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NASA NTRS2011

A Bootstrap Approach to an Affordable Exploration Program

This paper examines the potential to build an affordable sustainable exploration program by adopting an approach that requires investing in technologies that can be used to build a space infrastructure from very modest initial capabilities. Human exploration has had a history of flight programs that have high development and operational costs. Since Apollo, human exploration has had very constrained budgets and they are expected be constrained in the future. Due to their high operations costs it becomes necessary to consider retiring established space facilities in order to move on to the next exploration challenge. This practice may save cost in the near term but it does so by sacrificing part of the program s future architecture. Human exploration also has a history of sacrificing fully functional flight hardware to achieve mission objectives. An affordable exploration program cannot be built when it involves billions of dollars of discarded space flight hardware, instead, the program must emphasize preserving its high value space assets and building a suitable permanent infrastructure. Further this infrastructure must reduce operational and logistics cost. The paper examines the importance of achieving a high level of logistics independence by minimizing resource consumption, minimizing the dependency on external logistics, and maximizing the utility of resources available. The approach involves the development and deployment of a core suite of technologies that have minimum initial needs yet are able expand upon initial capability in an incremental bootstrap fashion. The bootstrap approach incrementally creates an infrastructure that grows and becomes self sustaining and eventually begins producing the energy, products and consumable propellants that support human exploration. The bootstrap technologies involve new methods of delivering and manipulating energy and materials. These technologies will exploit the space environment, minimize dependencies, and minimize the need for imported resources. They will provide the widest range of utility in a resource scarce environment and pave the way to an affordable exploration program.

Oeftering, Richard C.↗

NASA NTRS2016

Confidence Intervals for Laboratory Sonic Boom Annoyance Tests

Commercial supersonic flight is currently forbidden over land because sonic booms have historically caused unacceptable annoyance levels in overflown communities. NASA is providing data and expertise to noise regulators as they consider relaxing the ban for future quiet supersonic aircraft. One deliverable NASA will provide is a predictive model for indoor annoyance to aid in setting an acceptable quiet sonic boom threshold. A laboratory study was conducted to determine how indoor vibrations caused by sonic booms affect annoyance judgments. The test method required finding the point of subjective equality (PSE) between sonic boom signals that cause vibrations and signals not causing vibrations played at various amplitudes. This presentation focuses on a few statistical techniques for estimating the interval around the PSE. The techniques examined are the Delta Method, Parametric and Nonparametric Bootstrapping, and Bayesian Posterior Estimation.

Rathsam, Jonathan↗

DOE OSTI2021

SANS quantification of bound water in water-soluble polymers across multiple concentration regimes

Contrast-variation small-angle neutron scattering (CV-SANS) is a widely used technique for quantifying hydration water in soft matter systems, but it is predominantly applied in the dilute regime or for systems with a well-defined structure factor. Here, CV-SANS was used to quantify the number of hydration water molecules associating with three water-soluble polymers with different critical solution temperatures and types of water–solute interactions in dilute, semidilute, and concentrated solution through the exploration of novel methods of data fitting and analysis. Multiple SANS fitting workflows with varying levels of model assumptions were evaluated and compared to give insight into SANS model selection. These fitting pathways ranged from general, model-free algorithms to more standard form and structure factor fitting. In addition, Monte Carlo bootstrapping was evaluated as a method to estimate parameter uncertainty through simulation of technical replicates. The most robust fitting workflow for dilute solutions was found to be form factor fitting without CV-SANS ( i.e. polymer in 100% D 2 O). For semidilute and concentrated solutions, while the model-free approach can be mathematically defined for CV-SANS data, the addition of a structure factor imposes physical constraints on the optimization problem, suggesting that the optimal fitting pathway should include appropriate form and structure factor models. The measured hydration numbers were consistent with the number of tightly bound water molecules associated with each monomer unit, and the concentration dependence of the hydration number was largely governed by the chemistry-specific interactions between water and polymer. Polymers with weaker water–polymer interactions ( i.e. those with fewer hydration water molecules) were found to have more bound water at higher concentrations than those with stronger water–polymer interactions due to the increase in the number of forced water–polymer contacts in the concentrated system. This SANS-based method to count hydration water molecules can be applied to polymers in any concentration regime, which will lead to improved understanding of water–polymer interactions and their impact on materials design.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Bootstrap-determined p values in lattice QCD

We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p -value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling T 2 methods based on the conventional χ 2 statistic do not apply, such as for uncorrelated fits. Specifically, we analyze q 2 , defined as the correlated χ 2 statistic obtained using an arbitrary covariance matrix estimator, and show how to use the bootstrap as a data-driven method to determine the expected distribution of q 2 for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p -value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p -value of estimating population parameters from a single ensemble of N samples. The overall method is accurate up to a 1 / N bias which we do not attempt to quantify. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Bootstrapping 2d ϕ 4 theory with Hamiltonian truncation data

We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d Φ 4 theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the Φ 4 two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Lanczos Algorithm, the Transfer Matrix, and the Signal-to-Noise Problem

This Letter introduces a method for determining the energy spectrum of lattice quantum chromodynamics by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to filter out spurious eigenvalues. Proof-of-principle analyses of the simple harmonic oscillator and the lattice quantum chromodynamics proton mass demonstrate that this method provides faster ground-state convergence than the “effective mass,” which is related to the power-iteration algorithm. Lanczos provides more accurate energy estimates than multistate fits to correlation functions with small imaginary times while achieving comparable statistical precision. Two-sided error bounds are computed for Lanczos results and guarantee that excited-state effects cannot shift Lanczos results far outside their statistical uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n) O ( m ) × O ( n ) global symmetry in d=3 d = 3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-d ε = 4 − d and in 1/n 1 / n , with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n) O ( 2 ) × O ( n ) theories for various values of n n . Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilon ε and large- n n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Quantum state preparation with resolution refinement

We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then lifted to higher resolution and adiabatically evolved to produce the corresponding eigenstate of a higher-fidelity Hamiltonian. We give examples of resolution refinement applied to both single-particle basis states as well as a spatial lattice grid. For basis refinement, we compute few-body ground states of the Busch model for interacting particles in a harmonic trap in one dimension. For lattice refinement, we compute Hartree-Fock nuclear states for a central Woods-Saxon potential in three dimensions, and we compute bound states and continuum states in a multi-species Hubbard model of fermions in one dimension. In all cases, the method is efficient and requires an adiabatic evolution time that scales with the inverse of the energy gap times the square root of the system size. We show that this very favorable scaling arises from the fact that resolution refinement does not make large changes to the structure or energies of the low-energy eigenstates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Toward the analytic bootstrap of energy correlators

In this paper, we present a framework for the analytic bootstrap of three-point energy correlators, a crucial observable in $\mathcal{N}$ = 4 super Yang-Mills theory and quantum chromodynamics (QCD). Our approach combines spherical contour techniques, general physical constraints such as pole cancellations, and power correction data in the singular limits to determine its analytic expression. In contrast to previous bootstrap studies restricted to scattering amplitudes for supersymmetric theories, our framework makes use of the properties of Feynman integrals, marking a significant step toward bootstrapping realistic QCD observables. Using this method, we derive analytic expressions for leading-order three-point energy correlators in the multi-collinear limit with equal and unequal energy weights, where the latter are crucial ingredients for projected N -point energy correlators. We also apply the recently developed technique of analytic regression with lattice reduction as a way to bypass needing explicit expressions for the singular limits. Bridging theoretical advances in scattering amplitudes with the renewed interest in weighted cross-sections, our work opens the door to precision tests of QCD dynamics through analytic event-shape predictions.

jet substructure↗

DOE OSTI2025

Toward the Analytic Bootstrap of Energy Correlators

In this paper, we present a framework for the analytic bootstrap of three-point energy correlators, a crucial observable in N = 4 N=4 super Yang-Mills theory and quantum chromodynamics (QCD). Our approach combines spherical contour techniques, general physical constraints such as pole cancellations, and power correction data in the singular limits to determine its analytic expression. In contrast to previous bootstrap studies restricted to scattering amplitudes for supersymmetric theories, our framework makes use of the properties of Feynman integrals, marking a significant step toward bootstrapping realistic QCD observables. Using this method, we derive analytic expressions for leading-order three-point energy correlators with equal and unequal energy weights, where the latter are crucial ingredients for projected N N-point energy correlators. We also apply the recently developed technique of analytic regression with lattice reduction as a way to bypass needing explicit expressions for the singular limits. Bridging theoretical advances in scattering amplitudes with the renewed interest in weighted cross-sections, our work opens the door to precision tests of QCD dynamics through analytic event-shape predictions.

Gong, Jianyu [State Key Laboratory]↗

DOE OSTI2022

Optimization of quasi-symmetric stellarators with self-consistent bootstrap current and energetic particle confinement

Quasi-symmetry can greatly improve the confinement of energetic particles and thermal plasma in a stellarator. The magnetic field of a quasi-symmetric stellarator at high plasma pressure is significantly affected by the bootstrap current, but the computational cost of accurate stellarator bootstrap calculations has precluded use inside optimization. Here, a new efficient method is demonstrated for optimization of quasi-symmetric stellarator configurations such that the bootstrap current profile is consistent with the geometry. The approach is based on the fact that all neoclassical phenomena in quasi-symmetry are isomorphic to those in axisymmetry. Therefore, accurate formulas for the bootstrap current in tokamaks, which can be evaluated rapidly, can be applied also in stellarators. The deviation between this predicted parallel current and the actual parallel current in the magnetohydrodynamic equilibrium is penalized in the objective function, and the current profile of the equilibrium is included in the parameter space. Quasi-symmetric configurations with significant pressure are thereby obtained with self-consistent bootstrap current and excellent confinement. In a comparison of fusion-produced alpha particle confinement across many stellarators, the new configurations have significantly lower alpha energy losses than many previous designs.

Landreman, M. (ORCID:000000027233577X)↗

NASA NTRS2007

Bootstrap data methodology for sequential hybrid model building

A method for modeling engine operation comprising the steps of: 1. collecting a first plurality of sensory data, 2. partitioning a flight envelope into a plurality of sub-regions, 3. assigning the first plurality of sensory data into the plurality of sub-regions, 4. generating an empirical model of at least one of the plurality of sub-regions, 5. generating a statistical summary model for at least one of the plurality of sub-regions, 6. collecting an additional plurality of sensory data, 7. partitioning the second plurality of sensory data into the plurality of sub-regions, 8. generating a plurality of pseudo-data using the empirical model, and 9. concatenating the plurality of pseudo-data and the additional plurality of sensory data to generate an updated empirical model and an updated statistical summary model for at least one of the plurality of sub-regions.

Volponi, Allan J.↗

DOE OSTI2026

Towards utility-scale electronic structure with sample-based quantum bootstrap embedding

One of the main applications for which quantum computers are hoped to find utility is in simulating ground state energies and other observables of molecular chemical systems. The recently proposed sample-based diagonalization method is a readily implementable method for this task on current-day hardware using short circuit depths and has been demonstrated on as many as 85 qubits in recent studies. In this work, we combine the recently proposed quantum bootstrap embedding (QBE) method with sampled-based diagonalization (QBE-SQD) and present the first benchmarking study of the QBE method on real quantum hardware, ibm_pittsburgh, a Heron r3 processor with 156 qubits. Our test system is a hydrogen ring with 8 hydrogen atoms in the cc-pVDZ basis. We show that for this system, QBE-SQD using an active space of (8e, 19o) per fragment with a 43 qubit footprint produces a ground state energy accuracy which exceeds that of an SQD calculation with an (8e, 30o) active space with a 67 qubit footprint when using a comparable number of Slater determinants. This demonstrates that the use of quantum bootstrap embedding techniques is a promising path towards extending the capabilities of state-of-the-art quantum eigensolvers on near-term devices.

Bierman, Joel [North Carolina State University, Ra↗

DOE OSTI2019

Optimization of a superconducting adiabatic radio frequency neutron resonant spin flipper

The neutron radio frequency (RF) spin flipper is one of the key components to implement neutron resonance spin echo (NRSE) for high resolution measurements of dynamics in materials. Various types of RF flippers have been built and implemented including adiabatic and non-adiabatic RF flippers. For a pulsed neutron source, adiabatic RF flipper is more favorable due to its wide operation bandwidth. However, the optimization criteria of an adiabatic RF flipper is still lacking. Also they are difficult to be operated in bootstrap mode, which can be use to minimize the phase aberration and increase the achievable resolution. In the report by Dadisman et al. (2019), an adiabatic RF flipper has been built for the first time with superconducting technologies, which allows bootstrap mode. Here in this article, the method of optimizing the device and the detailed design will be discussed for each component of the device.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Review of the November 11, 1905 Earthquake: Seismic Intensity Data, Magnitude, and Location Report

The macroseismic location and magnitude of the Shoshone 1905 earthquake has been based on the application of objective and quantitative approaches that produce estimates of earthquake source location and magnitude, and associated uncertainties. The performance of all three approaches applied depends critically on the characteristics of the seismic intensity field. Regional intensity attenuation relations were derived based on a calibration set of earthquakes and then, the procedure was validated using three independent very recent events. The macroseismic epicenter location was determined by either a grid search procedure, the spatial distribution of the sites experiencing the largest intensities, or a combination of both. The macroseismic magnitude estimates are based on the derived regional intensity attenuation relations. There is consistency in the location and magnitude of the November 1905 earthquake as obtained by the three methods. The overlapping region of the 68% bootstrap resampling solutions suggests a reliable epicenter location within 41.550N ? 42.060N and 113.478W ? 112.320W. This region encloses the original Oaks (1992) epicenter location. Macroseismic magnitude estimates range between 5.87 and 6.05.

58 GEOSCIENCES↗

DOE OSTI2021

Predictive Battery Lifetime Modeling at NREL [Slides]

Battery lifetime models are used to extrapolate data from accelerated aging tests to simulate degradation in real-world applications such as electric vehicles and battery energy storage systems. Methods developed at NREL utilize both expert domain-knowledge and machine-learning to identify models, using statistical methods such as cross-validation and bootstrap resampling to interrogate model performance and quantify uncertainty. These models can be utilized in systems level simulations to predict battery performance or technoeconomic models to estimate the lifetime cost of battery systems.

25 ENERGY STORAGE↗

NASA NTRS2005

Comparison of Histograms for Use in Cloud Observation and Modeling

Cloud observation and cloud modeling data can be presented in histograms for each characteristic to be measured. Combining information from single-cloud histograms yields a summary histogram. Summary histograms can be compared to each other to reach conclusions about the behavior of an ensemble of clouds in different places at different times or about the accuracy of a particular cloud model. As in any scientific comparison, it is necessary to decide whether any apparent differences are statistically significant. The usual methods of deciding statistical significance when comparing histograms do not apply in this case because they assume independent data. Thus, a new method is necessary. The proposed method uses the Euclidean distance metric and bootstrapping to calculate the significance level.

Green, Lisa↗

NASA NTRSDate not supplied

Establishing the Framework for e-VTOL Flight Mission Scenario Development for Urban Air Mobility Research using Cognitive Task Analysis

This paper focuses on applying specific protocol aspects of Cognitive Task Analysis (CTA) methods to formulate non-routine flight mission use-case scenarios in support of a potential research study at the National Aeronautics and Space Administration (NASA) Langley Research Center under the Air Traffic Management – eXploration (ATM-X) Urban Air Mobility (UAM) sub-project. The objective of use-case scenarios is to provide a hypothetical situation to elicit expert knowledge and feedback in a specific subject matter area. Use-case scenarios in the field of aviation, including UAM, can help to support the safe integration of these vehicles into the National Airspace System (NAS) through the examination of airspace procedures during non-routine events. Inherent in this type of research is the need to study in-flight non-routine scenarios that the UAM vehicle could encounter. Situations categorized as non-routine events are any events that occur outside of the original flight plan such as a mechanical malfunction or other in-flight emergency requiring special procedures, which can include diversions to a specified, or non-specified, emergency landing area. In specific instances, some non-routine events could be considered as “routine” during in-flight operations, such as the need to perform a go-around due to a balked landing. As the rate of technological expansion surrounding UAM grows rapidly in modern aviation, so does the need for research that focuses on the safe integration of these vehicles including research with a focus on the methods and development of airspace operational procedures. Research rooted in CTA methods provides a framework for developing use-case scenarios appropriate for environments where mental demands are substantial. Substantial mental demands exist while operating in the NAS for pilots, airline dispatchers, and air traffic controllers among many others. With the focus on UAM in mind, it is critical to frame a baseline use-case scenario using information as it pertains to current-day airspace operations. According to Dr. Robert R. Hoffman’s “Protocols for Cognitive Task Analysis,” one of the first steps to applying CTA methods to research is the concept of “bootstrapping” in which the researcher(s) familiarize themselves with the domain that is being studied. To formulate the non-routine flight mission use-case scenarios for the purpose of this potential NASA ATM-X UAM research study, and to inform the baseline use-case scenario, the practice of bootstrapping was utilized to acquire knowledge of current-day airspace procedures.

Heidi S Glaudel↗