Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “statistical learning”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Kernel-based global sensitivity analysis obtained from a single data set

Results from global sensitivity analysis (GSA) often guide the understanding of complicated input–output systems. Kernel-based GSA methods have recently been proposed for their capability of treating a broad scope of complex systems. In this paper, we develop a new set of kernel GSA tools when only a single set of input–output data is available. Three key advances are made: (1) A new numerical estimator is proposed that demonstrates an empirical improvement over previous procedures. (2) A computational method for generating inner statistical functions from a single data set is presented. (3) A theoretical extension is made to define conditional sensitivity indices, which reveal the degree that the inputs carry shared information about the output when inherent input–input correlations are present. Utilizing these conditional sensitivity indices, a decomposition is derived for the output uncertainty based on what is called the optimal learning sequence of the input variables, which remains consistent when correlations exist between the input variables. Further, while these advances cover a range of GSA subjects, a common single data set numerical solution is provided by a technique known as the conditional mean embedding of distributions. The new methodology is implemented on benchmark systems to demonstrate the provided insights.

42 ENGINEERING↗
DOE OSTI2023

Infinite neural network quantum states: entanglement and training dynamics

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

quantum state supervised learning↗
DOE OSTI2025

Generalizable, fast, and accurate DeepQSPR with fastprop

Abstract Quantitative Structure–Property Relationship studies (QSPR), often referred to interchangeably as QSAR, seek to establish a mapping between molecular structure and an arbitrary target property. Historically this was done on a target-by-target basis with new descriptors being devised to specifically map to a given target. Today software packages exist that calculate thousands of these descriptors, enabling general modeling typically with classical and machine learning methods. Also present today are learned representation methods in which deep learning models generate a target-specific representation during training. The former requires less training data and offers improved speed and interpretability while the latter offers excellent generality, while the intersection of the two remains under-explored. This paper introduces , a software package and general Deep-QSPR framework that combines a cogent set of molecular descriptors with deep learning to achieve state-of-the-art performance on datasets ranging from tens to tens of thousands of molecules. provides both a user-friendly Command Line Interface and highly interoperable set of Python modules for the training and deployment of feedforward neural networks for property prediction. This approach yields improvements in speed and interpretability over existing methods while statistically equaling or exceeding their performance across most of the tested benchmarks. is designed with Research Software Engineering best practices and is free and open source, hosted at github.com/jacksonburns/fastprop.

Burns, Jackson W. (ORCID:0000000206579426)↗
DOE OSTI2023

Machine-learning-assisted analysis of transition metal dichalcogenide thin-film growth

In situ reflective high-energy electron diffraction (RHEED) is widely used to monitor the surface crystalline state during thin-film growth by molecular beam epitaxy (MBE) and pulsed laser deposition. With the recent development of machine learning (ML), ML-assisted analysis of RHEED videos aids in interpreting the complete RHEED data of oxide thin films. The quantitative analysis of RHEED data allows us to characterize and categorize the growth modes step by step, and extract hidden knowledge of the epitaxial film growth process. In this study, we employed the ML-assisted RHEED analysis method to investigate the growth of 2D thin films of transition metal dichalcogenides (ReSe2) on graphene substrates by MBE. Principal component analysis (PCA) and K-means clustering were used to separate statistically important patterns and visualize the trend of pattern evolution without any notable loss of information. Using the modified PCA, we could monitor the diffraction intensity of solely the ReSe2 layers by filtering out the substrate contribution. These findings demonstrate that ML analysis can be successfully employed to examine and understand the film-growth dynamics of 2D materials. Further, the ML-based method can pave the way for the development of advanced real-time monitoring and autonomous material synthesis techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2023

En echelon faults reactivated by wastewater disposal near Musreau Lake, Alberta

We use machine-learning and cross-correlation techniques to enhance earthquake detectability by two magnitude units for the earthquake sequence near Musreau Lake, Alberta, which is induced by wastewater disposal. This deep catalogue reveals a series of en echelon ~N–S oriented strike-slip faults that are favourably oriented for reactivation. These faults require only ~0.6 MPa overpressure for triggering to occur. Earthquake activity occurs in bursts, or episodes; episodes restricted to the largest fault tend to have earthquakes starting near the southern end (distant from injectors) and progressing northwards (towards the injectors). While most events are concentrated along these ~N–S oriented faults, we also delineate smaller faults. Together, these findings suggest pore pressure as the triggering mechanism, where a time-dependent increase in pore pressure likely caused these faults to progressively reawaken. Analysis of the ‘next record-breaking event’, a statistical model that forecasts the sequencing of earthquake magnitudes, suggests that the next largest event would be M L ~4.3. The seismically illuminated length of the largest fault indicates potential magnitudes as large as M w 5.3.

58 GEOSCIENCES↗
DOE OSTI2020

Genome-Wide Analysis of RNA Decay in the Cyanobacterium Synechococcus sp. Strain PCC 7002

ABSTRACT RNA degradation is an important process that influences the ultimate concentration of individual proteins inside cells. While the main enzymes that facilitate this process have been identified, global maps of RNA turnover are available for only a few species. Even in these cases, there are few sequence elements that are known to enhance or destabilize a native transcript; even fewer confer the same effect when added to a heterologous transcript. To address this knowledge gap, we assayed genome-wide RNA degradation in the cyanobacterium Synechococcus sp. strain PCC 7002 by collecting total RNA samples after stopping nascent transcription with rifampin. We quantified the abundance of each position in the transcriptome as a function of time using RNA-sequencing data and later analyzed the global mRNA decay map using machine learning principles. Half-lives, calculated on a per-ORF (open reading frame) basis, were extremely short, with a median half-life of only 0.97 min. Despite extremely rapid turnover of most mRNA, transcripts encoding proteins involved in photosynthesis were both highly expressed and highly stable. Upon inspection of these stable transcripts, we identified an enriched motif in the 3′ untranslated region (UTR) that had similarity to Rho-independent terminators. We built statistical models for half-life prediction and used them to systematically identify sequence motifs in both 5′ and 3′ UTRs that correlate with stabilized transcripts. We found that transcripts linked to a terminator containing a poly(U) tract had a longer half-life than both those without a poly(U) tract and those without a terminator. IMPORTANCE RNA degradation is an important process that affects the final concentration of individual mRNAs, affecting protein expression and cellular physiology. Studies of how RNA is degraded increase our knowledge of this fundamental process as well as enable the creation of genetic tools to manipulate RNA stability. By studying global transcript turnover, we searched for sequence elements that correlated with transcript (in)stability and used these sequences to guide tool design. This study probes global RNA turnover in a cyanobacterium, Synechococcus sp. strain PCC 7002, that both has a unique array of RNases that facilitate RNA degradation and is an industrially relevant strain that could be used to convert CO 2 and sunlight into useful products.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

A Multiple Filter Based Neural Network Approach to the Extrapolation of Adsorption Energies on Metal Surfaces for Catalysis Applications

Computational catalyst discovery involves the development of microkinetic reactor models based on estimated parameters determined from density functional theory (DFT). For complex surface chemistries, the number of reaction intermediates can be very large, and the cost of calculating the adsorption energies by DFT for all surface intermediates even for one active site model can become prohibitive. In this paper, we have identified appropriate descriptors and machine learning models that can be used to predict a significant part of these adsorption energies given data on the rest of them. Furthermore, our investigations also included the case when the species data used to train the predictive model are of different size relative to the species the model tries to predict—this is an extrapolation in the data space which is typically difficult with regular machine learning models. Due to the relative size of the available data sets, we have attempted to extrapolate from the larger species to the smaller ones in the current work. Here, we have developed a neural network based predictive model that combines an established additive atomic contribution based model with the concepts of a convolutional neural network that, when extrapolating, achieves a statistically significant improvement over the previous models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Efficient Super-Resolution of Near-Surface Climate Modeling Using the Fourier Neural Operator

Downscaling methods are critical in efficiently generating high-resolution atmospheric data. However, state-of-the-art statistical or dynamical downscaling techniques either suffer from the high computational cost of running a physical model or require high-resolution data to develop a downscaling tool. Here, we demonstrate a recently proposed zero-shot super-resolution method, the Fourier neural operator (FNO), to efficiently perform downscaling without the need for high-resolution data. Because the FNO learns dynamics in Fourier space, FNO is a resolution-invariant emulator; it can be trained at a coarse resolution and produces emulation at any high resolution. We applied FNO to downscale a 4-km resolution Weather Research and Forecasting (WRF) Model simulation of near-surface heat-related variables over the Great Lakes region. The FNO is driven by the atmospheric forcings, and topographic features used in the WRF model at the same resolution. We incorporated a physics-constrained loss in FNO by using the Clausius-Clapeyron relation to better constrain the relations among the emulated states. Trained on merely 600 WRF snapshots at 4-km resolution, the FNO shows comparable performance with a widely used convolutional network, U-Net, achieving averaged modified Kling-Gupta Efficiency of 0.88 and 0.94 on the test dataset for temperature and pressure, respectively. We then employed the FNO to produce 1-km emulations to reproduce the fine climate features. Further, by taking the WRF simulation as ground truth, we show consistent performances at the two resolutions, suggesting the reliability of FNO in producing high-resolution dynamics. Our study demonstrates the potential of using FNO for zero-shot super-resolution in generating first-order estimation on atmospheric modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Machine Learning for Daily Forecasts of Arctic Sea Ice Motion: An Attribution Assessment of Model Predictive Skill

Physics-based simulations of Arctic sea ice are highly complex, involving transport between different phases, length scales, and time scales. Resultantly, numerical simulations of sea ice dynamics have a high computational cost and model uncertainty. We employ data-driven machine learning (ML) to make predictions of sea ice motion. The ML models are built to predict present-day sea ice velocity given present-day wind velocity and previous-day sea ice concentration and velocity. Models are trained using reanalysis winds and satellite-derived sea ice properties. We compare the predictions of three different models: persistence (PS), linear regression (LR), and a convolutional neural network (CNN). We quantify the spatiotemporal variability of the correlation between observations and the statistical model predictions. Additionally, we analyze model performance in comparison to variability in properties related to ice motion (wind velocity, ice velocity, ice concentration, distance from coast, bathymetric depth) to understand the processes related to decreases in model performance. Results indicate that a CNN makes skillful predictions of daily sea ice velocity with a correlation up to 0.81 between predicted and observed sea ice velocity, while the LR and PS implementations exhibit correlations of 0.78 and 0.69, respectively. The correlation varies spatially and seasonally: lower values occur in shallow coastal regions and during times of minimum sea ice extent. LR parameter analysis indicates that wind velocity plays the largest role in predicting sea ice velocity on 1-day time scales, particularly in the central Arctic. Regions where wind velocity has the largest LR parameter are regions where the CNN has higher predictive skill than the LR.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Deep learning of parameterized equations with applications to uncertainty quantification

We propose a learning algorithm for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in particular those using deep neural network (DNN). We propose a DNN structure, largely based upon the residual network (ResNet), to not only learn the unknown form of the governing equation but also take into account the random effect embedded in the system, which is generated by the random parameters. Once the DNN model is successfully constructed, it is able to produce system prediction over longer term and for arbitrary parameter values. For uncertainty quantification, it allows us to conduct uncertainty analysis by evaluating solution statistics over the parameter space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The Evaluation of Machine Learning Techniques for Isotope Identification Contextualized by Training and Testing Spectral Similarity

Precise gamma-ray spectral analysis is crucial in high-stakes applications, such as nuclear security. Research efforts toward implementing machine learning (ML) approaches for accurate analysis are limited by the resemblance of the training data to the testing scenarios. The underlying spectral shape of synthetic data may not perfectly reflect measured configurations, and measurement campaigns may be limited by resource constraints. Consequently, ML algorithms for isotope identification must maintain accurate classification performance under domain shifts between the training and testing data. To this end, four different classifiers (Ridge, Random Forest, Extreme Gradient Boosting, and Multilayer Perceptron) were trained on the same dataset and evaluated on twelve other datasets with varying standoff distances, shielding, and background configurations. A tailored statistical approach was introduced to quantify the similarity between the training and testing configurations, which was then related to the predictive performance. Wilcoxon signed-rank tests revealed that the OVR-wrapped XGB significantly outperformed the other algorithms, with confidence levels of 99.0% or above for the 133Ba, 60Co, 137Cs, and 152Eu sources. The findings from this work are significant as they outline techniques to promote the development of robust ML-based approaches for isotope identification.

domain adaptation↗
DOE OSTI2026

Generation of random geological models using multi-randomization for machine learning

Generating high-fidelity geological models is essential for advancing machine learning (ML) methods in automated seismic interpretation. For instance, seismic images paired with corresponding fault labels are foundational for ML-based fault detection from seismic migration sections. While several open-access datasets of random geological models exist, open-source tools specifically designed to produce large volumes of such models for ML applications remain scarce. To address this gap, we present RGM (Random Geological Model), an open-source software package for efficiently generating 2D and 3D synthetic geological models tailored for ML workflows. RGM supports the creation of diverse model components, including medium property distributions (P-/S-wave velocities and density), seismic reflectivity images (i.e., synthetic migration sections), relative geological time, and discrete fault attributes such as probability, dip, strike, rake, and displacement. It also accommodates the creation of complex geological features such as salt bodies and unconformities. The model generation algorithm employs a multi-randomization strategy, yielding an effectively infinite-dimensional model space that encompasses a wide range of geological scenarios and associated seismic features. Furthermore, RGM incorporates a method to generate synthetic elastic migration images using analytical elastic reflection coefficients combined with frequency-dependent scaling. This functionality enables the creation of training datasets for ML models that leverage elastic seismic images. RGM is implemented in modern object-oriented Fortran, allowing users to flexibly control statistical parameters governing model variability. We demonstrate the capability, performance, and geological realism of the package through comprehensive 2D and 3D examples.

58 GEOSCIENCES↗
DOE OSTI2022

Monitoring the propagation of mechanical discontinuity using data-driven causal discovery and supervised learning

Mechanical wave transmission through a material is influenced by the mechanical discontinuity in the material. The propagation of embedded discontinuities can be monitored by analyzing the wave-transmission measurements recorded by a multipoint sensor system placed on the surface of the material. The proposed workflow monitors the propagation of mechanical discontinuity through three stages, namely initial, intermediate, and final stages, by using supervised learning followed by data-driven causal discovery. To the end, the workflow processes the multipoint waveform measurements resulting from a single impulse source, while considering the effects of wave attenuation, dispersion and multiple wave-propagation modes due to the discontinuity and material boundaries. Among various feature reduction techniques ranging from decomposition methods to manifold approximation methods, the features derived based on statistical parameterizations of the measured waveforms lead to reliable monitoring that is robust to changes in precision, resolution, and signal-to-noise ratio of the multipoint sensor measurements. The numbers of zero-crossing, negative-turning, and positive turning in the waveforms are the strongest causal signatures of the propagation of mechanical discontinuity. Higher order moments of the waveforms, such as variance, skewness and kurtosis, are also strong causal signatures of the propagation. Finally, the newly discovered causal signatures confirm that the statistical correlations and conventional feature rankings are not always statistically significant indicators of causality.

42 ENGINEERING↗
DOE OSTI2021

Sparse expansions of multicomponent oxide configuration energy using coherency and redundancy

We report that compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

QUOTAS: A New Research Platform for the Data-driven Discovery of Black Holes

We present QUOTAS, a novel research platform for the data-driven investigation of supermassive black hole (SMBH) populations. While SMBH data—observations and simulations—have grown in complexity and abundance, our computational environments and tools have not matured commensurately to exhaust opportunities for discovery. To explore the BH, host galaxy, and parent dark matter halo connection—in this pilot version—we assemble and colocate the high-redshift, z > 3 quasar population alongside simulated data at the same cosmic epochs. As a first demonstration of the utility of QUOTAS, we investigate correlations between observed Sloan Digital Sky Survey (SDSS) quasars and their hosts with those derived from simulations. Leveraging machine-learning algorithms (ML), to expand simulation volumes, we show that halo properties extracted from smaller dark-matter-only simulation boxes successfully replicate halo populations in larger boxes. Next, using the Illustris-TNG300 simulation that includes baryonic physics as the training set, we populate the larger LEGACY Expanse dark-matter-only box with quasars, and show that observed SDSS quasar occupation statistics are accurately replicated. First science results from QUOTAS comparing colocated observational and ML-trained simulated data at z3 are presented. QUOTAS demonstrates the power of ML, in analyzing and exploring large data sets, while also offering a unique opportunity to interrogate theoretical assumptions that underpin accretion and feedback models. QUOTAS and all related materials are publicly available at the Google Kaggle platform. (The full data set—observational data and simulation data—are available at: https://www.kaggle.com/ and the codes are available at:https://www.kaggle.com/datasets/quotasplatform/quotas)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

J/ψ Near-Threshold Photoproduction off the Proton and Neutron with CLAS12

In recent years, J/? photoproduction in the near-threshold region has seen a renewed theoretical interest due to the wealth of information it has to offer. Near-threshold J/? photopro-duction proceeds through the exchange of gluons in the t-channel and is expected to provide unique insight about the nucleon gluonic gravitational form factors (GFFs). Previous studies at the Thomas Jefferson National Accelerator Facility (JLab) in Virginia, USA, have already measured the total and differential cross section of J/? near-threshold photoproduction on the free proton. This thesis presents the first measurements of J/? near-threshold photoproduction on the bound proton and bound neutron in a deuteron target. The CEBAF Large Acceptance Spectrometer at 12 GeV (CLAS12) based at JLab?s Hall B uses a 11 GeV electron beam impinging on a fixed liquid deuteron target. J/? is then produced via the exchange of a quasi-real photon and decays to a lepton pair which is detected along-side the recoil nucleon by CLAS12. Analysis procedures and in particular machine learning based techniques were developed in order to correctly identify final state particles and select J/? photoproduction events. The total and differential cross section of J/? near-threshold photoproduction on the bound proton and bound neutron were then measured from the detected J/? photoproduction events. The measurements of the cross sections on the bound proton and bound neutron agree well within their statistical uncertainty. This is consistent with the assumed two-gluon exchange production mechanism which is isospin invariant. Overall a first measurement of the J/? near-threshold photoproduction cross sections on the bound proton and bound neutron was achieved. A better understanding of the mechanical properties of the nucleon, such as pressure and mass distributions, can be obtained by relating J/? production to the nucleon GFFs. This opens the way for exciting new insights into the internal structure of the nucleon, and in particular of the nucleon?s gluonic content. An upcoming overhaul of the CLAS12 reconstruction will increase the reconstruction efficiency and the statis- tical precision of the preliminary measurements described in this thesis, with an expected gain in statistics of at least 50%. Future upgrades at JLab will allow to test some of the theoretical assumptions made in relating J/? near-threshold photoproduction to the nucleon GFFs

Tyson, Richard↗