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At least 559 records · Page 31

Reconstructing the Stripping History of the Sagittarius Stream with Neural Networks

The Sagittarius (Sgr) Stream is produced by the ongoing disruption of the Sgr dwarf spheroidal (dSph) galaxy and is thought to contain multiple wraps that were stripped during different pericentric passages. In this study, we introduce a neural-network–based method trained on N-body simulations to infer the stripping time of Sgr Stream stars directly from their phase-space coordinates. We combine spectroscopic data from SEGUE, APOGEE DR17, and LAMOST DR7 low-resolution spectroscopic (LRS) survey with Gaia EDR3 astrometry and distance estimates from the latest StarHorse catalog to identify high-quality Sgr Stream members. Applying our method to these stars, we measure a clear metallicity gradient with stripping time, well described by a linear relation with slope ∼0.3 dex Gyr −1 . We further predict the stripping times of globular clusters previously suggested to originate from the Sgr dSph. M 54, Terzan 7, Terzan 8, and Arp 2 exhibit stripping times consistent with being currently bound to the Sgr remnant. Pal 12, Whiting 1, and NGC 2419 are inferred to have been stripped 0.9 ± 0.1, 1.1 ± 0.2, and 2.1 ± 0.2 Gyr ago, respectively. For NGC 4147 and NGC 5634, whose membership in the Sgr system remains uncertain, our analysis suggests stripping times of 1.1 ± 0.4 and 1.1 ± 0.1 Gyr, respectively, if they are ultimately confirmed as genuine Sgr members. These results demonstrate that data-driven models of dynamical stripping histories offer a promising approach for reconstructing the formation and chemical evolution of the Sgr Stream.

79 ASTRONOMY AND ASTROPHYSICS↗

Considerations for Optimizing the Photometric Classification of Supernovae from the Rubin Observatory

The Vera C. Rubin Observatory will increase the number of observed supernovae (SNe) by an order of magnitude; however, it is impossible to spectroscopically confirm the class for all SNe discovered. Thus, photometric classification is crucial, but its accuracy depends on the not-yet-finalized observing strategy of Rubin Observatory's Legacy Survey of Space and Time (LSST). We quantitatively analyze the impact of the LSST observing strategy on SNe classification using simulated multiband light curves from the Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC). First, we augment the simulated training set to be representative of the photometric redshift distribution per SNe class, the cadence of observations, and the flux uncertainty distribution of the test set. Then we build a classifier using the photometric transient classification library snmachine, based on wavelet features obtained from Gaussian process fits, yielding a similar performance to the winning PLAsTiCC entry. We study the classification performance for SNe with different properties within a single simulated observing strategy. We find that season length is important, with light curves of 150 days yielding the highest performance. Cadence also has an important impact on SNe classification; events with median inter-night gap <3.5 days yield higher classification performance. Interestingly, we find that large gaps (>10 days) in light-curve observations do not impact performance if sufficient observations are available on either side, due to the effectiveness of the Gaussian process interpolation. This analysis is the first exploration of the impact of observing strategy on photometric SN classification with LSST.

79 ASTRONOMY AND ASTROPHYSICS↗

Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators

The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.

93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗

A Systematic Evidence Based Performance Approach to Regulation of Nuclear Sites in England and Wales - 20058

The Environment Agency for England has developed a systematic evidence-based approach to pursue our strategic environmental objectives for the regulation of nuclear sites. We use an annual evidence review process to ensure effective and efficient targeting of limited resources to achieve those objectives. Over the last 8 years, we have been developing and refining this approach to ensure risk-based and value driven regulation. The approach comprises nuclear site and nuclear sector review processes known as Site Environment Review (SER) and Nuclear Environment Review (NER). This approach complements our regulation of nuclear site permit holders under the Environmental Permitting Regulations (EPR). We deliver our regulation of nuclear sites in England and Wales alongside the Office for Nuclear Regulation. The SER process involves the lead regulator for each nuclear site assessing the permit holder's environmental performance across 14 themes, set within the context of the site's main activities and associated waste disposals. Our themes include environmental leadership, resources and climate change, radioactive waste management, facility management and decommissioning, groundwater, and environmental radiological protection. We use evidence from site inspections and working within our subject matter groups to grade current and predicted future environmental performance. We are particularly interested in sustainability and the application of Best Available Techniques (BAT) to prevent the creation, and minimise the disposal, of radioactive wastes. We use risk analysis (strengths, weaknesses, threats and opportunities) to examine performance against our strategic environmental objectives, which are set out, in our 5-year Nuclear Delivery Plan (NDP). The output supports the targeting of our resources at each nuclear site. We consult the relevant permit holders on the SER priorities and use their feedback to refine our plans. We expect all permit holders to take account of our priorities when considering their own programmes of work, objectives and plans. The NER process brings together what we learn and achieve through regulation across the sector. It provides input to planning priorities, supported by qualitative and semi-quantitative evidence. It covers the 28 nuclear sites in England and Wales and spans the same 14 environmental themes. During the process we collate, compile and summarise evidence from the SERs and other sources such as inspection reports and evidence from our other nuclear work programmes. The output is the NER annual report. This provides a snapshot of the status of the nuclear sector and gives insights to enable us to regulate more efficiently and effectively. It also takes account of cross-cutting issues and risks such as changes in international standards, domestic policy, regulatory framework, domestic standards and guidance, learning from experience such as incidents, events and good practice, and innovation, research and development. It provides graphics that illustrate the grading of environmental performance for the nuclear sector across the fourteen environmental themes. This analysis allows benchmarking of nuclear site's environmental performance and the visualisation provides a convenient comparison of performance across themes, sites, and over time. We use this intelligence to inform our investment in training and development of our staff, and our cross-cutting engagement on strategic issues with government, the Nuclear Decommissioning Authority (NDA) and other corporate organisations. Adopting this approach can provide benefits with organisational reputation, stakeholder participation and ensuring value from the public investment. This paper describes the history of the SER/NER process, a selection of outputs from the process and ideas for improvement. The paper will be of interest to other regulators and organisations across the world that are interested in supporting continuous improvement. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Anomaly Detection for Online Monitoring of Thermocouple Sensors in the Advanced Test Reactor

This study explores data-driven anomaly detection methods to analyze sensor fail- ures in the Advanced Gas Reactor (AGR) nuclear fuel irradiation experiments. Specifically, we examine failures of thermocouples (TCs), which are critical for mon- itoring and controlling in-reactor temperatures during operation. Failures were pri- marily observed during abrupt power transitions and manifested as sensor drop-outs, drifts, or unexplained behavior. We applied three time-series analysis techniques— rolling mean smoothing, matrix profile, and vector auto-regression (VAR)—to de- tect anomalies in TC data prior to failure events. The rolling mean method effec- tively highlighted deviations aligned with reported failures, while the matrix profile provided partial early warning but sometimes flagged normal fluctuations during power-down periods. VAR shows potential in capturing multivariate dependencies but requires further calibration. A rare case of TC drift was also documented, which did not result in failure, underscoring the challenge of building predictive models with sparse positive examples. Our findings demonstrate that traditional statistical tools can aid anomaly detection but have limited predictive power without richer training data. We propose future directions including synthetic data generation, real- time surrogate modeling, and multi-modal feature integration. This work provides a foundation for applying robust anomaly detection frameworks to mission-critical sensor systems in experimental settings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Deep learning closure models for large-eddy simulation of flows around bluff bodies

Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.

Mechanics↗

Machine Learning‐Assisted Microearthquake Location Workflow for Monitoring the Newberry Enhanced Geothermal System

Abstract Enhanced geothermal systems (EGS) offer a sustainable energy source but face challenges in accurately locating microearthquakes induced during reservoir stimulation. Locating these microearthquakes provides reliable feedback on the stimulation progress. Current deep learning methods for locating earthquakes require extensive data sets for training, which is problematic as detected microearthquakes are often limited. To address the scarcity of training data, we propose a practical workflow using probabilistic multilayer perceptron (PMLP) which predicts microearthquake locations from cross‐correlation time lags in waveforms. Utilizing a 3D velocity model of Newberry site derived from ambient noise interferometry, we generate numerous synthetic microearthquakes and 3D acoustic waveforms for PMLP training. Accurate synthetic tests prompt us to apply the trained network to the 2012 and 2014 stimulation field waveforms. To enhance the accuracy of source localization, we carefully handpick the P‐arrival times. Predictions on the 2012 stimulation data set show major microseismic activity at depths of 0.5–1.2 km, correlating with a known casing leakage scenario. In the 2014 data set, the majority of predictions concentrate at 2.0–2.9 km depths, consistent with results obtained from conventional physics‐based inversion, and align with the presence of natural fractures from 2.0 to 2.7 km. We validate our findings by comparing the synthetic and field picks, demonstrating a satisfactory match for the first arrivals. By combining the benefits of quick inference speeds and accurate location predictions, we demonstrate the feasibility of using realistic synthetic data set to locate microseismicity for EGS monitoring.

15 GEOTHERMAL ENERGY↗

Multivariate Time Series Anomaly Detection with Few Positive Samples

Given the scarcity of anomalies in real-world applications, the majority of literature has been focusing on modeling normality. The learned representations enable anomaly detection as the normality model is trained to capture certain key underlying data regularities under normal circumstances. In practical settings, particularly industrial time series anomaly detection, we often encounter situations where a large amount of normal operation data is available along with a small number of anomaly events collected over time. This practical situation calls for methodologies to leverage these small number of anomaly events to create a better anomaly detector. In this paper, we introduce two methodologies to address the needs of this practical situation and compared them with recently developed state of the art techniques. Our proposed methods anchor on representative learning of normal operation with autoregressive (AR) model along with loss components to encourage representations that separate normal versus few positive examples. We applied the proposed methods to two industrial anomaly detection datasets and demonstrated effective performance in comparison with approaches from literature. Our study also points out additional challenges with adopting such methods in practical applications.

Xue, Feng↗

Implementing Mixed Reality Tools to Support Mission Delivery at Hanford - 20520

Mission Support Alliance's (MSA) Public Works and Information Systems organizations have been working with Microsoft Corporation to develop and implement mixed reality operational solutions using their HoloLens technology. This collaborative effort is intended to drive innovative solutions and significantly improve MSA's efficiency in performing work at the Hanford Site. HoloLens, a mixed reality tool, is a commercial off-the-shelf technology that combines a head-mounted viewing screen with applications to help people and organizations learn, communicate, and collaborate more effectively through the use of mixed reality. https://microsoft.com/en-us/hololens MSA's initial pilot successfully demonstrated its ability to use mixed reality utilizing HoloLens' advanced features in a variety of ways, illustrating the potential efficiency gains previously stated as goals of this pilot. These achievements include the development of proprietary technology that allows synchronization between a HoloLens device and a mobile device or alternate global positioning system (GPS) device. This synchronization enables the HoloLens device to access real time GPS location data anywhere on the Hanford Site. This real time location data, combined with MSA's improved Hanford Geographical Information System (GIS) data, enables the mixed reality pilot application to identify underground utility systems as well as related utility attributes. This ability will aid utility workers in several areas, including excavation activities, the placement of large cranes, identifying interactions and conflicts with future underground utility placements and, eventually, recognizing and de-conflicting tank waste transfer system valve alignments. The HoloLens mixed reality application is also able to provide full or small scale holographic images of a facility's digital twin. This feature will allow MSA's Water and Sewer Utilities team to train and validate procedures associated with the new water treatment facility virtually, before it is constructed. This reduces the amount of time it takes to complete the training and procedure validation, and accelerates the overall construction schedule. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Three-dimensional coherent X-ray diffraction imaging via deep convolutional neural networks

Abstract As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate ‘loss function’ alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Robust Event Classification Using Imperfect Real-world PMU Data

Here, this paper studies robust event classification using imperfect real-world phasor measurement unit (PMU) data. By analyzing the real-world PMU data, we find it is challenging to directly use this dataset for event classifiers due to the low data quality observed in PMU measurements and event logs. To address these challenges, we develop a novel machine learning framework for training robust event classifiers, which consists of three main steps: data preprocessing, fine-grained event data extraction, and feature engineering. Specifically, the data preprocessing step addresses the data quality issues of PMU measurements (e.g., bad data and missing data); in the fine-grained event data extraction step, a model-free event detection method is developed to accurately localize the events from the inaccurate event timestamps in the event logs; and the feature engineering step constructs the event features based on the patterns of different event types, in order to improve the performance and the interpretability of the event classifiers. Based on the proposed framework, we develop a workflow for event classification using the real-world PMU data streaming into the system in real time. Using the proposed framework, robust event classifiers can be efficiently trained based on many off-the-shelf lightweight machine learning models. Numerical experiments using the real-world dataset from the Western Interconnection of the U.S power transmission grid show that the event classifiers trained under the proposed framework can achieve high classification accuracy while being robust against low-quality data.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

First Search for Dark-Trident Processes Using the MicroBooNE Detector

This thesis presents a first search for dark-trident scattering in a neutrino beam using a data set corresponding to $7.2 \times 10^{20}$ protons on target taken with the MicroBooNE detector at Fermilab. Proton interactions in the neutrino target at the Main Injector produce $\pi^0$ and $\eta$ mesons, which could decay into dark matter (DM) particles via a dark photon $A^{\prime}$. A convolutional neural network is trained to identify interactions of the DM particles in the liquid-argon time projection chamber (LArTPC) exploiting its image-like reconstruction capability. In the absence of a DM signal, limits at the $90\%$ confidence level on the squared kinematic mixing parameter $\varepsilon^2$ as a function of the dark-photon mass in the range $10\le M_{A^\prime}\le 400$~MeV are provided. The limits cover previously unconstrained parameter space for the production of fermion or scalar DM particles $\chi$ for two benchmark models with mass ratios $M_{\chi}/M_{A^\prime}=0.6$ and $2$ and for dark fine-structure constants $0.1\le\alpha_D\le 1$.Date of Award1 Aug 2024Original languageEnglishAwarding InstitutionThe University of ManchesterSupervisorStefan Soldner-Rembold (Supervisor) & Justin Evans (Supervisor)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Transfer learning for metamaterial design and simulation

Abstract We demonstrate transfer learning as a tool to improve the efficacy of training deep learning models based on residual neural networks (ResNets). Specifically, we examine its use for study of multi-scale electrically large metasurface arrays under open boundary conditions in electromagnetic metamaterials. Our aim is to assess the efficiency of transfer learning across a range of problem domains that vary in their resemblance to the original base problem for which the ResNet model was initially trained. We use a quasi-analytical discrete dipole approximation (DDA) method to simulate electrically large metasurface arrays to obtain ground truth data for training and testing of our deep neural network. Our approach can save significant time for examining novel metasurface designs by harnessing the power of transfer learning, as it effectively mitigates the pervasive data bottleneck issue commonly encountered in deep learning. We demonstrate that for the best case when the transfer task is sufficiently similar to the target task, a new task can be effectively trained using only a few data points yet still achieve a test mean absolute relative error of 3 % with a pre-trained neural network, realizing data reduction by a factor of 1000.

Peng, Rixi↗

Time-lapse seismic inversion for CO 2 saturation with SeisCO2Net: An application to Frio-II site

Seismic monitoring of geological CO 2 storage (GCS) involves highly nonlinear seismic inversion and petrophysical inversion, making it challenging to estimate CO 2 volume efficiently and detect possible early CO 2 leakages. Deep learning (DL) using convolutional neural networks (CNNs) has shown promise in solving highly nonlinear seismic inversion problems. However, direct estimation of CO 2 plume extent/saturation from time-lapse seismic gathers using DL is still underexplored, with no reported field applications to date. The investigation of field data is primarily hindered by scarcity of field data for neural network training. Other obstacles include highly nonlinear seismic-petrophysics inverse relationship, and presence of noise in field seismic data. We introduce SeisCO2Net, a deep CNN that predicts CO 2 saturation maps directly from time-lapse full waveform shot gathers. For training, we use site-specific geological information, fluid flow physics, rock physics, and seismic modeling to generate synthetic datasets that closely resemble the CO 2 storage site. Synthetic tests show promising results, inspiring us to apply SeisCO2Net's trained weights on field data collected at Frio-II GCS site by leveraging transfer learning principles. As reference, we compare SeisCO2Net's predicted CO 2 saturation maps with results obtained from physics-based inversion. Our analyses show both methods display similar CO 2 plume shapes, reasonable CO 2 plume characteristics, and comparable saturation values. Our results suggest pre-training CNNs on physics-informed synthetic datasets and then applying the learned weights to field data is a viable approach to estimating field CO 2 saturation. This method effectively addresses the scarcity of field training data, thus encouraging the feasibility of long-term GCS monitoring.

58 GEOSCIENCES↗

Multimodal sensor fusion for real-time standoff estimation in directed energy deposition

In Laser Powder-based Direct Energy Deposition (LP-DED) systems, achieving consistency, precision and quality of produced parts requires tight control over printing parameters. One of the critical parameters is the standoff distance. Maintaining an optimal standoff height is crucial for achieving correct laser power density and powder catchment efficiency, as both laser and powder streams are focused at this distance. Here, this study introduces a novel approach using multimodal sensor fusion to predict standoff height in real-time. The proposed system integrates two low-profile, cost-effective sensors: an RGB coaxial camera and a high frequency and high dynamic range microphone. By utilizing a simple fully connected neural network, trained on a limited dataset, data fusion of these sensors allowed for the real-time prediction of the standoff height. The results demonstrate high resolution and accuracy of the predictions across multiple geometries and a wide range of standoff heights. This approach offers a simple, and cost-effective solution for real-time standoff height monitoring and lays the groundwork for future integration into commercial LP-DED systems.

42 ENGINEERING↗

Monitoring Fracture Hydromechanical Evolution in the Lab and Field Using Unsupervised Metric Learning

Fractures evolve in time through thermal‐hydraulic‐mechanical‐chemical (THMC) processes that alter their long‐range hydraulic transport properties and modify subsurface behavior and activities. The location of subsurface fractures makes it necessary to use remote sensing techniques such as passive or active seismic monitoring for fracture characterization. In this paper, we develop a machine learning approach to monitor the evolution of fracture properties using passive seismic sources in a laboratory setting and using active seismic monitoring from the Sanford Underground Research Facility in Lead, South Dakota, at a depth of 1.25 km in amphibolite rock during stimulation of natural fractures as well as during induced fracturing. The unsupervised metric learning technique applies tandem neural networks (twin (Siamese) or triplet) with contrastive loss and adaptive margins to track slowly varying systems for which class or similarity labels are not available. The approach adopts locality‐sensitive hashing to divide time‐ordered contiguous data into an arbitrary number of pseudo‐classes. Contrastive‐loss training with many hash bins generates an evolving latent‐space trajectory. This approach enables unsupervised metric learning for seismic data stacks under the condition of contiguous state sampling and slowly varying fracture properties. The displacement discontinuity theory provides a mechanistic foundation for the fracture‐dependent trajectories that are related to relaxation of fractures with time‐dependent specific stiffness responding to changes in stress or fluid saturation.

02 PETROLEUM↗