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DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Cyber-physical security framework for Photovoltaic Farms

With the evolution of PV converters, a growing number of vulnerabilities in PV farms are exposing to cyber threats. To mitigate the influence of cyber-attack on PV farms, it is necessary to study attacks' impact and propose detection methods. To meet this requirement, a cyber-physical security framework is proposed for PV farms. Data integrity attacks (DIAs) are studied on different control loops. As μPMU is gaining in popularity, a lower sampling rate of μPMU data is applied to develop a detection algorithm. We have evaluated two data-driven methods, which are support vector machine (SVM) and long short-term memory (LSTM). Lastly, the data-driven methods verify the feasibility of μPMU data in attack detection.

Attack Impact Analysis↗

DOE OSTI2020

Development of Prognostic Models Using Plant Asset Data

The recent growth of machine learning and artificial intelligence technologies provides opportunities for leveraging data-driven algorithms to address the problems of diagnostics and prognostics in the nuclear power industry. The use of machine learning and other statistical methods as prognostic models is of particular interest in the nuclear industry to accurately predict future equipment or plant state given a set of measurements. Such predictive capability will enable predictive assessment of component condition and remaining life and allow for condition-based predictive maintenance. The resulting optimization of maintenance scheduling and reduction in unnecessary maintenance activities will lower overall maintenance costs and improve the economics of nuclear power. This report discusses the various aspects of data processing and model development that are likely to influence the performance of prognostic models. Data from a boiling-water reactor was used to evaluate several prognostic models to identify key considerations for developing such models to predict data-driven plant state and equipment degradation condition. Preliminary results indicate the need for data sets that are relevant to the problem at hand and contain signatures that may be correlated to the prediction problem. Assuming such data exist, development of prognostic models using data-driven methods requires an understanding of the various sources of influence on the prediction accuracy (such as the model architecture, data preprocessing approaches, and potentially external factors influencing the equipment or plant system under assessment). Ongoing research is evaluating these factors in greater detail and examining techniques for calculating prediction uncertainty bounds.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Evaluating proxies for the drivers of natural gas productivity using machine-learning models

We report the extensive development of unconventional reservoirs using horizontal drilling and multistage hydraulic fracturing has generated large volumes of reservoir characterization and production data. The analysis of this abundant data using statistical methods and advanced machine-learning (ML) techniques can provide data-driven insights into well performance. Most predictive modeling studies have focused on the impact that different well completion and stimulation strategies have on well production but have not fully exploited the available in situ rock property data to determine its role in reservoir productivity. We have used machine-learning techniques to rank rock mechanical properties, microseismic attributes, and stimulation parameters in the order of their significance for predicting natural gas production from an unconventional reservoir. The data for this study came from a hydraulically fractured well in the Marcellus Shale in Monongalia County, West Virginia. The data classes included measurements aggregated by well completion stage that included (1) gas production, (2) well-log-derived measurements including bulk density, elastic moduli, shear impedance, compressional impedance, brittleness, and gamma measurements, (3) microseismic attributes, (4) long-period long-duration (LPLD) event counts, (5) fracture counts, and (6) stimulation parameters that included the fluid injection volume and average pumping pressure. To identify observable proxies for the drivers of gas production, we evaluated five commonly used ML approaches including multivariate adaptive regression spline, Gaussian mixture model, random forest, gradient boosting, and neural network. We selected five variables including LPLD event count, seismogenic b-value, hydraulic diffusivity, cumulative moment, and fluid volume as the features most likely to impact gas productivity at the stage level in the study area. The data-driven selection of these parameters for their importance in determining gas production can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs. Plain language summary: We use machine-learning methods and data-driven selection of reservoir parameters to rank and better understand their importance in determining gas production, which can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs.

58 GEOSCIENCES↗

DOE OSTI2023

Using a physics-informed neural network and fault zone acoustic monitoring to predict lab earthquakes

Abstract Predicting failure in solids has broad applications including earthquake prediction which remains an unattainable goal. However, recent machine learning work shows that laboratory earthquakes can be predicted using micro-failure events and temporal evolution of fault zone elastic properties. Remarkably, these results come from purely data-driven models trained with large datasets. Such data are equivalent to centuries of fault motion rendering application to tectonic faulting unclear. In addition, the underlying physics of such predictions is poorly understood. Here, we address scalability using a novel Physics-Informed Neural Network (PINN). Our model encodes fault physics in the deep learning loss function using time-lapse ultrasonic data. PINN models outperform data-driven models and significantly improve transfer learning for small training datasets and conditions outside those used in training. Our work suggests that PINN offers a promising path for machine learning-based failure prediction and, ultimately for improving our understanding of earthquake physics and prediction.

42 ENGINEERING↗

DOE OSTI2022

G2Aero (Separable shape tensors for aerodynamic design) [SWR-22-44]

G2Aero is a flexible and practical tool for design and deformation of 2D airfoils and 3D blades using data-driven approaches. G2Aero utilizes the geometry of matrix manifolds—specifically the Grassmannian—to build a novel framework for representing physics-based separable deformations of shapes. G2Aero offers the flexibility to generate perturbations in a customizable way over any portion of the blade. The G2Aero framework utilizes data-driven methods based on a curated database of physically relevant airfoils. Specific tools include: - principal geodesic analysis over normal coordinate neighborhoods of matrix manifolds; - a variety of data-regularized deformations to nominal 2D airfoil shapes; - Riemannian interpolation connecting a sequence of airfoil cross-sections to build 3D blades from 2D data; - consistent perturbations over the span of interpolated 3D blades based on dominant modes from the data-driven analysis.

Doronina, Olga↗

DOE OSTI2023

Efficient Optimization of Energy Recovery From Geothermal Reservoirs With Recurrent Neural Network Predictive Models

Improving the long-term energy production performance of geothermal reservoirs can be accomplished by optimizing field development and management plans. Reliable prediction models, however, are needed to evaluate and optimize the performance of the underlying reservoirs under various operation and development strategies. In traditional frameworks, physics-based simulation models are used to predict the energy production performance of geothermal reservoirs. However, detailed simulation models are not trivial to construct, require a reliable description of the reservoir conditions and properties, and entail high computational complexity. Data-driven predictive models can offer an efficient alternative for use in optimization workflows. This paper presents an optimization framework for net power generation in geothermal reservoirs using a variant of the recurrent neural network (RNN) as a data-driven predictive model. The RNN architecture is developed and trained to replace the simulation model for computationally efficient prediction of the objective function and its gradients with respect to the well control variables. The net power generation performance of the field is optimized by automatically adjusting the mass flow rate of production and injection wells over 12 years, using a gradient-based local search algorithm. Two field-scale examples are presented to investigate the performance of the developed data-driven prediction and optimization framework. Furthermore, the prediction and optimization results from the RNN model are evaluated through comparison with the results obtained by using a numerical simulation model of a real geothermal reservoir.

15 GEOTHERMAL ENERGY↗

DOE OSTI2019

Advanced High-Fidelity Lumped EMT Grid Modelling & Comparison

There is increased interest in performing electromagnetic transient (EMT) studies of large power grids for stability purposes. The large power grids may not represent the entire grid, but portions of interest. For example, studies are being performed to identify the impact of extreme events on solar power plants in California that requires the EMT model of the grid in California, but not the complete western interconnection (WI) grid model to which the grid in California is connected. The EMT models of grids are necessary to perform integration studies of large power electronics systems like utility-scale photovoltaic (PV) systems, high-voltage direct current (HVdc) systems, flexible alternating current transmission systems (FACTs), and others. Traditionally, models of grids available to utilities are the transient stability (TS) models. Hence, it assumes significance to identify methods of developing high-fidelity EMT models for portions of the grid (of interest) from the information available in the existing TS models of the entire grid. In this paper, a conversion mechanism along with upgradation based on data-driven methods is applied to develop EMT models of grids. The conversion mechanism utilizes information from TS models of grids to generate EMT models of grids. These models can be extracted for the required portion of the grid. While these models adequately represent the local voltage behaviour of the grid, they are inadequate in representing the frequency behaviour of the grid. The data-driven methods are applied to identify frequency dynamics of the grid, and the EMT models are upgraded with the data-driven methods. The resulting upgraded EMT models of grids can perform the studies mentioned above. These models are tested under contingencies of interest to validate the developed models.

Debnath, Suman↗

NASA NTRSDate not supplied

Advancing Open Science in Atmospheric Research: Integrating Data Usability and Machine Learning

In the dynamic realm of atmospheric sciences, the convergence of data science methodologies and open data marks a transformative era, driving research advancements and nurturing aspiring scientists. This abstract highlights two pivotal projects that epitomize open science principles, aligning seamlessly with the session's objective of interdisciplinary synergy and the cultivation of emerging talent. As a NASA-certified data center, our foremost endeavor focuses on enhancing the visibility and traceability of NASA datasets within atmospheric science research. This initiative not only elevates these datasets' prominence but also establishes a robust framework ensuring their credibility in scholarly discourse. By bridging the gap between data sources and research publications, this project serves as an educational catalyst, nurturing a new generation of scholars in open collaboration and dataset authenticity. Concurrently, our second project pioneers an early warning system for flooding events, utilizing machine learning algorithms to predict flooded fractions. Through multi-source data fusion and predictive modeling, this initiative goes beyond forecasting; it embodies the core of open science by enabling proactive risk mitigation strategies. This project not only advances atmospheric sciences but also fosters an environment where young scholars engage in practical, data-driven solutions. These intertwined projects exemplify the fusion of data science with open data solutions, ensuring both the usability of quality datasets and the cultivation of scientific knowledge among emerging scholars. By spotlighting these impactful use cases, our aim is to foster discussions emphasizing the importance of open collaboration, data integrity, and the nurturing of scientific talent in atmospheric sciences." "In the dynamic realm of atmospheric sciences, the convergence of data science methodologies and open data marks a transformative era, driving research advancements and nurturing aspiring scientists. This abstract highlights two pivotal projects that epitomize open science principles, aligning seamlessly with the session's objective of interdisciplinary synergy and the cultivation of emerging talent. As a NASA-certified data center, our foremost endeavor focuses on enhancing the visibility and traceability of NASA datasets within atmospheric science research. This initiative not only elevates these datasets' prominence but also establishes a robust framework ensuring their credibility in scholarly discourse. By bridging the gap between data sources and research publications, this project serves as an educational catalyst, nurturing a new generation of scholars in open collaboration and dataset authenticity. Concurrently, our second project pioneers an early warning system for flooding events, utilizing machine learning algorithms to predict flooded fractions. Through multi-source data fusion and predictive modeling, this initiative goes beyond forecasting; it embodies the core of open science by enabling proactive risk mitigation strategies. This project not only advances atmospheric sciences but also fosters an environment where young scholars engage in practical, data-driven solutions. These intertwined projects exemplify the fusion of data science with open data solutions, ensuring both the usability of quality datasets and the cultivation of scientific knowledge among emerging scholars. By spotlighting these impactful use cases, our aim is to foster discussions emphasizing the importance of open collaboration, data integrity, and the nurturing of scientific talent in atmospheric sciences.

Jennifer Wei↗

DOE OSTI2023

Operator inference with roll outs for learning reduced models from scarce and low-quality data

Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. Here, in this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM—the Desai-Zwanzig model—in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation (ODE) in these coordinates. Additionally, we identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE—enabled through an odd symmetry transformation—to construct the bifurcation diagram exhibiting the phase transition.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

A hybrid building thermal modeling approach for predicting temperatures in typical, detached, two-story houses

Within the residential building sector, the air-conditioning (AC) load is the main target for peak load shifting and reduction since it is the largest contributor to peak demand. By leveraging its power flexibility, residential AC is a good candidate to provide building demand response and peak load shifting. For realization of accurate and reliable control of AC loads, a building thermal model, which characterizes the properties of a building’s envelope and its thermal mass, is an essential component for accurate indoor temperature or cooling/heating demand prediction. Building thermal models include two types: “Forward” and “Data-Driven”. Due to time-saving and cost-effective characteristics, different data-driven models have been developed in a number of research studies. However, few developed models can predict temperatures in respective zones of a multiple-zone building with an open air path between zones e.g., an open stairwell connecting two floors of a home. In this research, a novel hybrid modeling approach is proposed to predict the average indoor air temperatures of both the upstairs and downstairs. This “hybrid” solution integrates both gray-box, i.e. RC model and black-box models. A developed RC model is used to predict the building mean temperature, and black-box model, in which the supervised machine learning algorithms are leveraged, is used to predict the temperature difference between the downstairs and upstairs. Compared with the measured data from a real house, the results obtained have acceptable/satisfactory accuracy. The method proposed in this study integrates the advantages of black-box and gray-box modeling. As a result, it can be used as a reliable alternative to predict the average temperatures in respective floors of typical detached two-story houses.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2017

Can We Practically Bring Physics-based Modeling Into Operational Analytics Tools?

We present that analytics software is increasingly used to improve and maintain operational efficiency in commercial buildings. Energy managers, owners, and operators are using a diversity of commercial offerings often referred to as Energy Information Systems, Fault Detection and Diagnostic (FDD) systems, or more broadly Energy Management and Information Systems, to cost-effectively enable savings on the order of ten to twenty percent. Most of these systems use data from meters and sensors, with rule-based and/or data-driven models to characterize system and building behavior. In contrast, physics-based modeling uses first-principles and engineering models (e.g., efficiency curves) to characterize system and building behavior. Historically, these physics-based approaches have been used in the design phase of the building life cycle or in retrofit analyses. Researchers have begun exploring the benefits of integrating physics-based models with operational data analytics tools, bridging the gap between design and operations. In this paper, we detail the development and operator use of a software tool that uses hybrid data-driven and physics-based approaches to cooling plant FDD and optimization. Specifically, we describe the system architecture, models, and FDD and optimization algorithms; advantages and disadvantages with respect to purely data-driven approaches; and practical implications for scaling and replicating these techniques. Finally, we conclude with an evaluation of the future potential for such tools and future research opportunities.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Improving Solar and Solar+Storage Screening Techniques to Reduce Utility Interconnection Time and Costs (Final Technical Report)

Residential PV installations have increased rapidly over the last decade, and the increased application volume has caused permitting delays and lower overall adoption rates. In this project, we developed and evaluated whether data-driven secondary modeling and screening techniques can help utilities assess customer applications more accurately than traditional screening shortcuts. Secondary topologies are predicted using decision trees and commonly available information, such as service transformer, customer, and street locations. Conductors were predicted using a logistic regression method based on real world object (RWO) types, service transformer ratings, conductor length, and distance to transformer. After developing the combined primary and secondary distribution network model, hosting capacity results were used to train a random forest model to predict the pass/fail likelihood of a customer application. Powerflow based models with predicted secondaries and data-driven methods both increased the screening success rate, relative to common utility heuristics, by as much as 55 percentage points. Data-driven screening techniques were described by one utility as a "right-sized" approach for residential customers given the low-risk of small errors and the high-cost of accurate modeling.

14 SOLAR ENERGY↗

DOE OSTI2023

Scientific machine learning for modeling and simulating complex fluids

The formulation of rheological constitutive equations—models that relate internal stresses and deformations in complex fluids—is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine-learning based constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these “digital fluid twins” to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation—a task that is not achievable using any previously developed data-driven rheological equation of state.

Science & Technology - Other Topics↗

DOE OSTI2022

Machine Learning-based Prediction of Departure from Nucleate Boiling Power for the PSBT Benchmark

Machine Learning (ML) has seen an exponential growth in its applications due to its advanced data driven prediction capabilities. The study presents a data-driven approach as a preliminary attempt to predict the power at which departure from nucleate boiling (DNB) occurs in pressurized water reactors (PWRs) by constructing an advanced ML algorithm that takes outlet pressure, inlet temperature and inlet mass flux as the input features. DNB is a critical heat flux (CHF) phenomenon seen in PWRs. The experimental data from the PWR subchannel and bundle tests (PSBT) benchmark is first used to train an artificial neural network (ANN) to predict the DNB power, which produces a root mean square error (RMSE) of 6.89 kW/m when tested on a blind subset of the PSBT data. Since the PSBT dataset is relatively small to train an accurate ANN, a data augmentation methodology based on generative adversarial networks (GANs) is used to expand the training dataset. By assuming that the real data follows a certain distribution, GANs try to learn that underlying distribution to generate similar synthetic data to augment the database and to improve the predictive capabilities of the ANN. The data generated from GANs are validated using 1-nearest neighbor and kernel maximum mean discrepancy. To further ensure data from GAN is similar to PSBT, the data is tested and filtered out using the sub-channel thermal-hydraulic code CTF. The results indicate that with the addition of 120 data points from GAN the RMSE reduces to 4.84 kW/m showing promising results for future developments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

Electromagnetic Shower from Cosmic Muons in NOvA Detector

NO$\nu$A (NuMI Off-Axis $\nu_e$ Appearance) experiment is a neutrino $\nu_\mu \rightarrow \nu_e$ oscillation experiment with a baseline of 810 km. The signature for a $\nu_\mu \rightarrow \nu_e$ oscillation in the far detector is the production of an electromagnetic (EM) shower due to the charge current (CC) interaction of $\nu_e$ with the detector material. Cosmic muon induced electromagnetic showers can serve as a source of EM shower sample that can be used as a data-driven method for validating the EM shower modelling and EM shower identification algorithms at NO$\nu$A. The work reported in the thesis is the first ever implementation of cosmic muon induced EM shower for such a purpose in the NO$\nu$A experiment. We extracted EM shower sample from two sources - muon undergoing bremsstrahlung (Brem) and muon decay in flight to electron (DiF). Brem sample, extracted from cosmic muon, turns out to be a very useful data-driven method for testing EM shower modelling and the part icle identification (PID) algorithms for the detection of $\nu_e$-CC interactions. A new muon removal (MR) technique is developed and applied to remove the muon hits inside the bremsstrahlung shower. However, a complete removal of the muon energy in the event is not possible with high efficiency. DiF induced EM shower, on the other hand, is exactly similar to $\nu_e$-CC EM shower because DiF is a pure electron initiated EM shower. Therefore, DiF EM shower, once extracted, mimicks the shower of a $\nu_e$-CC interaction event. We present the extraction methods for both brem and DiF events in MC and cosmic data in far and near detector of NO$\nu$A and its use in data driven validation of $\nu_e$ EM shower modelling and $\nu_e$ signal selection efficiency across the detector. A systematic uncertainty is also assigned on $\nu_e$ appearance signal selection based on this study to take into account the difference in EM shower modelling in data and MC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

The anomalous magnetic moment of the muon in the Standard Model: an update

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, a μ , updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the e + e - → π + π - cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a^{SM}_{μ}$ = 116 592 033 (62) x $10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1–6 of E989 at Fermilab, one finds $a^{exp}_{μ} -a^{SM}_{μ}= 38 (63)$ x $10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗