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At least 919 records · Page 51

Comparison of machine learning and electrical resistivity arrays to inverse modeling for locating and characterizing subsurface targets

Here, this study evaluates the performance of multiple machine learning (ML) algorithms and electrical resistivity (ER) arrays for inversion with comparison to a conventional Gauss-Newton numerical inversion method. Four different ML models and four arrays were used for the estimation of only six variables for locating and characterizing hypothetical subsurface targets. The combination of dipole-dipole with Multilayer Perceptron Neural Network (MLP-NN) had the highest accuracy. Evaluation showed that both MLP-NN and Gauss-Newton methods performed well for estimating the matrix resistivity while target resistivity accuracy was lower, and MLP-NN produced sharper contrast at target boundaries for the field and hypothetical data. Both methods exhibited comparable target characterization performance, whereas MLP-NN had increased accuracy compared to Gauss-Newton in prediction of target width and height, which was attributed to numerical smoothing present in the Gauss-Newton approach. MLP-NN was also applied to a field dataset acquired at U.S. DOE Hanford site.

54 ENVIRONMENTAL SCIENCES↗

Near-Infrared Photoluminescence from Spin-Flip Excited States of π-Conjugated Tris(quinolinolate) Chromium(III) Complexes

Tuning metal–ligand covalency offers promising design strategies to tailor the photoluminescence (PL) emission energies of metal-centered, spin-flip excited states. Herein, we report a series of tris(quinolinolate) chromium(III) complexes that exhibit record-low near-infrared II emission energies in a fluid solution at room temperature, afforded by their strong metal–ligand covalencies. Appending π-conjugated arylethynyl substituents to quinolinolate ligands resulted in minimal changes to metal–ligand bond lengths, facilitating nearly indiscriminate metal–ligand covalencies for each tris(quinolinolate) chromium(III) complex. As a result, near-infrared II emission was observed across the series, while simultaneously affording careful tuning of the 4 LMCT/ 4 ( 1 ILCT) electronic transition energies across the visible region. Here, detailed analyses of ground-state electronic structures and excited-state electronic transitions revealed that PL arises from a ligand-field, 2 E excited state, admixed with charge-transfer character. This assignment was supported by solvent-dependent near-infrared emission energies and long excited-state lifetimes, consistent with spin-forbidden relaxation (ranging from 115 ± 5 to 123 ± 1 ns across the series). Utilizing spectroscopic data, ligand-field parameters were quantified, further rationalizing the role of strong metal–ligand covalency in enabling near-infrared II emission. Supported by these results, this study presents a new class of ligands that enable room-temperature near-infrared II emission in chromium(III)-based spin-flip excited states.

Absorption spectroscopy↗

Deep learning to estimate permeability using geophysical data

Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. Each measurement in both synthetic and field data is standardized by removing the mean and scaling the time-series to unit variance. This pre-processing step is necessary to bring simulation data closer to field observations. Subsurface process models based on hydrogeophysics are used to generate this synthetic data. Training performed on limited simulation data resulted in the DL model over-fitting. An advanced data augmentation based on mixup is implemented to generate additional training samples to overcome this issue. This mixup technique creates weakly labeled (low-fidelity) samples from strongly labeled (high-fidelity) data. The weakly labeled training data is then used to develop DL-enabled inverse models and reduce over-fitting. As both time-lapse ERT (1133048 features/realization) and 3D permeability (585453 features/realization) data samples are from a high-dimensional space, principal component analysis (PCA) is employed to reduce dimensionality. Encoded ERT and encoded permeability are generated using the trained PCA estimators. A deep neural network is then trained to map the encoded ERT to encoded permeability. This mixup training and unsupervised learning allowed us to build a fast and reasonably accurate DL-based inverse model under limited simulation data. Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. Quantitatively, the average mean squared error (in terms of the natural log) on the strongly labeled training, validation, and test datasets is less than 0.5. The R 2 -score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. Finally, an added benefit in terms of computational cost is that the proposed DL-based inverse model is at least O(10 4 ) times faster than running a forward model once it is trained. Data generation, DL model training, and hyperparameter tuning to identify optimal neural network architectures utilized high-performance computing resources while the DL inference is performed on a standard laptop. Approximately, O(10 5 ) processor hours are used for generating data and DL tuning and training. We acknowledge that the data generation and DL model development are expensive. But once a DL model is trained, it can be re-used for inversion rapidly for the given system, with set physics and domain. Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. This computational savings ≈ O(10 5 ) – O(10 7 )) makes the proposed DL-based inverse model attractive for subsurface imaging and real-time ERT monitoring applications due to fast and yet reasonably accurate estimations of permeability field.

58 GEOSCIENCES↗

The Edge of Exploration: An Edge Storage and Computing Framework for Ambient Noise Seismic Interferometry Using Internet of Things Based Sensor Networks

Recent technological advances have reduced the complexity and cost of developing sensor networks for remote environmental monitoring. However, the challenges of acquiring, transmitting, storing, and processing remote environmental data remain significant. The transmission of large volumes of sensor data to a centralized location (i.e., the cloud) burdens network resources, introduces latency and jitter, and can ultimately impact user experience. Edge computing has emerged as a paradigm in which substantial storage and computing resources are located at the “edge” of the network. In this paper, we present an edge storage and computing framework leveraging commercially available components organized in a tiered architecture and arranged in a hub-and-spoke topology. The framework includes a popular distributed database to support the acquisition, transmission, storage, and processing of Internet-of-Things-based sensor network data in a field setting. We present details regarding the architecture, distributed database, embedded systems, and topology used to implement an edge-based solution. Lastly, a real-world case study (i.e., seismic) is presented that leverages the edge storage and computing framework to acquire, transmit, store, and process millions of samples of data per hour.

58 GEOSCIENCES↗

Chemically Enabled CO 2 -Enhanced Oil Recovery in Multi-Porosity, Hydrothermally Altered Carbonates in the Southern Michigan Basin (Final Technical Report)

This is the Final Technical Report for the project "Chemically Enabled CO 2 -Enhanced Oil Recovery in Multi-Porosity, Hydrothermally Altered Carbonates in the Southern Michigan Basin." Over the course of six years of collaboration between Battelle and project partners, all stated objectives of the program have been completed, including full geological characterization of the TBR trend (See companion report for Task2), laboratory and modeling experiments to determine the optimum composition and design of CO 2 -EOR operations in the TBR trend, execution of a field test of chemically-enhanced CO 2 in a TBR well, and integration of the data and learnings gathered during these efforts into a full-trend development plan. Detailed reporting on these activities, their outcomes, and implications for trend-wide development is provided in the report. This report and encompassed data will provide TBR field operators with detailed information on what worked, what did not work, and how to proceed with production optimization of their TBR assets using chemically-enhanced CO 2 -EOR. CO 2 -EOR is a relatively well understood and broadly implemented strategy for increasing incremental production across the oil and gas industry, but its application has been primarily focused on reservoirs with limited heterogeneity. The intention of this project was show first that the same physical mechanisms that improve recovery factors in homogeneous reservoirs (namely wettability alteration, viscosity alteration, oil swelling, and mobility control) are at play in heterogeneous reservoirs. This was proven by the project’s laboratory studies and dynamic simulations, with the potential exception of mobility control, which needs further study. The second intention was to demonstrate via direct field testing that CO 2 -EOR can work in a strongly heterogeneous reservoir. While the field test strategy implemented during this project did not succeed in producing oil, data gathered during the test sheds light on what may work for field operators who try chemically-enhanced CO 2 -EOR within their own reservoirs, significantly reducing the level of uncertainty carried by first-of-a-kind commercial efforts that could (and should) follow this test. Simultaneously, the project has identified several large-volume ethanol plants and other sources of CO 2 emissions in the region and provided a handrail that CO 2 emitters and field operators can leverage to capture, transport, and inject that CO 2 into their fields. This project has also shown that, in many cases, the economics of CO 2 -EOR in the TBR are attractive. And finally, by completing a project of this scope in the southern Michigan Basin, the project has contributed to the knowledge base and operational experience of field operators, state regulatory agencies, local service companies, and state universities, with CO 2 -EOR projects which should allow follow-on projects to proceed safely and efficiently.

02 PETROLEUM↗

Real-Time, Simultaneous Soil Water Content and Meteorological Data Measurement to Support TRACER over Harris County, Texas Field Campaign Report: Part II

The main purpose of this project was to provide ground-truth and satellite-based soil water content data in the Houston, Texas, area to support the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility’s 2022 field campaign, the Tracking Aerosol Convection Interactions ExpeRiment (TRACER). This involved installing four soil monitoring stations at different locations in the Houston area, two of which were part of the ARM facility and two were ancillary. The two stations associated directly with ARM were installed alongside other facilities managed and maintained by the TRACER research team during the intensive operational period (IOP), one located at the La Porte, Texas airport and the other located near Guy, Texas. Data from these stations were assimilated with similar data collected by the Harris County Flood Control District (HCFCD) to improve the spatial coverage of the real-time monitoring network. The ground-truth data were compared to the satellite-based (National Aeronautics and Space Administration [NASA]’s Soil Moisture Active Passive [SMAP] mission) data in the TRACER area of interest, and analyzed further to nowcast gridded data over the Houston area. The nowcasted, gridded data product was made available to TRACER researchers for use in climate and land-atmosphere interaction modeling that can help understand formation and persistence of convective storms in dense urban areas, and predict possible environmental events such as floods.

54 ENVIRONMENTAL SCIENCES↗

Machine learning for reactor power monitoring with limited labeled data

Real-time reactor power monitoring is critical for a variety of nuclear applications, spanning safety, security, operations, and maintenance. While machine learning methods have shown promise in monitoring reactor power levels, there is limited research on their efficacy in label-starved environments. The goal of this work is to assess the feasibility of classifying nuclear reactor power level using multisource data in scenarios with limited labels. Data were collected using low-resolution multisensors at four nuclear reactor facilities: two large research reactors and two TRIGA reactors. Within each pair, one reactor dataset served as the source and the other as the target in a transfer learning paradigm. Twenty-three supervised models were trained on labeled sequences of magnetic field and acceleration data from each of the target sites. Self-learning and transfer learning methods were applied to the top performing models to assess their classification performance with increasing amounts of labeled data. While reactor power level classification was achieved with a Matthews Correlation Coefficient of up to 0.739 ± 0.003 and 0.622 ± 0.009 with only 400 sequences per power state for the large research reactor and TRIGA target sites, respectively, self-learning and transfer learning leveraging source site data did not improve target classification performance. These findings suggest that alternative methods, such as higher sensitivity sensors, digital twins, or the use of physics-informed models, are required to enable high-performance classification in machine learning approaches to reactor monitoring with a dearth of target ground truth.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A study on the clustering properties of radio-selected sources in the Lockman Hole region at 325 MHz

Studying the spatial distribution of extragalactic source populations is vital in understanding the matter distribution in the Universe. It also enables understanding the cosmological evolution of dark matter density fields and the relationship between dark matter and luminous matter. Clustering studies are also required for EoR foreground studies since it affects the relevant angular scales. This paper investigates the angular and spatial clustering properties and the bias parameter of radio-selected sources in the Lockman Hole field at 325 MHz. The data probes sources with fluxes ≳0.3 mJy within a radius of 1.8° around the phase centre of a 6° × 6° mosaic. Based on their radio luminosity, the sources are classified into Active Galactic Nuclei (AGNs) and Star-Forming Galaxies (SFGs). Clustering and bias parameters are determined for the combined populations and the classified sources. The spatial correlation length and the bias of AGNs are greater than SFGs- indicating that more massive haloes host the former. This study is the first reported estimate of the clustering property of sources at 325 MHz, intermediate between the pre-existing studies at high and low-frequency bands. It also probes a well-studied deep field at an unexplored frequency with moderate depth and area. Clustering studies require such observations along different lines of sight, with various fields and data sets across frequencies to avoid cosmic variance and systematics. Thus, an extragalactic deep field has been studied in this work to contribute to this knowledge.

79 ASTRONOMY AND ASTROPHYSICS↗

An ML-based terrestrial data fusion and augmentation framework to enable advanced understanding of the terrestrial carbon and water interactions

Soil moisture is essential to the terrestrial carbon and water cycles and land–atmosphere interactions. There are various types of soil moisture data, and each type has the distinct spatiotemporal strengths and limitations, depending on the diverse applications and retrieval methodologies of different data types (Li et al., in review; The PNNL-82151 FY23 Report). However, the limitations of different soil moisture data in terms of accuracy and spatiotemporal coverage hinder our ability to further understand the soil moisture dynamics across scales. To have a gap free soil moisture data product with a fine spatiotemporal coverage and vertical profiles, we train extreme gradient boosting (XGBoost) models by using (1) in-situ soil moisture measurements from the International Soil Moisture Network (ISMN), (2) soil moisture from the ECMWF reanalysis (ERA) at the 9 km and sub-daily spatiotemporal resolution, (3) the Daymet meteorological fields, and (4) data products that characterize surface conditions, including soil texture, organic content, topography, vegetation type, and rooting depth. We use the trained XGBoost models that have consistent performance across seven soil layers, i.e., 0–5 cm, 5–10 cm, 10–20 cm, 20–40 cm, 40–60 cm, 60–100 cm, and 100–200 cm, and the gridded model predictors to generate a soil moisture data at the 1 km and daily spatiotemporal resolution for the Continental United States (CONUS) from 2001–2020. This dataset can be broadly used for Earth system model benchmark, monitoring extreme weathers, making informed decisions regarding agriculture, water resource management, climate change mitigation, and ecosystem preservation.

58 GEOSCIENCES↗

TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclones

Tropical cyclones (TCs) are among the most destructive weather systems. Realistically and efficiently detecting and tracking TCs are critical for assessing their impacts and risks. In particular, the eye is a signature feature of a mature TC. Therefore, knowing the eyes’ locations and movements is crucial for both operational weather forecasts and climate risk assessments. Recently, a multilevel robustness framework has been introduced to study the critical points of time-varying vector fields. The framework quantifies the robustness (i.e., structural stability) of critical points across varying neighborhoods. By relating the multilevel robustness with critical point tracking, the framework has demonstrated its potential in cyclone tracking. An advantage is that it identifies cyclonic features using only 2D wind vector fields, which is encouraging as most tracking algorithms require multiple dynamic and thermodynamic variables at different altitudes. A disadvantage is that the framework does not scale well computationally for datasets containing a large number of cyclones. Herein this paper introduces a topologically robust physics-informed tracking framework (TROPHY) for TC tracking. The main idea is to integrate physical knowledge of TC to drastically improve the computational efficiency of multilevel robustness framework for large-scale climate datasets. First, during preprocessing, we propose a physics-informed feature selection strategy to filter 90% of critical points that are short-lived and have low stability, thus preserving good candidates for TC tracking. Second, during in-processing, we impose constraints during the multilevel robustness computation to focus only on physics-informed neighborhoods of TCs. We apply TROPHY to 30 years of 2D wind fields from reanalysis data in ERA5 and generate a number of TC tracks. In comparison with the observed tracks, we demonstrate that TROPHY can capture TC characteristics (e.g., frequency, intensity, duration, latitudes with maximum intensity, and genesis) that are comparable to and sometimes even better than a well-validated TC tracking algorithm that requires multiple dynamic and thermodynamic scalar fields.

97 MATHEMATICS AND COMPUTING↗

Our teams design high-resolution MeV x-ray radiography systems for National security missions [Poster]

The NNSS has been at the forefront of custom high-fidelity x-ray/gamma radiographic imaging solutions that serve our national security for over five decades. Our radiography team utilizes expertise in physics modeling and analysis, along with optical, mechanical, and electrical design, in close collaboration with our customers, to develop imaging methods and capabilities that go beyond their needs. Conceptual designs are developed through R&D efforts to provide solutions for the specific problem at hand. Field systems are designed and built in-house, then qualified utilizing a range of facilities across the National Security Enterprise. Radiographic imaging systems are deployed by our team in the most challenging environments. The NNSS has a strong math and programming team that provides novel on-site image analysis methods that extract crucial information from data returned in field tests.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: large-scale structure catalogues and measurement of the isotropic BAO between redshift 0.6 and 1.1 for the Emission Line Galaxy Sample

ABSTRACT We present the Emission Line Galaxy (ELG) sample of the extended Baryon Oscillation Spectroscopic Survey from the Sloan Digital Sky Survey IV Data Release 16. We describe the observations and redshift measurement for the 269 243 observed ELG spectra, and then present the large-scale structure catalogues, used for the cosmological analysis, and made of 173 736 reliable spectroscopic redshifts between 0.6 and 1.1. We perform a spherically averaged baryon acoustic oscillations (BAO) measurement in configuration space, with density field reconstruction: the data two-point correlation function shows a feature consistent with that of the BAO, the BAO model being only weakly preferred over a model without BAO (Δχ2 < 1). Fitting a model constrained to have a BAO feature provides a 3.2 per cent measurement of the spherically averaged BAO distance DV(zeff)/rdrag = 18.23 ± 0.58 at the effective redshift zeff = 0.845.

Raichoor, Anand↗

A portable application framework for energy management and information systems (EMIS) solutions using Brick semantic schema

This paper introduces a portable framework for developing, scaling and maintaining energy management and information systems (EMIS) applications using an ontology-based approach. Key contributions include an interoperable layer based on Brick schema, the formalization of application constraints pertaining metadata and data requirements, and a field demonstration. The framework allows for querying metadata models, fetching data, preprocessing, and analyzing data, thereby offering a modular and flexible workflow for application development. Its effectiveness is demonstrated through a case study involving the development and implementation of a data-driven anomaly detection tool for the photovoltaic systems installed at the Politecnico di Torino, Italy. During eight months of testing, the framework was used to tackle practical challenges including: (i) developing a machine learning-based anomaly detection pipeline, (ii) replacing data-driven models during operation, (iii) optimizing model deployment and retraining, (iv) handling critical changes in variable naming conventions and sensor availability (v) extending the pipeline from one system to additional ones.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Extensive analysis of reconstruction algorithms for DESI 2024 baryon acoustic oscillations

Reconstruction of the baryon acoustic oscillation (BAO) signal has been a standard procedure in BAO analyses over the past decade and has helped to improve the BAO parameter precision by a factor of ∼2 on average. The Dark Energy Spectroscopic Instrument (DESI) BAO analysis for the first year (DR1) data uses the “standard” reconstruction framework, in which the displacement field is estimated from the observed density field by solving the linearized continuity equation in redshift space, and galaxy and random positions are shifted in order to partially remove non-linearities. There are several approaches to solving for the displacement field in real survey data, including the multigrid (MG), iterative Fast Fourier Transform (iFFT), and iterative Fast Fourier Transform particle (iFFTP) algorithms. In this work, we analyze these algorithms and compare them with various metrics including two-point statistics and the displacement itself using realistic DESI mocks. We focus on three representative DESI samples, the emission line galaxies (ELG), quasars (QSO), and the bright galaxy sample (BGS), which cover the extreme redshifts and number densities, and potential wide-angle effects. We conclude that the MG and iFFT algorithms agree within 0.4% in post-reconstruction power spectrum on BAO scales with the RecSym convention, which does not remove large-scale redshift space distortions (RSDs), in all three tracers. The RecSym convention appears to be less sensitive to displacement errors than the RecIso convention, which attempts to remove large-scale RSDs. However, iFFTP deviates from the first two; thus, we recommend against using iFFTP without further development. In addition, we provide the optimal settings for reconstruction for five years of DESI observation. The analyses presented in this work pave the way for DESI DR1 analysis as well as future BAO analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

Integrated Large-Scale Data Management Platform for Photovoltaic Power Conversion Equipment (PCE) Reliability Data

To meet the demand for accuracy and real-time capability of PV system degradation evaluation, massive volume data is needed to run high-fidelity and high-efficiency simulations and perform advanced data analysis. However, PV farm operators have a series of difficulties with PV inverter data, such as data collection from multiple channels, massive data storage, data management and massive data analysis. To address these challenges, we developed an integrated data management platform capable of data acquisition, processing, storage, query, and performing big data analysis utilizing AI algorithms. The platform can also achieve data correctness verification and provide an effective distributed data management solution to retrieve massive data and establish a connection to distributed computational frameworks.

data management platform↗

The Helicity Sign of Flux Transfer Event Flux Ropes and Its Relationship to the Guide Field and Hall Physics in Magnetic Reconnection at the Magnetopause

Flux Transfer Events (FTEs) are transient magnetic flux ropes typically found at the Earth's magnetopause on the dayside. While it is known that FTEs are generated by magnetic reconnection, it remains unclear how the details of magnetic reconnection controls their properties. A recent study showed that the helicity sign of FTEs positively correlates with the east-west (B y ) component of the Interplanetary Magnetic Field (IMF). With data from the Cluster and Magnetospheric Multiscale missions, we performed a statistical study of 166 quasi force-free FTEs. We focus on their helicity sign and possible association with upstream solar wind conditions and local magnetic reconnection properties. Using both in situ data and magnetic shear modeling, we find that FTEs whose helicity sign corresponds to the IMF B y are associated with moderate magnetic shears while those that do not correspond to the IMF B y are associated with higher magnetic shears. While uncertainty in IMF propagation to the magnetopause may lead to randomness in the determination of the flux rope core field and helicity, we rather propose that for small IMF B y , which corresponds to high shear and low guide field, the Hall pattern of magnetic reconnection determines the FTE core field and helicity sign. In that context we explain how the temporal sequence of multiple X-line formation and the reconnection rate are important in determining the flux rope helicity sign. This work highlights a fundamental connection between kinetic processes at work in magnetic reconnection and the macroscale structure of FTEs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

ESS-DIVE Reporting Format for Amplicon Abundance Table

While standardized sequencing data is available in public repositories and efforts such as MIxS for common sample collection and processing metadata are well established, the lack of common bioinformatic processing metadata has hindered the ability to do large-scale metaanalyses and the potential for data re-use by non-experts such as ecosystem, watershed, or earth system modelers. To address this need for Department of Energy researchers, we have developed an amplicon reporting format which captures both sample preparation and bioinformatic processing metadata and stores processed amplicon data as a paired abundance table and sequencing file to maximize the potential for re-use of these data. To aid in the adoption of accessible and reproducible analysis workflows, this reporting format was developed in concert with amplicon functionality within the Department of Energy’s Systems Biology Knowledgebase (KBase) to ensure common data and metadata requirements and facilitate seamless transfer between these platforms.This dataset contains support documentation for the amplicon reporting format (README.md and instructions.md), templates for both bioinformatic and sequencing metadata (amplicon_bioinformatic_metadata_template_2021_10_03.csv and amplicon_sequencing_metadata_template_2021_10_03.csv), a crosswalk indicating how this reporting format relates to the current MIxS format (ESSDIVE-MIxS_crosswalk.csv), a list of available instrument terms (amplicon_seq_instrument_terms_2021_10_03.csv), a map between QIIME2 parameter settings and metadata fields (amplicon_qiime2_plugin_metadata_map.csv), a data dictionary (amplicon_CSV_dd.csv), and file-level metadata (amplicon_FLMD.csv).

54 ENVIRONMENTAL SCIENCES↗

Critical magnetic fields and electron pairing in magic-angle twisted bilayer graphene

The velocities of the quasiparticles that form Cooper pairs in a superconductor are revealed by the upper critical magnetic field. Here we use this property to assess superconductivity in magic-angle twisted bilayer graphene (MATBG), which has been observed over a range of moiré band-filling, twist angle, and screening environment conditions. An average Fermi velocity can be defined as $v$$^{*}_{F}$ ≡ k B T c ℓ c /ℏ, where T c and ℓ c are the critical temperature and magnetic length, respectively. An advantage of this definition is that $v$$^{*}_{F}$ can be directly extracted from the existing experimental data. Mean-field theory calculations of upper critical fields in model superconductors are consistent with the expectation that Fermi velocities defined in this way are nearly independent of the strength of pairing interaction. Moreover, for fixed strength pairing interaction, minima in $v$$^{*}_{F}$ as a function of band filling are coincident with maxima in T c , as expected from the McMillan formula. Since no association between T c maxima and $v$$^{*}_{F}$ minima is present in MATBG experimental data, we argue that the pairing interaction in MATBG is strongly filling-factor dependent. Furthermore, any theory of MATBG superconductivity must explain this dependence, which is apparently primarily responsible for the observed superconducting domes.

2-dimensional systems↗