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DOE OSTI2023

BEYONDPLANCK X. Planck Low Frequency Instrument frequency maps with sample-based error propagation

We present Planck Low Frequency Instrument (LFI) frequency sky maps derived within the BEYONDPLANCK framework. This framework draws samples from a global posterior distribution that includes instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δg 0 /g 0 = 5 x 10 -5 , which is nominally 40 times smaller than that reported by Planck 2018. However, we also note that the original Planck 2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB) B-mode experiments aiming at nanokelvin precision.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Analyzing Hardware and Software Common Cause Failures in Digital Instrumentation and Control Systems using Dual Error Propagation Method

This paper develops a methodology for quantifying software common cause failures (CCFs) in digital instrumentation and control (I&C) systems of nuclear power plants. To support the transition of analog I&C systems to digital in nuclear power plants, probabilistic risk assessment (PRA) techniques are used. The hardware components of the I&C systems have reliability databases that can be used in the PRA studies. However, the failure data for redundant software components of the systems is sparse. Failure of components constitutes a CCF, wherein two or more components or systems fail due to a single shared cause and coupling mechanism. This paper proposes a quantification approach that can simultaneously model hardware and software components, incorporate the CCFs of software systems in the models, and bridge the gap between the failure quantification of models and the development of CCF parametric databases. We demonstrate the dual error propagation method (DEPM) by developing I&C systems failure models for a representative digital reactor trip system. The DEPM models are built to simulate the control and data flows within the systems and can accommodate failure states. By expanding DEPM to software CCFs, we generated alpha factor parameter estimates for each of the modeled error propagation mechanisms.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

BeyondPlanck: XII. Cosmological parameter constraints with end-to-end error propagation

We present cosmological parameter constraints estimated using the Bayesian BEYONDPLANCK analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data onto final cosmological parameters. As a first demonstration of the method, we analyzed time-ordered Planck LFI observations, combined with selected external data (WMAP 33–61 GHz, Planck HFI DR4 353 and 857 GHz, and Haslam 408 MHz) in the form of pixelized maps that are used to break critical astrophysical degeneracies. Overall, all the results are generally in good agreement with previously reported values from Planck 2018 and WMAP, with the largest relative difference for any parameter amounting about 1σ when considering only temperature multipoles between 30 ≤ ℓ ≤ 600. In cases where there are differences, we note that the BEYONDPLANCK results are generally slightly closer to the high-ℓ HFI-dominated Planck 2018 results than previous analyses, suggesting slightly less tension between low and high multipoles. Using low-ℓ polarization information from LFI and WMAP, we find a best-fit value of τ = 0.066 ± 0.013, which is higher than the low value of τ = 0.052 ± 0.008 derived from Planck 2018 and slightly lower than the value of 0.069 ± 0.011 derived from the joint analysis of official LFI and WMAP products. Most importantly, however, we find that the uncertainty derived in the BEYONDPLANCK processing is about 30 % greater than when analyzing the official products, after taking into account the different sky coverage. We argue that this uncertainty is due to a marginalization over a more complete model of instrumental and astrophysical parameters, which results in more reliable and more rigorously defined uncertainties. We find that about 2000 Monte Carlo samples are required to achieve a robust convergence for a low-resolution cosmic microwave background (CMB) covariance matrix with 225 independent modes, and producing these samples takes about eight weeks on a modest computing cluster with 256 cores.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Understanding and Estimating Error Propagation in Neural Networks for Scientific Data Analysis

Neural networks are increasingly integrated into scientific discovery, where input data reduction and model quantization play a key role in accelerating inference. However, understanding and mitigating the impact of these techniques on output error is critical for ensuring reliable results, particularly in tasks demanding high numerical precision. This paper introduces a comprehensive framework for optimizing neural network inference in scientific computing by combining data reduction and weight quantization while maintaining error-controlled outcomes. We develop theoretical analyses to bound error propagation under these reductions and propose a framework that balances computational performance with error constraints. Evaluation on real-world learning-based combustion simulations and satellite image classification demonstrates that our derived error bounds accurately predict observed errors while enabling significant computational speedup under our framework. This work highlights the potential for further leveraging advancements in modern lossy compression algorithms and hardware accelerators that support lower-precision formats.

He, Weiming [New Jersey Institute of Technology]↗
DOE OSTI2023

BEYONDPLANCK XI. Bayesian CMB analysis with sample-based end-to-end error propagation

We present posterior sample-based cosmic microwave background (CMB) constraints from Planck LFI and WMAP observations as derived through global end-to-end Bayesian processing within the BeyondPlanck framework. We first use these samples to study correlations between CMB, foreground, and instrumental parameters, and we identify a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), which is mitigated through model reduction, masking, and resampling. We compare our posterior-based CMB results with previous Planck products, and find generally good agreement, although with notably higher noise due to our exclusion of HFI data. We find a best-fit CMB dipole amplitude of 3362.7 ± 1.4 µK, in excellent agreement with previous Planck results. The quoted dipole uncertainty is derived directly from the sampled posterior distribution, and does not involve any ad hoc contributions for Planck instrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of ${σ}_{2}^{TT}$ = 229 ± 97 µK 2 , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is an order of magnitude larger than the naive diagonal Fisher uncertainty. Relatedly, we find lower evidence for a possible alignment between the quadrupole and octopole than previously reported due to a much larger scatter in the individual quadrupole coefficients, caused both by marginalizing over a more complete set of systematic effects, but also by our more conservative analysis mask required to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both Planck and WMAP. At the same time, we note that this is the first time the sample-based asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to ℓ ≤ 600, and it now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation, and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Investigating Resilience of Loops in HPC Programs: A Semantic Approach with LLMs

Soft errors have become one of the major concerns for the error resilience of the HPC applications as those errors may cause HPC applications to generate serious outcomes such as silent data corruptions (SDCs). Protecting the applications from soft errors is an essential while challenging task. Among different approaches, obtaining a profound understanding of the resilience proneness of an application is very important to devise efficient error detection and recovery strategies. Given the scale of the HPC applications both in the code size and execution time, there are often cases that the error propagation analysis on such applications would produce a massive volume of unstructured data, which requires a significant amount of efforts, to process and to obtain indicating actions towards error protection. In this paper, we present a control-flow based visual analysis framework to help the users conduct error propagation analysis and identify the critical sections of a program that may have a higher likelihood of leading to erroneous outcomes when affected by the control flow related errors. We also design and implement the scalable visualization framework - ResilienceVis that efficiently and effectively visualizes the affected program states under errors and the propagation traces for an application in a user-friendly manner, and eventually, we combine the analysis and visualization to exhibit the error-proneness of the different sections of applications.

Jiang, Hailong↗
DOE OSTI2023

BEYONDPLANCK II. CMB mapmaking through Gibbs sampling

We present a Gibbs sampling solution to the mapmaking problem for cosmic microwave background (CMB) measurements that builds on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem into two separate steps: noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods and it allows us, for the first time, to bring the destriping baseline length to a single sample. Here, we applied the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them in with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we are able to compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without the need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of the total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction. This methodology thus forms the conceptual basis for the mapmaking algorithm employed in the BEYONDPLANCK framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Multi-phenomenology Yield Characterization

This report serves as the first delivery of a four-year applied science effort to transform and advance the error bounds for the yield estimate of an explosion. Each year’s delivery will be in this form, culminating in the submission of this work for peer review to a scientific journal. Importantly, the yearly progress reports can then also be viewed as expanding drafts working towards a formal journal article submission. For the first tranche of funding, we collaborated with Air Force Technical Applications Center (AFTAC) scientists to identify unclassified real-world data that demonstrate and validate our advanced error propagation methods. Collaboration includes visits to AFTAC and telecons. For this development, we illustrate the fusion of seismic, acoustic, optical, and surface effect signatures from an explosion. The mathematics and code being adapted to this specific application (Williams et al., 2021) involves physics models of multiple sensor signatures. We have also identified related physics models and have integrated them into code. Current methods of underground explosion yield estimation for the Threshold Test Ban Treaty (TTBT) have served the US treaty monitoring mission well for decades. A research objective of the Defense Nuclear Nonproliferation Research and Development (DNN R&D) office of the National Nuclear Security Administration (NNSA) has always been to provide new technical capabilities for monitoring lower thresholds. The general model and error propagation code to be developed in this project is based on significant advances in error modeling and propagation needed to analyze data at lower detection thresholds. The second tranche of funding for this project began on May 1, 2022, and planned work for the second tranche includes: i) completing the integration of physical model code into the general error model framework; this code accommodates a wide range of linear/nonlinear source models, fixed/ random effects, and frequentist/Bayesian analyses (the purpose of which is not to dictate to users how to analyze data, but instead to allow users the maximum flexibility in their work); ii) illustrative application of code to identified data, and; iii) initial planning with AFTAC researchers on delivery of code to the Common Development Environment at AFTAC, and continued writing of the planned final journal article submission (year two of this progress report), with particular emphasis on descriptions of data identified for this effort.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2023

Unraveling the 2021 Central Tennessee flood event using a hierarchical multi-model inundation modeling framework

Flood prediction systems need hierarchical atmospheric, hydrologic, and hydraulic models to predict rainfall, runoff, streamflow, and floodplain inundation. The accuracy of such systems depends on the error propagation through the modeling chain, sensitivity to input data, and choice of models. In this study, we used multiple precipitation forcings (hindcast and forecast) to drive hydrologic and hydrodynamic models to analyze the impacts of various drivers on the estimates of flood inundation depth and extent. We implement this framework to unravel the August 2021 extreme flooding event that occurred in Central Tennessee, USA. We used two radar-based quantitative precipitation estimates (STAGE4 and MRMS) as well as quantitative precipitation forecasts (QPF) from the National Weather Service Weather Prediction Center (WPC) to drive a series of models in the hierarchical framework, including the Variable Infiltration Capacity (VIC) land surface model, the Routing Application for Parallel Computation of Discharge (RAPID) river routing model, and the AutoRoute and TRITON inundation models. An evaluation with observed high-water marks demonstrates that the framework can reasonably simulate flood inundation. Despite the complex error propagation mechanism of the modeling chain, we show that inundation estimates are most sensitive to rainfall estimates. Most notably, QPF significantly underestimates flood magnitudes and inundations leading to unanticipated severe flooding for all stakeholders involved in the event. Finally, we discuss the implications of the hydrodynamic modeling framework for real-time flood forecasting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Diabatic error and propagation of Majorana zero modes in interacting quantum dots systems

Motivated by recent experimental progress in realizing Majorana zero modes (MZMs) using quantum dot systems, we investigate the diabatic errors associated with the movement of those MZMs. The movement is achieved by tuning time-dependent gate potentials applied to individual quantum dots, effectively creating a moving potential wall. To probe the optimized movement of MZMs, we calculate the experimentally accessible time-dependent fidelity and local density-of-states using many-body time-dependent numerical methods. Furthermore, our analysis reveals that an optimal potential wall height is crucial to preserve the well-localized nature of the MZM during its movement. Moreover, we analyze diabatic errors in realistic quantum-dot systems, incorporating the effects of repulsive Coulomb interactions and disorder in both hopping and pairing terms. Additionally, we provide a comparative study of diabatic errors arising from the simultaneous versus sequential tuning of multiple gates during the MZMs movement. Finally, we estimate the timescale required for MZM transfer in a six-quantum-dot system, demonstrating that MZM movement is feasible and can be completed well within the qubit's operational lifetime in practical quantum-dot setups.

Density of states↗
DOE OSTI2024

On the Representativity of Electrode Microstructure Parameters and Their Electrochemical Response for Lithium Ion Batteries

Lithium-ion battery electrochemical models require an accurate description of the electrodes microstructures to be predictive that can be achieved through nanoscale imaging. Such observations are however limited by their field of view (FOV), as they provide only a subset of the whole electrode volume that does not necessarily represent the whole electrode microstructure heterogeneity, and therefore can bias the microstructure analysis. A microstructure scale electrochemical model was used to investigate lithium plating onset, material non-uniform utilization, and in-plane heterogeneities for an NMC-graphite full cell. To evaluate the representativeness, and thus relevance, of these model predictions, a coupled representativity analysis has been performed on the microstructure parameters and, in a novel way, on the full cell electrochemical response. Electrode microstructure parameters representativeness has been first quantified using the representative volume element (RVE) methodology. The RVE major flaw is that ultimately it can only conclude if a FOV contains representative subvolumes of the FOV, but not if the FOV itself is representative of the electrode volume. Analysis can conclude negatively ('FOV is not representative'), but not positively ('FOV is representative'). One major contribution of this work was to quantify the convergence of the RVE size with the FOV, to actually investigate the FOV representativeness and thus partly remedy this intrinsic limitation. The analysis determined that performing a standard RVE calculation, without exploring its FOV convergence, is likely to strongly underestimate the actual RVE size. The new RVE methodology has been automated in the NREL open-source Microstructure Analysis Toolbox (MATBOX) and is available to the battery community. Representativeness of microstructure parameters is however only an intermediate step, as the end-results of an electrochemical model are performances predictions. Indeed, what is the practical consequence of a given deviation for a microstructure parameter? The microstructure parameter deviation propagations to the 3D microstructure scale electrochemical response have been then quantified for different charge rates. This defines a threshold for the microstructure parameters FOV for a desired maximum deviation of the electrochemical response. Such deviation propagation analysis is analogous to error propagation analysis and is necessary to determine the relevance of microstructure scale model predictions for macroscale predictions. Electrochemical model shows cell representative section areas are increasing with C-rate, due to higher in-plane heterogeneities, indicating larger FOVs are required specifically for fast charge modeling. Therefore, we introduced the novel concept of electrochemical RVE (eRVE) that is a function of the operating conditions (thus defined as a dynamic RVE), with an increasing dependence with the C-rate. Representativity analysis of the investigated cell determined a FOV of 144.4 x 54.4 m2 is large enough to establish a convergence on the representative section areas for low to intermediate C-rate (=2.5C), but not large enough to conclude for higher rates. This work aims to emphasize the importance of representativity analysis for LIB electrode microstructures, as it is required to estimate the error, and thus the relevance, of microstructure parameters intended to be used in macroscale models. The methodology and results can help researchers to select the relevant imaging and associated FOV required to provide accurate enough microstructure parameters.

ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

A New Modeling Approach for a Priori Uncertainties of Laser Tracker Angle Measurements

Methods for modeling the uncertainty in laser tracker angle measurements vary within the metrology industry, leading to confusion and questionable stochastic modeling for survey network adjustments and error propagation analysis. Interpreting the published laser tracker manufacturer performance specifications to determine an a priori sigma value for weighting azimuth and zenith angle measurements can be confusing and has led to differing implementations. Furthermore, this paper proposes a unique way to model survey network a priori laser tracker angular uncertainties based on laser tracker manufacturers’ published maximum permissible error (MPE) values referenced to current standards for weighting survey network measurements. This paper’s proposed model takes into account the disparate effects that pointing errors, target centering errors, and leveling errors have on azimuth and zenith angular uncertainties for measurements with steep sightings and at near ranges.

42 ENGINEERING↗
DOE OSTI2023

Evaluation of dual-weighted residual and machine learning error estimation for projection-based reduced-order models of steady partial differential equations

Projection-based reduced-order models (pROMs) show great promise as a means to accelerate many-query applications such as forward error propagation, solving inverse problems, and design optimization. In order to deploy pROMs in the context of high-consequence decision making, accurate error estimates are required to determine the region(s) of applicability in the parameter space. The following paper considers the dual-weighted residual (DWR) error estimate for pROMs and compares it to another promising pROM error estimate, machine learned error models (MLEM). Here, we show how DWR can be applied to ROMs and then evaluate DWR on two partial differential equations (PDEs): a two-dimensional linear convection–reaction–diffusion equation, and a three-dimensional static hyper-elastic beam. It is shown that DWR is able to estimate errors for pROMs extrapolating outside of their training set while MLEM is best suited for pROMs used to interpolate within the pROM training set.

42 ENGINEERING↗
DOE OSTI2025

Logical error rates for the surface code under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions

With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical errors in plausible hardware implementations of quantum error-correcting codes. Detailed error modeling of computational instructions on particular FTQC architectures will enable the better prediction of error propagation in FT-encoded quantum circuits while revealing where greater attention is needed in hardware design. In this work, we consider logical error rates for the surface code implemented on a hypothetical grid-based trapped-ion quantum charge-coupled device architecture. Specifically, we construct logical channels for the idling surface code and examine its diamond error under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions. We include the coherent dephasing noise that is known to accumulate during physical qubit idling and transport in these systems, determining idling and transport durations using the time-resolved output of an open-source trapped-ion surface code compiler. To estimate expectation values of logical Pauli observables following hardware circuits containing non-Clifford sources of noise, we utilize a Monte Carlo technique to sample from an underlying quasiprobability distribution of Clifford circuits that we independently simulate in a phase-sensitive fashion. We verify error suppression up to code distance 𝑑 = 11 at coherent dephasing rates near and below those of current-generation trapped-ion quantum computers and find that logical error rates align with those of analogous fully stochastic simulations in this regime. Exploring higher dephasing rates at 𝑑 = 3−5, we find evidence for growing coherent rotations about all three logical Pauli axes, increased diagonal logical error process matrix elements relative to those of stochastic simulations, and a reduced dephasing rate threshold. Overall, our work paves a way toward realistic hardware emulation of small fault-tolerant quantum processes, e.g., members of an FTQC instruction set.

Quantum benchmarking↗
DOE OSTI2023

Cold neutron-deuteron capture and Wigner-SU(4) symmetry

We calculate the cold neutron-deuteron (nd) capture cross section,σ nd to next-to-next-to leading order (NNLO) using the model-independent approach of pionless effective-field theory [EFT(π)]. At leading order we find σ nd = 0.314 ± 0.217 mb, while the experimental result is 0.508(15) mb for a laboratory neutron velocity of 2200 m/s. At next-to-leading-order (NLO), we show that σnd is sensitive to the low-energy constant (LEC) $L$$^{(0)}_{1}$ of the two-nucleon isovector current appearing at NLO. A fit of $L$$^{(0)}_{1}$ at NLO to the triton magnetic moment yields a NLO prediction of σ nd = 0.393 ± 0.164 mb, where the error comes from propagating the error from the $L$$^{(0)}_{1}$ fit. At NNLO, we find that a new three-nucleon magnetic moment counterterm is required for renormalization-group invariance of both σnd and the triton magnetic moment. Fitting the NNLO correction to $L$$^{(0)}_{1}$ (denoted $L$$^{(1)}_{1}$) to cold neutron-proton capture (σnp) yields a NNLO prediction of σ nd = 0.447 ± 0.130 mb, where the error comes from propagating the error from the $L$$^{(1)}_{1}$ fit. We also study different fittings of $L$$^{(0)}_{1}$ and $L$$^{(1)}_{1}$ to σ np , σ nd , and/or the triton magnetic moment. For example, fitting $L$$^{(0)}_{1}$ simultaneously to σ np , σ nd , and the triton magnetic moment at NLO, and fitting $L$$^{(1)}_{1}$ simultaneously to σ np and σnd at NNLO, yields σ nd = 0.480 ± 0.114 mb and 0.511 ± 0.042 mb, respectively, where errors are naively estimated from EFT(π) power counting. Additionally, we discuss how Wigner SU(4) symmetry may alter the naive EFT(π) expansion of σ nd .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Propagation of Noise Uncertainty Through Virtual Strain Gauge Formulations for 2D Digital Image Correlation

The effect of displacement uncertainty is examined on 2-dimensional strain, calculated using linear surfaces fitted to the displacement field. A classical engineering error propagation method is used to calculate uncertainty in Green-Lagrangian strain calculations. The derived uncertainty is compared to a Monte Carlo simulation and discrepancies under 2% are seen between these two methods. The effect of virtual strain gauge size, displacement uncertainty, and boundaries on the region of interest on the strain uncertainty are considered. Here, an exponential decay relationship is observed between strain uncertainty and virtual strain gauge size, while a linear relationship is seen between strain and displacement uncertainty. For boundaries in the region of interest, strain uncertainty is affected by the reduced number of points available to perform the regression.

42 ENGINEERING↗