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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.

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DOE OSTI2021

Get on the BAND Wagon: a Bayesian framework for quantifying model uncertainties in nuclear dynamics

In this paper, we describe the Bayesian Analysis of Nuclear Dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodology's ability to leverage insight from multiple models. In order to facilitate understanding of these tools we provide a simple and accessible example of the BAND framework's application. Four case studies are presented to highlight how elements of the framework will enable progress on complex, far-ranging problems in nuclear physics. By collecting notation and terminology, providing illustrative examples, and giving an overview of the associated techniques, this paper aims to open paths through which the nuclear physics and statistics communities can contribute to and build upon the BAND framework.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Veridical data science

Building and expanding on principles of statistics, machine learning, and scientific inquiry, we propose the predictability, computability, and stability (PCS) framework for veridical data science. Our framework, composed of both a workflow and documentation, aims to provide responsible, reliable, reproducible, and transparent results across the data science life cycle. The PCS workflow uses predictability as a reality check and considers the importance of computation in data collection/storage and algorithm design. It augments predictability and computability with an overarching stability principle. Stability expands on statistical uncertainty considerations to assess how human judgment calls impact data results through data and model/algorithm perturbations. As part of the PCS workflow, we develop PCS inference procedures, namely PCS perturbation intervals and PCS hypothesis testing, to investigate the stability of data results relative to problem formulation, data cleaning, modeling decisions, and interpretations. We illustrate PCS inference through neuroscience and genomics projects of our own and others. Moreover, we demonstrate its favorable performance over existing methods in terms of receiver operating characteristic (ROC) curves in high-dimensional, sparse linear model simulations, including a wide range of misspecified models. Finally, we propose PCS documentation based on R Markdown or Jupyter Notebook, with publicly available, reproducible codes and narratives to back up human choices made throughout an analysis. The PCS workflow and documentation are demonstrated in a genomics case study available on Zenodo.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Band-limited photodetection of temporal coherence

The quantum theory of optical coherence plays a ubiquitous role in identifying optical emitters. An unequivocal identification, however, presumes that the photon number statistics is resolved from timing uncertainties. We demonstrate from first principle that the observed nth-order temporal coherence is a n-fold convolution of the instrument responses and the expected coherence. The consequence is detrimental in which the photon number statistics is masked from the unresolved coherence signatures. The experimental investigations are thus far consistent with the theory developed. We envision the present theory will mitigate the false identification of optical emitters and enlarge the coherence deconvolution to an arbitrary order.

42 ENGINEERING↗
DOE OSTI2021

Uncertainty Visualization for Renewable Energy Potential

In this paper, we present the reV (Renewable Energy Potential) Dashboard, an interactive browser-based tool for uncertainty visualization and data exploration built using customized plotly dash components. With continuing development and utilization of computational models to study the power sector there is an increasing need for data-driven visualization tools which allow scientists, researchers, and engineers to interact with their data in real-time. Our principle motivation for developing this interactive uncertainty visualization was to provide domain scientists and modelers a platform which allows them to better understand and communicate scientific findings stemming from intricate information encoded in their data that is otherwise difficult to capture by conventional analysis. The development of customized dashboard components using the React programming paradigm, combined with fully pre-processed data, allows for users to select a variety of data options to update and manipulate the visualization in a straightforward computationally efficient manner.

dashboard↗
DOE OSTI2021

Calibration of the Diffusivity Predictions of Centipede Using Approximate Bayesian Computation and Applications in Nyx (Engineering Scale) and Xolotl-MARMOT (Meso-Scale) Simulations

Fission gas evolution and release in UO 2 nuclear fuel are important fuel performance metrics and occur in several distinct stages: 1) nucleation, growth and resolution of intra-granular bubbles, 2) diffusion to grain boundaries and 3) nucleation and growth of bubbles at grain boundaries, which eventually form a connected network (percolation) enabling release of gas from grain boundaries through connections to triple junctions, grain edges or free surfaces. The NE-SciDAC project is developing several computational tools to model this problem, which are connected in a hierarchical multi-scale framework. The information transfer in the multi-scale framework is a critical step that, in addition to best-estimates, should include uncertainty quantification. Despite taking a first-principles multi-scale approach, there is a need to perform parameter calibration to ensure consistency with available experimental data. In the present study, uncertainty quantification (UQ) and parameter calibration is demonstrated for one of the lower length scale codes in the multi-scale framework (Centipede) and then the results, including instances of the propagated uncertainties, are used in other codes within the framework, specifically Nyx and Xolotl-MARMOT. We calibrated the model parameters in Centipede, a computer code used to predict diffusivities of uranium (U) and xenon (Xe) in the context of the simulation of fission gas in uranium oxide (UO 2 ) nuclear fuel. The Centipede code depends on 183 parameters, all of which are subject to uncertainty. The three data sets used in our calibration effort are taken from the literature. This data is available as a set of measurements, including measurement errors. Our goal is to calibrate a statistical model that predicts both the value of the measurement and the uncertainty associated with the measurement. We perform a Bayesian calibration of the model parameters using a dedicated approximate Bayesian computation (ABC) likelihood function. To avoid excessive computational costs, we replace the expensive Centipede simulation code by a higher-order surrogate model, constructed using only the 9 most important parameters. These important parameters are identified by a preliminary global sensitivity analysis (GSA) study. Among the important parameters are T0 (the temperature at which UO 2 is perfectly stoichiometric) and Hf_pO2 (the temperature dependence of the oxygen (O) partial pressure) that should be considered as operating conditions to be estimated along with the other parameters. We consider two different cases: one where we define one set of these operating conditions for all data sets, and one where we define distinct operating condition parameters for each data set. The Xe diffusivities predicted by the latter case show distinct features that could not be observed in the former. Next, we use the diffusivity predictions by Centipede as input to Nyx, a reduced order fuel performance code focused on gas behavior alone, in order to estimate quantities associated with inter-granular bubble formation at conditions specified by the experiments. Finally, the diffusivities obtained from the calibrated Centipede runs were used in coupled Xolotl-MARMOT simulations of intra- and inter-granular gas evolution. The results are compared to simulations using the baseline diffusivities from Turnbull et al.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Automated Generation of Microkinetics for Heterogeneously Catalyzed Reactions Considering Correlated Uncertainties**

Abstract The study presents an ab‐initio based framework for the automated construction of microkinetic mechanisms considering correlated uncertainties in all energetic parameters and estimation routines. 2000 unique microkinetic models were generated within the uncertainty space of the BEEF‐vdW functional for the oxidation reactions of representative exhaust gas emissions from stoichiometric combustion engines over Pt(111) and compared to experiments through multiscale modeling. The ensemble of simulations stresses the importance of considering uncertainties. Within this set of first‐principles‐based models, it is possible to identify a microkinetic mechanism that agrees with experimental data. This mechanism can be traced back to a single exchange‐correlation functional, and it suggests that Pt(111) could be the active site for the oxidation of light hydrocarbons. The study provides a universal framework for the automated construction of reaction mechanisms with correlated uncertainty quantification, enabling a DFT‐constrained microkinetic model optimization for other heterogeneously catalyzed systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications

Abstract Robust quantification of predictive uncertainty is a critical addition needed for machine learning applied to weather and climate problems to improve the understanding of what is driving prediction sensitivity. Ensembles of machine learning models provide predictive uncertainty estimates in a conceptually simple way but require multiple models for training and prediction, increasing computational cost and latency. Parametric deep learning can estimate uncertainty with one model by predicting the parameters of a probability distribution but does not account for epistemic uncertainty. Evidential deep learning, a technique that extends parametric deep learning to higher-order distributions, can account for both aleatoric and epistemic uncertainties with one model. This study compares the uncertainty derived from evidential neural networks to that obtained from ensembles. Through applications of the classification of winter precipitation type and regression of surface-layer fluxes, we show evidential deep learning models attaining predictive accuracy rivaling standard methods while robustly quantifying both sources of uncertainty. We evaluate the uncertainty in terms of how well the predictions are calibrated and how well the uncertainty correlates with prediction error. Analyses of uncertainty in the context of the inputs reveal sensitivities to underlying meteorological processes, facilitating interpretation of the models. The conceptual simplicity, interpretability, and computational efficiency of evidential neural networks make them highly extensible, offering a promising approach for reliable and practical uncertainty quantification in Earth system science modeling. To encourage broader adoption of evidential deep learning, we have developed a new Python package, Machine Integration and Learning for Earth Systems (MILES) group Generalized Uncertainty for Earth System Science (GUESS) (MILES-GUESS) ( https://github.com/ai2es/miles-guess ), that enables users to train and evaluate both evidential and ensemble deep learning. Significance Statement This study demonstrates a new technique, evidential deep learning, for robust and computationally efficient uncertainty quantification in modeling the Earth system. The method integrates probabilistic principles into deep neural networks, enabling the estimation of both aleatoric uncertainty from noisy data and epistemic uncertainty from model limitations using a single model. Our analyses reveal how decomposing these uncertainties provides valuable insights into reliability, accuracy, and model shortcomings. We show that the approach can rival standard methods in classification and regression tasks within atmospheric science while offering practical advantages such as computational efficiency. With further advances, evidential networks have the potential to enhance risk assessment and decision-making across meteorology by improving uncertainty quantification, a longstanding challenge. This work establishes a strong foundation and motivation for the broader adoption of evidential learning, where properly quantifying uncertainties is critical yet lacking.

Schreck, John S.↗
DOE OSTI2020

Nuclear Data Covariances and Sampling

In this report, we present an overview of the task of producing sample nuclear data sets for the purpose of exploring the effects of nuclear data uncertainties on physics simulations. These sample data sets (or, as we sometimes call them variations) are produced based on uncertainties specified in the ENDF/B-VIII nuclear data library, although the principles discussed here apply to sampling based on similar libraries, such as JENDL. The uncertainties in ENDF and similar libraries are given in the form of mean values (a mean vector) and a covariance matrix. The components of the mean vector are what are normally thought of as the values of the nuclear data (cross sections, $\bar{v}$, the prompt fission neutron spectrum, etc.) and the covariance matrix contains the information about the uncertainties in these values and correlations between them, including correlations across different energies in a single channel and correlations across different channels.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

BUQEYE guide to projection-based emulators in nuclear physics

The BUQEYE collaboration (Bayesian Uncertainty Quantification: Errors in Your effective field theory) presents a pedagogical introduction to projection-based, reduced-order emulators for applications in low-energy nuclear physics. The term emulator refers here to a fast surrogate model capable of reliably approximating high-fidelity models. As the general tools employed by these emulators are not yet well-known in the nuclear physics community, we discuss variational and Galerkin projection methods, emphasize the benefits of offline-online decompositions, and explore how these concepts lead to emulators for bound and scattering systems that enable fast and accurate calculations using many different model parameter sets. We also point to future extensions and applications of these emulators for nuclear physics, guided by the mature field of model (order) reduction. All examples discussed here and more are available as interactive, open-source Python code so that practitioners can readily adapt projection-based emulators for their own work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Ab initio nucleon-nucleus elastic scattering with chiral effective field theory uncertainties

Effective interactions for nucleon-nucleus elastic scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations and a consistent treatment of the relevant operators at each order. Systematic investigations of the effect of truncation uncertainties of chiral nucleon-nucleon ( N N ) forces have been carried out for scattering observables in the two- and three-nucleons system as well as for bound-state properties of light nuclei. Here we extend this type of study to proton and neutron elastic scattering for 16 O and 12 C. Using the frameworks of the spectator expansion of multiple scattering theory as well as the no-core shell model, we employ one specific chiral interaction from the LENPIC collaboration and consistently calculate the leading-order effective nucleon-nucleus interaction up to the third chiral order, from which we extract elastic scattering observables. Then we apply pointwise as well as correlated uncertainty quantification for the estimation of the chiral truncation error. We calculate and analyze proton elastic scattering observables for 16 O and 12 C as well as neutron elastic scattering observables for 12 C between 65 and 185 MeV projectile kinetic energy. We find in all cases qualitatively similar results for the chiral truncation uncertainties as in few-body systems and assess them using similar diagnostic tools. The order-by-order convergence of the scattering observables for 16 O and 12 C is very reasonable around 100 MeV, while for higher energies the chiral expansion parameter becomes too large for convergence. Comparing proton and neutron differential cross sections reveals that their description is comparable up to around 100 MeV. Here, we also find a nearly perfect correlation between the differential cross section for neutron scattering and the N N Wolfenstein amplitudes for small momentum transfers. The diagnostic tools for studying order-by-order convergence in observables in few-body systems can be employed for observables in nucleon-nucleus scattering with only minor modifications provided the momentum scale in the problems is not too large. We also find that the chiral N N interaction on which our study is based gives a very good description of differential cross sections for 16 O and 12 C as low as 65-MeV projectile energy, particularly in the forward direction. In addition, the very forward direction of the neutron differential cross section mirrors the behavior of the N N interaction amazingly well.

6 ≤ A ≤ 19↗
DOE OSTI2026

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗
DOE OSTI2026

Reimagining How Flood Warnings Can Inform Decision‐Making and Community Actions

Society faces increasingly severe flood hazards, intensifying demand for flood early warning systems (FEWS) that deliver accurate and actionable information. However, most existing FEWS remain prediction‐centric, treating decision‐making as a downstream consumer of hazard forecasts while offering limited support for uncertainty interpretation, risk communication, and real‐world response. This Perspective presents a vision and blueprint for a novel inland FEWS‐decision‐making (FEWS‐DM) framework that repositions decision‐making as an equal partner in the forecasting process—not a passive recipient of its outputs. The framework is built on three tightly coupled, co‐evolving thrusts: Physical Science (T1), which advances flood prediction with quantified uncertainty informed by decision relevance; Human Science (T2), which incorporates psychology, behavior, and cultural and institutional context; and Decision Science (T3), which unifies physical predictions and human factors through principled, utility‐based decision support with end‐to‐end uncertainty management. Rather than treating T1 as a solved problem, FEWS‐DM recognizes that forecast development itself must be shaped by decision needs through continuous bidirectional feedback. We identify key scientific, behavioral, and operational challenges limiting such integration and discuss the enabling role of AI, while emphasizing human‐centered design and community feedback as essential for building trust and improving flood risk management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Statistical Uncertainty of Inhalation Dose Coefficients in Consequence Management: Propagated Dose Uncertainty in ICRP 66 Human Respiratory Tract Model

Reference inhalation dose models rely on deterministic biokinetics and reference computational phantoms, limiting their applicability to the variability present in population-specific exposures encountered in emergency response scenarios. Here, this study introduces REDCAL, a Python-based computational framework developed to propagate uncertainty in inhalation dose coefficients using the International Commission on Radiological Protection (ICRP) Publication 66 Human Respiratory Tract Model. REDCAL integrates ICRP deposition and clearance models, systemic biokinetics, and governing physics principles, and leverages Sandia National Laboratories’ Dakota toolkit for uncertainty quantification via Latin Hypercube Sampling. REDCAL was validated against DCAL, with biokinetic retention results differing by less than 1% and effective dose coefficients by less than 2% across all tested radionuclides. Stochastic sampling introduced variability in dose coefficients, with geometric standard deviations (GSD) in committed effective dose coefficients (CEDC) ranging from 1.0 to 1.5, based on lognormal distribution fits. Analysis demonstrated that variations in the activity median aerodynamic diameter (AMAD) notably influenced the computed CEDC values. Smaller particles (<1 µm) increased doses by 20–30% due to deeper lung deposition and prolonged retention for alpha emitting radionuclides, such as 241 Am and 239 Pu. Radionuclides with fast clearance, such as 133 I, demonstrated a dose reduction exceeding 50%, as AMAD increased beyond 5 µm due to upper airway deposition and rapid mucociliary clearance. The greatest GSD among the radionuclides reported in this study was for 241 Am. In most cases, the largest GSDs in the CEDC were associated with larger particle sizes, an expected outcome, as ICRP Publication 66 defines GSD in particle size as a function of AMAD, resulting in an extended tail of the lognormal distribution. The findings support improved inhalation dose assessments and enhance consequence management strategies for the U.S. Federal Radiological Monitoring and Assessment Center by quantifying uncertainty in dose coefficients and strengthening decision-making for emergency response scenarios.

Biokinetic Modeling↗
DOE OSTI2023

Deep Learning with Physics Priors as Generalized Regularizers

In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method to incorporate these approximate models as physics priors in modeling, to prevent overfitting and enhancing the generalization capabilities of the trained models. Utilizing the structural risk minimization (SRM) inductive principle pioneered by Vapnik, this approach structures the physics priors into generalized regularizers. The experimental results demonstrate that our method achieves up to two orders of magnitude of improvement in testing accuracy.

Liu, Frank↗
DOE OSTI2021

Decision-Making Under Uncertainty for a Digital Thread-Enabled Design Process

Abstract Digital thread is a data-driven architecture that links together information from all stages of the product lifecycle. Despite increasing application in manufacturing, maintenance/operations, and design related tasks, a principled formulation of analyzing the decision-making problem under uncertainty for the digital thread remains absent. The contribution of this article is to present a formulation using Bayesian statistics and decision theory. First, we address how uncertainty propagates in the product lifecycle and how the digital thread evolves based on the decisions we make and the data we collect. By using these mechanics, we explore designing over multiple product generations or iterations and provide an algorithm to solve the underlying multistage decision problem. We illustrate our method on an example structural design problem where our method can quantify and optimize different types and sequences of decisions, ranging from experimentation, manufacturing, and sensor placement/selection, to minimize total accrued costs.

Engineering↗
DOE OSTI2020

Analytic marginalization of N(z) uncertainties in tomographic galaxy surveys

In this paper, we present a new method to marginalize over uncertainties in redshift distributions, N(z), within tomographic cosmological analyses applicable to current and upcoming photometric galaxy surveys. We allow for arbitrary deviations from the best-guess N(z) governed by a general covariance matrix describing the uncertainty in our knowledge of redshift distributions. In principle, this is marginalization over hundreds or thousands of new parameters describing potential deviations as a function of redshift and tomographic bin. However, by linearly expanding the theory predictions around a fiducial model, this marginalization can be performed analytically, resulting in a modified data covariance matrix that effectively downweights the modes of the data vector that are more sensitive to redshift distribution variations. We showcase this method by applying it to the galaxy clustering measurements from the Hyper Suprime-Cam first data release. We illustrate how to marginalize over sample variance of the calibration sample and a large general systematic uncertainty in photometric estimation methods, and explore the impact of priors imposing smoothness in the redshift distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Neutrino Flavor Model Building and the Origins of Flavor and CP Violation

The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a rand unified theory (GUT), which is a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained ab initio in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters. Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such a framework affords a novel origin of CP violation from group theory due to the intimate connection between physical CP transformation and group theoretical properties of non-Abelian discrete groups. Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated upcoming data from neutrino experiments. Non-Abelian discrete flavor symmetries and their modular variants can result from compactification of a higher-dimensional theory. Pursuit of flavor model building based on such frameworks thus also provides the connection to possible UV completions: in particular, to string theory. We emphasize the importance of constructing models in which the uncertainties of theoretical predictions are smaller than, or at most compatible with, the error bars of measurements in neutrino experiments. While there exist proof-of-principle versions of bottom-up models in which the theoretical uncertainties are under control, it is remarkable that the key ingredients of such constructions were discovered first in top-down model building. We outline how a successful unification of bottom-up and top-down ideas and techniques may guide us towards a new era of precision flavor model building in which future experimental results can give us crucial insights into the UV completion of the SM.

Almumin, Yahya (ORCID:0000000196396772)↗
DOE OSTI2021

Constraints on Neutrino Oscillation Parameters from Neutrinos and Antineutrinos with Machine Learning

NOvA is a two detector, long baseline neutrino oscillation experiment measuring the oscillations of muon neutrinos from the \numi neutrino beam over a baseline of \SI{810}{km}. The experiment uses four oscillation channels, $\numu \rightarrow \numu$, $\numubar \rightarrow \numubar$, $\numu \rightarrow \nue$, and $\numubar \rightarrow \nuebar$, with a peak neutrino energy of \SI{1.8}{GeV}. This dissertation describes the analysis of these channels using a dataset of $13.6\times10^{20}$ protons on target neutrino beam mode and $12.5\times10^{20}$ protons on target antineutrino beam mode. The analysis makes use of improvements in the treatment of systematic uncertainties and machine learning techniques to reconstruct neutrino interactions. A technique for decorrelating systematic errors using principle component analysis was utilized to reduce and optimize neutrino cross section and beam related uncertainties. The improved machine learning algorithms make use of convolutional ne ural net works for neutrino event classification, particle classification, and instance segmentation. The selection of neutrino signal events utilizing the neutrino event classifier shows an efficiency of 63\% for the selection of electron neutrinos in neutrino beam mode and 75\% for electron antineutrinos in antineutrino beam mode. Using this algorithm, 82 appearing electron neutrino candidates and 33 appearing electron antineutrino candidates were observed with expected backgrounds of 26.8 and 14.0 respectively. In addition, 211 surviving muon neutrino candidates and 105 muon antineutrino candidates were identified with a purity of more than 96\% using the same neutrino event classifier. Fitting these data to the three flavor neutrino oscillation model, using constraints on \thetaonetwo, \thetaonethree, and \dmsqonetwo from solar and reactor neutrino experiments, the oscillation parameters are measured to be $\sintwothree = 0.57^{+0.04}_{-0.03}$, $\dmsqthreetwo = \SI[parse-numbers= false]{+ 2.41\pm0.07 \times 10^{-3}}{eV^2}$, and $\dcp=0.82^{+0.27}_{-0.87}\pi$ with a preference for the normal neutrino mass hierarchy. Leading systematic uncertainties for these measurements come from detector calibration and neutrino interaction models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗