, the comparative methods outperformed the LOVO model. However, the comparative methods required selecting a latent size, and these conclusions pertain to using the optimal size. In practice, it would not be feasible to always select the optimal value, and incorrect selections impacted performance. In contrast, the LOVO model does not require a latent space. For identification using synthetic data, the LOVO model was slightly outperformed in interpretability and repeatability but still demonstrated impressive results. These outcomes suggest that the LOVO model is an effective model and may be more easily implemented without the challenging tuning process of selecting a latent size.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Remote-sensing detectability of airborne Arctic dust

Remote-sensing (RS)-based estimates of Arctic dust are oftentimes overestimated due to a failure in separating out the dust contribution from that of spatially homogeneous clouds or low-altitude cloud-like plumes. A variety of illustrations are given with a particular emphasis on questionable claims of using brightness temperature differences (BTDs) as a signature indicator of Arctic dust transported from mid-latitude deserts or generated by local Arctic sources. While there is little dispute about the presence of both Asian and local dust across the Arctic, the direct RS detectability of airborne dust, as ascribed to satellite (MODIS and AVHRR) measurements of significantly negative brightness temperature differences at 11 and 12 µm (BTD 11–12 ), has been misrepresented in certain cases. While it is difficult to account for all examples of strongly negative BTD 11–12 values in the Arctic, it is unlikely that airborne dust plays a significant role. One much more likely contributor would be water clouds in the Arctic inversion layer. The RS detectability of the impact of Arctic dust (notably due to Arctic dust from local sources) can, however, be of significance. Sustained dust deposition can substantially decrease (visible to shortwave IR) snow and ice reflectance albedo (pan-chromatic reflectance) and the signal measured by satellite sensors. Significantly negative BTD 11–12 values would, however, only represent a limited area near the drainage basin sources according to our event-level case studies. The enhanced ice-nucleating particle (INP) role of local Arctic dust can, for example, induce significant changes in the properties of low-level mixed-phase clouds (cloud optical depth changes <~ 1) that can readily be detected by active and passive RS instruments. It is critical that the distinction between the RS detectability of airborne Arctic dust versus the RS detectability of the impacts of that dust be understood if we are to appropriately parameterize, for example, the radiative forcing influence of dust in this climate-sensitive region.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Use of Rig Parameter Data in Bit Constraint Models for Improved Drilling Performance at The Geysers

Surface parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. However, these measurements are of reduced value without a standard to aid in evaluation and decision making. A method is demonstrated whereby drill bit constraint models are used to interpret drilling response parameters. Drill rig parameter data for well GDC-36 at the Geysers Geothermal Field Power were acquired by Geysers Power Company and drilling contractor Kenai Drilling using Pason US DataHub and evaluated. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) along with other model constraints in computational algorithms. The method is used to evaluate overall bit performance, monitor bit integrity, and detect the presence of drillstring vibrations and other conditions contributing to bit failure; comparisons are made to observations of bit wear and damage. The method will be applied in real-time to improve decision-making on subsequent wells and has applicability to development of advanced analytics on future geothermal wells using real-time electronic drilling recorder (EDR) data for improved performance and reduced drilling costs.

15 GEOTHERMAL ENERGY↗

DOE OSTI2025

Cold Spray Cobalt Magnetostrictive Electromagnetic Acoustic Transducers for High Temperature Structure Monitoring

The Department of Energy’s Advanced Sensors and Instrumentation program seeks to develop and qualify advanced sensors for the nuclear industry. Reliable high temperature and high radiation sensors for detection and characterization of structural flaws in pipes, vessels, and structurally critical components is a weakness for both conventional light water reactors with coolant T-hot approaching 350oC, and for advanced reactors with T-hot temperatures in excess of 500 to 800oC. Magnetostrictive Electromagnetic Acoustic Transducers using a cold spray cobalt coating have been proposed as a sensor design that can withstand these kinds of temperatures and radiation levels to serve as online sensors to detect flaws before cracks, pits, or erosion/corrosion flaws progress to through-wall failures. This report tests cold spray cobalt as part of a magnetostrictive EMAT for high temperature service. Cobalt is known to have strong magnetostrictive properties however the effect of cold spray application is not well studied. This program was surprised to discover that cold sprayed cobalt exhibited little or no magnetostrictive behavior until it was thermally annealed. Following annealing to 650oC however, cold spray cobalt did exhibit a magnetostrictive response. Work to date prior to this milestone report publication showed that magnetostrictive EMAT was successfully tested to 400oC with an alnico permanent magnet. The program plans to extend testing with an electromagnet to higher temperatures. This follow-on work will be reported under subsequent publications or as a revision to this report.

Glass, Samuel W.↗

DOE OSTI2025

Improved guided-wave acoustic defect detection and localization in pipes under varying temperature conditions using deep learning

Early defect detection in pipelines is critical across industries, particularly in the oil and gas sector, where failures result in significant maintenance costs and operational disruptions. Acoustic guided-wave techniques are widely used for nondestructive evaluation of pipeline defects due to their long-distance propagation capability. However, environmental variations, sensitivity limitations, and complex signal interpretation challenges limit the effectiveness of traditional signal processing approaches with guided-wave signals. Recent advances in deep learning methods have demonstrated remarkable success in solving complex real-world problems in many fields. In particular, deep-learning-based signal processing holds substantial promise to overcome limitations and challenges of conventional signal processing. This study presents a deep learning framework for pipeline inspection using acoustic guided-wave signals under temperature varying environments. The proposed framework employs a dual-path one-dimensional convolutional autoencoder that combines defect detection, localization, and temperature prediction functions. The proposed system utilizes multi-mode and broadband acoustic waves with an optimized number of sensors that provide high accuracy while retaining practical simplicity. Experimental validation is performed on a carbon steel pipe. The results indicate exceptional defect detection accuracy and precise defect localization with a mean absolute error of 66 mm. The proposed technique also predicts the effective average temperature of the pipe with a mean absolute error of 0.2°C. Comparative analysis shows superior performance of the proposed method over a traditional method previously developed by the authors' team. These results highlight the potential of integrating deep learning methods into guided-wave pipeline inspection systems to improve reliability under varying environmental conditions.

42 ENGINEERING↗

DOE OSTI2026

Portable and Cost-Effective Device for Reliable Detection of Counterfeit and Non-compliant Refrigerants in Diverse Applications

Counterfeit refrigerants pose significant challenges to safety, system reliability, and operational effectiveness due to their harmful contaminants or incompatible chemical compositions. Utilizing these noncompliant products can lead to reduced efficiency, equipment failures, and expensive repairs. Additionally, heightened demand for alternative refrigerants during the industry's transition has created supply gaps, enabling counterfeit products to proliferate. Accurate detection and analysis tools are therefore essential to verify refrigerant authenticity and ensure system integrity in diverse applications. This paper presents the development of a portable device designed for reliable identification and detailed analysis of refrigerant composition. By integrating precision gas sampling, controlled pressure regulation, and automated sensor technology, the device not only detects deviations from standard refrigerant properties but also provides a comprehensive composition breakdown. Pre-calibrated sensors measure the refrigerant gas to identify specific concentrations and contaminants, with an intuitive LED-based indicator system ensuring quick interpretation of results. The user-friendly interface enables operators to select refrigerant types for targeted testing, further enhancing accuracy and usability for field technicians. Comprehensive testing was conducted on mildly flammable A2L refrigerants, showcasing the device’s robustness and adaptability in analyzing composition and detecting discrepancies. The device demonstrated consistent accuracy across a range of refrigerant samples, affirming its reliability in diverse operational environments. Its design minimizes contamination risks during sampling and provides detailed composition results within 90 seconds, ensuring efficient and precise analysis. With a projected price point under $150, the proposed solution delivers affordability alongside its lightweight portability and straightforward operation. Unlike complex and costly alternatives, such as gas chromatography systems, this device provides an accessible option for technicians, customs personnel, and industry operators in need of quick and effective refrigerant verification. Compatible with both current formulations and emerging refrigerant technologies, the device addresses critical counterfeit detection needs across a range of applications. By delivering accurate composition analysis and counterfeit identification, this innovation enhances system performance, safety, and operational reliability in crucial industries.

Cheekatamarla, Praveen [ORNL] (ORCID:0000000248827↗

DOE OSTI2025

Monte Carlo Dropout Uncertainty Quantification of Long Short-Term Memory Autoencoder Anomaly Detection in a Liquid Sodium Cold Trap

Advanced high-temperature fluid reactors, such as sodium-cooled fast reactors (SFRs) and molten salt–cooled reactors (MSCRs), require coolant purification systems to prevent fluid contamination and local freezing that can lead to plugging. Liquid sodium purification can be achieved with a cold trap, where the sodium temperature is reduced to a near-freezing point to precipitate out impurities. Automation of monitoring of the cold trap performance with machine learning algorithms can aid in early detection of incipient anomalies. An efficient approach to loss-of-coolant–type anomaly detection in a cold trap monitored with more than two dozen thermal-hydraulic sensors consists of a long short-term memory (LSTM) autoencoder. This work develops the uncertainty quantification of the LSTM autoencoder performance for cold trap anomaly detection using the Monte Carlo (MC) dropout method. The MC dropout methodology creates a distribution of sister distributions that all slightly differ from each other because of random neurons being turned off for testing. The variances of the sister network distributions are used to make an uncertainty interval. Our analysis shows that the uncertainty in the autoencoder performance is largest near the peak of the anomaly signal. Using the MC dropout method, we investigate the uncertainty in the anomaly detection with missing sensor inputs. This capability allows the reactor operator to evaluate resilience of the anomaly detection system and to make informed decisions about continuity of operation in the event of sensor failure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Infrared thermography NDT for in-situ defect detection in sandwich composite panel manufacturing

Composite manufacturing presents numerous challenges, as defects can arise from various sources throughout the process. In sandwich composite structures, the integration of a foam core introduces additional complexity and increases the likelihood of defect formation like delamination. To mitigate these issues and reduce the risk of future structural failures, in-situ monitoring during manufacturing is essential. This study investigates infrared (IR) thermography as a non-destructive technique for detecting manufacturing defects in foam-core sandwich composite panels under thermally excited conditions representative of in-situ processing. A stationary FLIR A8590 IR camera (640 × 512 pixels, 30Hz, 17mm lens, 9 ft stand-off distance) was used to monitor prefabricated panels subjected to controlled external heating simulating compression molding and resin cure exotherm. Interlaminar delamination defects with characteristic sizes ranging from 0.25 × 0.25in² to 5 × 5in² produced measurable surface temperature depressions of approximately 4–10°C during transient cooling, exceeding the effective noise floor of the camera by more than two standard deviations. Thicker laminates exhibited prolonged defect detectability windows due to increased thermal diffusion time. In contrast, embedded Teflon inclusions generated weak thermal contrasts of ≤ 3°C, approaching the measurement noise floor, due to limited thermal property contrast with the surrounding glass fiber composite. These results establish quantitative detectability limits for stationary thermographic inspection of sandwich composite panels under manufacturing-representative thermal cycles.

Barakat, Abdallah [ORNL] (ORCID:0000000296141398)↗

DOE OSTI2026

Spatiotemporal Learning in Power Modules: Wavelet-Enhanced Forecasting of Thermomechanical Degradation

Detecting internal defects in power electronics packages is critical for their performance and reliability, especially under extreme operating conditions, as these defects can lead to catastrophic failure if not properly addressed. Confocal scanning acoustic microscopy (C-SAM) plays a key role in the nondestructive evaluation of bond layer degradation within a power electronics package by detecting defects such as delamination, voids, and cracks. However, accurately quantifying and predicting these defects from C-SAM images remains a significant challenge due to the low noise-to-signal ratio, which typically arises from both imaging process and bond patterns itself. In this paper, we explore machine learning strategies for processing C-SAM images and providing predictive models of defect growth. We use C-SAM images of sintered copper and sintered silver samples, which are obtained under accelerated thermal experiments, as the representative dataset for our study. We investigate the effect of Fourier transforms and wavelet transforms on these datasets to remove high-frequency noise and address noise across multiple scales with histogram equalization to enhance the contrast and improve the visibility of defects. As a result, defect boundaries can be clearly distinguished, enabling more accurate tracking of their growth over time. We then employ different time-series forecasting algorithms on the denoised images to formulate an image-based lifetime prediction model. Statistical models and deep-learning techniques are trained on images obtained in the early stages of thermal shock, and defect growth in the later stages is predicted. Our work serves as a preliminary attempt to improve the accuracy of lifetime prediction models of power electronics packages, which is critical under extreme operating environments.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Limitations of Hydrogen Detection After 150 Years of Research on Hydrogen Embrittlement

Hydrogen's significance in contemporary society lies in its remarkable energy density, yet its integration into the worldwide energy grid presents a substantial challenge. Exposing materials to hydrogen environments leads to degradation of mechanical properties, damage, and failure. While the current approach for assessing hydrogen's impact on materials involves mainly multiscale modeling and mechanical testing, there exists a significant deficiency in detecting the intricate interactions between hydrogen and materials at the nanoatomic scales and under in situ conditions. This perspective review highlights the experimental endeavors aimed at bridging this gap, pointing toward the imminent need for new experimental techniques that can detect and map hydrogen in materials’ microstructures and their site‐specific dependencies.

Tunes, Matheus A.↗

DOE OSTI2024

Coincident learning for unsupervised anomaly detection of scientific instruments

Abstract Anomaly detection is an important task for complex scientific experiments and other complex systems (e.g. industrial facilities, manufacturing), where failures in a sub-system can lead to lost data, poor performance, or even damage to components. While scientific facilities generate a wealth of data, labeled anomalies may be rare (or even nonexistent), and expensive to acquire. Unsupervised approaches are therefore common and typically search for anomalies either by distance or density of examples in the input feature space (or some associated low-dimensional representation). This paper presents a novel approach called coincident learning for anomaly detection (CoAD), which is specifically designed for multi-modal tasks and identifies anomalies based on coincident behavior across two different slices of the feature space. We define an unsupervised metric, F ^ β , out of analogy to the supervised classification F β statistic. CoAD uses F ^ β to train an anomaly detection algorithm on unlabeled data , based on the expectation that anomalous behavior in one feature slice is coincident with anomalous behavior in the other. The method is illustrated using a synthetic outlier data set and a MNIST-based image data set, and is compared to prior state-of-the-art on two real-world tasks: a metal milling data set and our motivating task of identifying RF station anomalies in a particle accelerator.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Quantitative insights for diagnosing performance bottlenecks in lithium–sulfur batteries

Lithium–sulfur (Li–S) batteries hold significant promise for electric vehicles and aviation due to their high energy density and cost-effectiveness. However, understanding the root causes of performance degradation remains a formidable challenge, as the interplay of multiple factors obscures key failure mechanisms. A major limitation has been the inability to quantify soluble sulfur species within practical detection limits accurately and to correlate electrochemical processes with associated physical inventory changes. Here, we introduce the high-performance liquid chromatography-ultraviolet spectroscopy and gas chromatography sequential characterization (HUGS) toolkit, capable of precisely quantifying seven distinct sulfur and polysulfide species at concentrations as low as 40 ppb. HUGS has been successfully applied to practical coin and pouch cells without requiring cell modification. Furthermore, our self-developed software, Dr HUGS, enhanced the data analysis speed by over 30 times, enabling multi-source data integration and delivering comprehensive analysis results within minutes. Using HUGS, we identify significant capacity losses from inactive lithium and sulfur during initial cycles and sulfide-rich solid–electrolyte interphase (SEI) formation on the anode during later cycles. Notably, our findings reveal that soluble polysulfides have minimal contributions to capacity loss, challenging long-standing assumptions. Moreover, HUGS demonstrates that constant-pressure setups in Li–S pouch cells improve compositional uniformity compared to constant-gap configurations. For sulfurized polyacrylonitrile (SPAN) cathodes, unique issues such as non-sulfide SEI formation and lithium pulverization are observed, which can be mitigated through localized high-concentration electrolytes to enhance lithium inventory retention. By enabling precise quantification of critical inventory components, HUGS provides transformative insights into failure mechanisms across various electrolytes and cathode chemistries, guiding rational design strategies for next-generation energy storage systems.

25 ENERGY STORAGE↗

DOE OSTI2024

Anomaly Detection in Materials Digital Twins with Multiscale ICME for Additive Manufacturing

Detecting anomaly in fatigue and fracture experimental materials science is an interesting yet challenging topic. The reasons are threefold. First, the anomalous microstructure feature that gives rise to structural failure is small, sometimes in the order of 10 -7 of the interrogated volume. This, in turn, results in a highly imbalanced classification problem in machine learning (ML). Second, the consequence is high, in the sense that the test specimen is destructed in such case. Third, the convolution between microstructure stochasticity and the small probability of void nucleation, growth, and coalescence makes failure and fracture a hard-to-predict and challenging problem in materials science due to its irreproducibility, even experimentally. In this paper, we developed a materials digital twin and applied anomaly detection methods to detect voids and anomaly in additive manufacturing (AM). The materials digital twin is driven by two integrated computational materials engineering (ICME) models, which are kinetic Monte Carlo (kMC) and crystal plasticity finite element method (CPFEM). In conclusion, we demonstrated that by using anomaly detection, it is possible to detect voids and other defects in materials digital twin, which paves way for future research in integrating materials digital twin with its physical counterpart.

ICME↗

DOE OSTI2025

Destructive PIE and Safety Testing of Six AGR-5/6/7 Capsule 2 Compacts

This study evaluates fission product retention and particle failure mechanisms in AGR-5/6/7 Capsule 2 uranium carbide and uranium oxide (UCO) tristructural isotropic (TRISO) fuel under high-temperature gas reactor accident-relevant conditions using high-temperature safety tests and destructive postirradiation examination. Three Capsule 2 compacts were held isothermally at 1600°C for approximately 300 hours and one compact at 1800°C for approximately 300 hours; two additional compacts were examined in the as-irradiated state. Post-test deconsolidation–leach–burn–leach (DLBL) quantified nuclide inventories in matrix and particles. Individual particles were surveyed for radioisotope inventories, and microanalytical approaches resolved microstructural evolution and fission product distributions within the coating layers. At 1600°C, no krypton was detected above the minimum detectable limit, and cesium releases were far below a single particle equivalent, indicating the absence of full TRISO failure or SiC failures. Silver releases were limited and primarily reflected depleted postirradiation inventories, consistent with prior compact-level exams indicating substantial in-pile 110mAg loss. At 1800°C, cumulative 134Cs release of approximately 2.5 particle equivalents and delayed 85Kr totaling approximately 0.53 particle equivalents were consistent with one full TRISO failure and two SiC failures. Europium and strontium releases were roughly one order of magnitude higher than at 1600°C and comparable to AGR-1/AGR-2 high-temperature tests, with sustained late-hold rates indicating diffusion through intact coatings coupled with matrix depletion. Overall, AGR-5/6/7 Capsule 2 UCO fuel demonstrated fission product retention during safety testing consistent with prior AGR campaigns, while distinctive in-pile 110mAg depletion and measurable 1600°C europium loss motivate targeted follow-on studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Destructive PIE and Safety Testing of Six AGR-5/6/7 Capsule 2 Compacts

This study evaluates fission product retention and particle failure mechanisms in AGR-5/6/7 Capsule 2 uranium carbide and uranium oxide (UCO) tristructural isotropic (TRISO) fuel under high-temperature gas reactor accident-relevant conditions using high-temperature safety tests and destructive post-irradiation examination. Three Capsule 2 compacts were held isothermally at 1600°C for approximately 300 hours and one compact at 1800°C for approximately 300 hours; two additional compacts were examined in the as-irradiated state. Post-test deconsolidation–leach–burn–leach (DLBL) quantified nuclide inventories in matrix and particles. Individual particles were surveyed for radioisotope inventories, and microanalytical approaches resolved microstructural evolution and fission product distributions within the coating layers. At 1600°C, no krypton was detected above the minimum detectable limit, and cesium releases were far below a single particle equivalent, indicating the absence of full TRISO failure or SiC failures. Silver releases were limited and primarily reflected depleted post-irradiation inventories, consistent with prior compact-level exams indicating substantial in-pile 110m Ag loss. At 1800°C, cumulative 134 Cs release of approximately 2.5 particle equivalents and delayed 85 Kr totaling approximately 0.53 particle equivalents were consistent with one full TRISO failure and two SiC failures. Europium and strontium releases were roughly one order of magnitude higher than at 1600°C and comparable to AGR-1/AGR-2 high-temperature tests, with sustained late-hold rates indicating diffusion through intact coatings coupled with matrix depletion. Overall, AGR-5/6/7 Capsule 2 UCO fuel demonstrated fission product retention during safety testing consistent with prior AGR campaigns, while distinctive in-pile 110m Ag depletion and measurable 1600°C europium loss motivate targeted follow-on studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Explainable machine learning for incipient anomaly detection in compact molten salt heat exchanger with overlapping feature distributions

High-temperature molten salt-cooled reactors (MSCRs) are a promising next-generation nuclear technology option, offering efficient power conversion and inherent safety features. However, the reliability of these systems depends on the robust operation of heat exchangers (HXs), which are susceptible to failure due to temperature gradients and channel plugging caused by fluid freezing. Conventional monitoring methods, relying on inlet and outlet measurements, lack the spatial resolution needed to detect early-stage faults. We propose a novel design of a compact salt-to-salt matrix-type HX design consisting of interleaved arrays of parallel tubes, with integrated synthetic fiber optic distributed temperature sensing (DTS) to enable localized detection of incipient faults. To evaluate performance of this design, we generate high-fidelity synthetic data using heat transfer computational modeling to simulate channel plugging, and introduce sensor noise for realistic modeling of measurements. The dataset comprises of 97% normal operation and 3% anomaly cases, with each anomaly class representing 1% of the data. These early anomalies result in overlapping temperature profiles between normal and faulty channels, producing a non-separable dataset that challenges traditional classification techniques. We benchmark eight supervised machine learning (ML) models and demonstrate that XGBoost achieves the highest performance. To improve transparency, we develop an explainability framework combining Shapley values and partially ordered sets (POSETs) to quantify and structurally analyze feature importance. This approach identifies both dominant predictors and ambiguous feature relationships, enhancing trust and interpretability. Our results highlight the potential of combining DTS and explainable ML with intelligent feature selection to improve predictive maintenance and ensure operational resilience in advanced nuclear systems.

Prantikos, Konstantinos [Argonne National Laborato↗

DOE OSTI2025

Unsupervised Clustering of Microseismic Events and Focal Mechanism Analysis at the CO 2 Injection Site in Decatur, Illinois

Characterization of induced microseismicity at a carbon dioxide (CO 2 ) storage site is critical for preserving reservoir integrity and mitigating seismic hazards. We apply a multilevel machine learning (ML) approach that combines the nonnegative matrix factorization and hidden Markov model to extract spectral representations of microseismic events and cluster them to identify seismic patterns at the Illinois Basin-Decatur Project. Unlike traditional waveform correlation methods, this approach leverages spectral characteristics of first arrivals to improve event classification and detect previously undetected planes of weakness. By integrating ML-based clustering with focal mechanism analysis, we resolve small-scale fault structures that are below the detection limits of conventional seismic imaging. Our findings reveal temporal bursts of microseismicity associated with brittle failure, providing insights into the spatio-temporal evolution of fault reactivation during CO 2 injection. This approach enhances seismic monitoring capabilities at CO 2 injection sites by improving fault characterization beyond the resolution of standard geophysical surveys.

Willis, Rachel Marie [Sandia National Laboratories↗

DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗