Results for “Cross-validation” — Page 5

DOE OSTI2026

Transverse BBU Suppression with Feedback for Energy-Recovery Linacs

The Electron–Ion Collider (EIC) achieves its design luminosity by cooling the ion beam with a high-current electron beam generated in an energy-recovery linac (ERL). The baseline ERL lattice employs a BNL five-cell cavity that is frequency-scaled to 197 MHz, 591 MHz, and 1.773 GHz, raising concerns about multibunch beam-breakup (BBU) instabilities. Threshold currents for each frequency option are established with two independent BBU tracking codes, providing cross-validated operating margins that guide cavity selection. To further increase the current limit, we incorporate a digital transverse feedback (FB) system that targets the dominant higher-order modes (HOMs). Simulations show the FB raises the BBU threshold by roughly an order of magnitude: power-spectral-density analysis of the beam centroid at the linac exit confirms strong suppression of the aliased HOM peak, although some spectral growth appears at secondary frequencies. This combined study quantifies baseline BBU limits, demonstrates effective active mitigation, and charts a practical path toward robust, high-current operation of the EIC ERL.

Accelerator Physics↗

DOE OSTI2025

INFN LASA in-kind contribution to PIP-II

This paper reports the status and recent progress of INFN LASA’s in-kind contribution to the PIP-II project at Fermilab, with updates on key activities and major procurements. Production efforts for the 38 INFN LASA-designed, 5-cell cavities (β=0.61) for the LB650 section of the linac are underway and two pre-series prototypes are being realized as a first step to validate the manufacturing and treatment sequence. Concurrently, preliminary testing on existing prototypes is progressing to gain a deeper understanding of the surface preparation and qualification procedures, including cross-validation at different infrastructures. Series LB650 cavities will be industrially produced and surface-treated to achieve the stringent performance targets, qualified via vertical cold tests at DESY AMTF, and delivered installation-ready for string assembly.

Paparella, Rocco [INFN, Pisa; LASA, Segrate]↗

DOE OSTI2023

Improved Biofuel Production through Discovery and Engineering of Terpene Metabolism in Switchgrass

Project Objectives - Of the myriad specialized metabolites that plants deploy to adapt to environmental challenges, terpenes form the largest group. In many major crops, unique terpene blends serve as key stress defenses that directly impact plant fitness and yield. In addition, terpenes, such as bisabolene and pinene, are used for producing renewable biofuels. Essential to advancing a broader use of terpenes for biofuel feedstock engineering is a system-wide knowledge of the diverse biosynthetic machinery and defensive potential of often species-specific terpene blends. The proposed project would merge genome-wide enzyme discovery with comparative –omics, protein structural and plant microbiome studies to define the biosynthesis and stress-defensive functions of the switchgrass (Panicum virgatum) terpene network. These insights would be combined with developing and applying non-transgenic genome editing tools to design plants with desirable terpene blends for higher productivity and biofuel production on marginal lands. As a dedicated lignocellulosic feedstock for U.S. biofuel production with high net energy yield, stress tolerance, and available genome resources, switchgrass is well-suited for devising new avenues for biofuel production. Project Description – The diversity of plant terpene defenses is governed by species-specific families of terpene synthase (TPS) and cytochrome P450 monooxygenase (P450) enzymes. Mining of the switchgrass genome (genotype Alamo) identified ~100 TPS and P450 candidate genes, and combinatorial biochemical analysis of synthesized TPSs and P450s revealed more than a dozen enzymes with common and novel activities. In addition, several identified terpene metabolites and the corresponding transcripts were up-regulated in response to abiotic stressors. These findings demonstrate a unique switchgrass terpene network with probable importance to abiotic stress tolerance, thus providing a large chemical portfolio for optimizing crop resistance, yield, and biofuel composition. Leveraging these preliminary data, we propose to generate a genome-wide map of the switchgrass terpene metabolic network through multi-gene co-expression analyses that allow the efficient cross-validation of TPS and P450 functions. Key enzymes would further be applied to structure-function studies via X-ray protein crystallography, homology modeling and site-directed mutagenesis to gain mechanistic insight into the catalytic specificity of switchgrass terpene metabolism and provide gene and amino acid targets for genome editing. In tandem with terpene pathway discovery, system-wide metabolomics, transcriptomics and proteomics studies in switchgrass accessions of contrasting drought tolerance would define the role of switchgrass terpene metabolism in conferring abiotic stress resilience. Metabolic changes would be assessed in a combined approach of targeted (terpenes) and untargeted metabolite profiling using a high-resolution LC-MS/MS approach, differential gene expression analyses through multiplexed Illumina RNA sequencing, and quantitative analysis of high-priority pathway enzymes using multiple reaction monitoring (MRM). Drawing on these insights, knock-down/out mutants of stress-associated pathway nodes would be generated by optimizing transient virus-induced gene silencing (VIGS) and CRISPR/Cas9 systems under control of the Tobacco Rattle Virus (TRV). The resulting mutant lines would then be analyzed for stress susceptibility and the impact on the root microbiome to define gene functions in planta. Knowledge of terpene pathways, enzyme mechanisms and bioactivities would be applied to enhance switchgrass stress resilience and to tailor-make terpene blends for biofuel production. Here, TRV-enabled CRISPR/Cas9 genome editing, including allele-specific knock-out of redundant genes, engineering of enzyme specificity via structure-guided point mutations, and overexpression of terpene genes relevant to stress-protection or biofuel production, would be used to increase metabolic flux toward desired pathways. Broader Impacts - Integrating the system-wide discovery, mechanistic analysis and non-transgenic genome engineering of the switchgrass terpene network aligns the required steps to unlock the chemical potential of this important metabolite class to generate crops that are more resistant to stress and provide advanced biofuel production in light of rising climate pressures as foreseeable challenges for bioenergy crop cultivation. The proposed project would further offer interdisciplinary student training through active involvement in the project and integration of research concepts and outcomes into newly-developed graduate and undergraduate courses on Plant Biotechnology.

09 BIOMASS FUELS↗

DOE OSTI2024

Super Resolution for Renewable Energy Resource Data With Wind From Reanalysis Data (Sup3rWind) and Application to Ukraine [Slides]

In this work we present a novel deep learning-based downscaling method, using generative adversarial networks (GANs), for generating high-resolution wind resource data from ECMWF Reanalysis v5 data (ERA5). We show that by training a GAN model on ERA5, as opposed to coarsened high-resolution data, we achieve results that are competitive with conventional dynamical downscaling. This GAN-based downscaling method additionally reduces computational costs over dynamical downscaling by two orders of magnitude. All GANs are trained on data sampled from CONUS, selected to provide a diverse sampling of terrain conditions, and validated on observational data along with data held out from training. This cross-validation shows low error and high correlations with observations and excellent agreement with hold out data across physical distributions. Our approach is finally used to downscale 30km hourly ERA5 to 2-km 5-minute wind data, for January 2000 through December 2023, at multiple hub heights, over Ukraine, Moldova, and part of Romania. Comparisons against observational data from Meteorological Assimilation Data Ingest System (MADIS) and multiple wind farms show the same level of performance as for CONUS validation. This 24 year data record is the first member of the "super resolution for renewable energy resource data with wind from reanalysis data" dataset (Sup3rWind).

17 WIND ENERGY↗

DOE OSTI2024

Evaluating large scale aqueous organic redox flow battery performance with a hybrid numerical and machine learning framework

Aqueous organic redox flow battery (AORFB) is a promising cost-competitive technology for large-scale energy storage. Among existing work, the dihydroxyphenazine (DHP)-based AORFB has demonstrated high energy density and low-capacity degradation in 10 cm$^2$ cells during lab tests. However, its commercial-scale performance in more complex environments remains unknown, posing a barrier to commercialization. To address this gap, this work presents a comprehensive performance evaluation of a 780 cm$^2$ DHP-based AORFB by combining a physics-based numerical model, machine learning (ML)-based surrogate models, and ML-derived sensitivity quantification. Specifically, we first select 12 key battery parameters that include 10 physicochemical and 2 operation quantities, then select 6 performance metrics that include energy efficiency (EE), discharging capacity, charging energy, and power losses due to concentration, activation, and ohmic over-potentials. With such selection, 12800 combinations of the 12 parameters are subsequently generated using the Latin Hypercube Sampling method. Such combinations, together with 38 pre-defined State of Charge, are then integrated to a validated AORFB model developed in COMSOL to compute the performance metrics. With both input parameters and performance metrics, 60 deep neural network (DNN) surrogate models are then trained to approximate the relationship between the 10 physicochemical quantities and 6 performance metrics at each flow rate and current density. Sensitivity scores are then calculated based on the DNN models. Two additional sensitivity analysis tools, i.e., MARS, and SHAP, are also used to cross-validate the sensitivity scores from the DNN. The results demonstrate that 1) the standard potential ranks first in controlling EE and charging energy, 2) the membrane conductivity is most critical for power loss and EE, and 3) specific area and reaction rate control activation power loss.

25 ENERGY STORAGE↗

DOE OSTI2025

Dual-Comb Spectroscopy to Tethered Balloon System (DCS to TBS) Field Campaign Report

There is a critical need for the ability to detect, quantify, and attribute sources and sinks of greenhouse gases (GHGs) with high temporal and spatial resolution. Current methods are typically based on continuously operating near-surface point sensors or intermittent aerial/satellite observations. Dual optical frequency comb spectroscopy (“dual-comb spectroscopy”; DCS) is a laser-based technique that can bridge this sensing gap by providing high-precision, high-accuracy, and high-temporal-resolution detection and quantification of trace gases over kilometer-length scales, connecting local and regional observations. A single DCS system can also provide spatial resolution for source/sink attribution with the addition of a few minor optical elements, enabling cross-validation of other observations (e.g., Total Carbon Column Observing Network [TCCON], Orbiting Carbon Observatory [OCO-2/3], Greenhouse Gases Observing Satellite [GOSAT-1/2][).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Seismic Elastic Double-Beam Characterization of Faults and Fractures for CO₂ Storage Site Selection

Site characterization for underground injection and storage of gigatonne-scale CO₂ requires reliable and cost-effective methods to detect and characterize faults and fractures and to assess their stress state and fault activation potential. This is critical, as wastewater injection and disposal have been shown to activate faults and induce earthquakes, and CO₂ leakage remains a key concern for long-term storage. In this project, we developed seismic methods to detect and characterize large-scale sedimentary and crystalline basement faults and associated small-scale fractures below conventional seismic imaging resolution using multicomponent (9C) surface seismic data. Machine learning was used to automatically interpret large-scale faults, providing key information for estimating the maximum magnitude of potential induced earthquakes. High-fidelity imaging was achieved by exploiting redundancy across multiple elastic wave modes, where independent images from different modes and frequencies cross-validate each other. We also used our nonlinear signal comparison (NLSC) method for ground roll removal, improving data quality in complex near-surface conditions. The methods were validated using field data acquired in central Montana. Results show that basement faults extend into the sedimentary section and that small-scale fractures are widespread above the basement. The inferred stress orientation is consistent with regional stress data, and the estimated maximum induced earthquake magnitude is small (Mw ~2.3). The developed workflow provides a practical approach for fault and fracture characterization and for assessing induced seismicity and leakage risk. It is directly applicable to CO₂ storage site selection and to other subsurface systems.

02 PETROLEUM↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

Virtual Growth of SRF Materials

Niobium's native surface oxide affects SRF cavity and superconducting qubit performance, motivating interest in controlling its crystalline structure. We combine a literature-derived machine-learning analysis with temperature-dependent XRD to study crystalline ordering in Nb2O5. Random Forest models, trained on 74 processing conditions from 17 papers and validated by leave-one-group-out cross-validation, predicted broad crystallinity outcomes well (balanced accuracy 0.809), but struggled with specific polymorph identity (0.577). Annealing temperature was the dominant predictor across all targets; oxygen partial pressure showed negligible importance, reflecting narrow literature coverage rather than physical irrelevance. Temperature-dependent XRD on anodized and H2O2-treated Niobium showed structural evolution consistent with the machine learning predictions. Our model and overall approach provide a data-driven framework for identifying and optimizing conditions that promote crystallization in initially amorphous oxides. This framework can guide the selection of growth and post-annealing conditions for Nb surfaces by narrowing the experimental parameter space, thereby reducing trial-and-error efforts in developing oxide structures relevant to SRF applications.

Tilkin, Anthony [Fermilab]↗

DOE OSTI2025

Developing predictive models for µ opioid receptor binding using machine learning and deep learning techniques

Opioids exert their analgesic effect by binding to the µ opioid receptor (MOR), which initiates a downstream signaling pathway, eventually inhibiting pain transmission in the spinal cord. However, current opioids are addictive, often leading to overdose contributing to the opioid crisis in the United States. Therefore, understanding the structure-activity relationship between MOR and its ligands is essential for predicting MOR binding of chemicals, which could assist in the development of non-addictive or less-addictive opioid analgesics. This study aimed to develop machine learning and deep learning models for predicting MOR binding activity of chemicals. Chemicals with MOR binding activity data were first curated from public databases and the literature. Molecular descriptors of the curated chemicals were calculated using software Mold2. The chemicals were then split into training and external validation datasets. Random forest, k-nearest neighbors, support vector machine, multi-layer perceptron, and long short-term memory models were developed and evaluated using 5-fold cross-validations and external validations, resulting in Matthews correlation coefficients of 0.528–0.654 and 0.408, respectively. Furthermore, prediction confidence and applicability domain analyses highlighted their importance to the models’ applicability. Our results suggest that the developed models could be useful for identifying MOR binders, potentially aiding in the development of non-addictive or less-addictive drugs targeting MOR.

Research & Experimental Medicine↗

DOE OSTI2025

Optimizing Deep Learning Models for Climate-Related Natural Disaster Detection from UAV Images and Remote Sensing Data

This research study utilized artificial intelligence (AI) to detect natural disasters from aerial images. Flooding and desertification were two natural disasters taken into consideration. The Climate Change Dataset was created by compiling various open-access data sources. This dataset contains 6334 aerial images from UAV (unmanned aerial vehicles) images and satellite images. The Climate Change Dataset was then used to train Deep Learning (DL) models to identify natural disasters. Four different Machine Learning (ML) models were used: convolutional neural network (CNN), DenseNet201, VGG16, and ResNet50. These ML models were trained on our Climate Change Dataset so that their performance could be compared. DenseNet201 was chosen for optimization. All four ML models performed well. DenseNet201 and ResNet50 achieved the highest testing accuracies of 99.37% and 99.21%, respectively. This research project demonstrates the potential of AI to address environmental challenges, such as climate change-related natural disasters. This study’s approach is novel by creating a new dataset, optimizing an ML model, cross-validating, and presenting desertification as one of our natural disasters for DL detection. Three categories were used (Flooded, Desert, Neither). Our study relates to AI for Climate Change and Environmental Sustainability. Drone emergency response would be a practical application for our research project.

AI↗

DOE OSTI2025

A Scalable Gaussian Process Approach to Shear Mapping with MuyGPs

Analysis of cosmic shear is an integral part of understanding structure growth across cosmic time, which in turn provides us with information about the nature of dark energy. Conventional methods generate shear maps from which we can infer the matter distribution in the universe. Current methods (e.g., Kaiser–Squires inversion) for generating these maps, however, are tricky to implement and can introduce bias. Recent alternatives construct a spatial process prior for the lensing potential, which allows for inference of the convergence and shear parameters given lensing shear measurements. Realizing these spatial processes, however, scales cubically in the number of observations—an unacceptable expense as near-term surveys expect billions of correlated measurements. Therefore, we present a linearly scaling shear map construction alternative using a scalable Gaussian process prior called MuyGPs. MuyGPs avoids cubic scaling by conditioning interpolation on only nearest neighbors and fits hyperparameters using batched leave-one-out cross-validation. This work is the first step toward a full, scalable mass mapping method. We work in a simplified regime where we validate our method by interpolating and analyzing maps given noisy point-estimate data from all three shear fields, taken from a suite of N -body ray-tracing simulations. We also show that we can perform these operations at the scale of billions of galaxies on high-performance computing platforms.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Window observables for benchmarking parton distribution functions

Global analysis of collider and fixed-target experimental data and calculations from lattice quantum chromodynamics (QCD) are used to gain complementary information on the structure of hadrons. We propose novel ``window observables'' that allow for higher precision cross-validation between the different approaches, a critical step for studies that wish to combine the datasets. Global analyses are limited by the kinematic regions accessible to experiment, particularly in a range of Bjorken-x, and lattice QCD calculations also have limitations requiring extrapolations to obtain the parton distributions. We provide two different ``window observables'' that can be defined within a region of x where extrapolations and interpolations in global analyses remain reliable and where lattice QCD results retain sensitivity and precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

A robust approach to Gaussian process implementation

Abstract. Gaussian process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset has a large number of observations. To address this challenge, we introduce a scalable GP algorithm, termed MuyGPs, which incorporates nearest-neighbor and leave-one-out cross-validation during training. This approach enables the evaluation of large spatial datasets with state-of-the-art accuracy and speed in certain spatial problems. Despite these advantages, conventional quadratic loss functions used in the MuyGPs optimization, such as root mean squared error (RMSE), are highly influenced by outliers. We explore the behavior of MuyGPs in cases involving outlying observations and, subsequently, develop a robust approach to handle and mitigate their impact. Specifically, we introduce a novel leave-one-out loss function based on the pseudo-Huber function (LOOPH) that effectively accounts for outliers in large spatial datasets within the MuyGPs framework. Our simulation study shows that the LOOPH loss method maintains accuracy despite outlying observations, establishing MuyGPs as a powerful tool for mitigating unusual observation impacts in the large data regime. In the analysis of US ozone data, MuyGPs provides accurate predictions and uncertainty quantification, demonstrating its utility in managing data anomalies. Through these efforts, we advance the understanding of GP regression in spatial contexts.

Mukangango, Juliette↗

DOE OSTI2026

Adaptive spectra-to-exposure conversion using ridge regularized polynomial response models

Real-time gamma spectra-to-exposure conversion in aerial and ground monitoring commonly relies on calibration-derived, detector- or system-specific conversion coefficients that are assumed to generalize across operational environments. In practice, deployment specific differences in spectral composition and transport conditions can introduce systematic bias relative to reference instruments, motivating methods that adapt coefficients using minimal field supervision while explicitly limiting overfitting. In this work, we present a conservative coefficient adaptation framework that updates a baseline polynomial energy-weighting function using ridge-regularized regression, with leave-one-out cross-validation (LOOCV) used to select the regularization strength. The findings support ridge-constrained minimal-supervision adaptation as a practical mechanism to suppress site-specific bias without destabilizing a calibration-derived baseline.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2026

Virtual Growth of SRF Materials: A Machine Learning Approach to Predict the Crystalline Structural Ordering in Nb Surface Oxides

Niobium's native surface oxide affects SRF cavity and superconducting qubit performance, motivating interest in controlling its crystalline structure. We combine a literature-derived machine-learning analysis with temperature-dependent XRD to study crystalline ordering in Nb2O5. Random Forest models, trained on 74 processing conditions from 17 papers and validated by leave-one-group-out cross-validation, predicted broad crystallinity outcomes well (balanced accuracy 0.809), but struggled with specific polymorph identity (0.577). Annealing temperature was the dominant predictor across all targets; oxygen partial pressure showed negligible importance, reflecting narrow literature coverage rather than physical irrelevance. Temperature-dependent XRD on anodized and H2O2-treated Niobium showed structural evolution consistent with the machine learning predictions. Our model and overall approach provide a data-driven framework for identifying and optimizing conditions that promote crystallization in initially amorphous oxides. This framework can guide the selection of growth and post-annealing conditions for Nb surfaces by narrowing the experimental parameter space, thereby reducing trial-and-error efforts in developing oxide structures relevant to SRF applications.

Tilkin, Anthony [Unlisted, US, IL; Fermilab]↗

DOE OSTI2026

In-Situ Magnetic Field Reconstruction in the MAGIS-100 Experiment

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.; Ferm↗