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DOE OSTI2021

Mitigating baryonic effects with a theoretical error covariance

ABSTRACT One of the primary sources of uncertainties in modelling the cosmic-shear power spectrum on small scales is the effect of baryonic physics. Accurate cosmology for stage-IV surveys requires knowledge of the matter power spectrum deep in the non-linear regime at the per cent level. Therefore, it is important to develop reliable mitigation techniques to take into account baryonic uncertainties if information from small scales is to be considered in the cosmological analysis. In this work, we develop a new mitigation method for dealing with baryonic physics for the case of the shear angular power spectrum. The method is based on an augmented covariance matrix that incorporates baryonic uncertainties informed by hydrodynamical simulations. We use the results from 13 hydrodynamical simulations and the residual errors arising from a fit to a ΛCDM model using the extended halo model code HMCode to account for baryonic physics. These residual errors are used to model a so-called theoretical error covariance matrix that is added to the original covariance matrix. In order to assess the performance of the method, we use the 2D tomographic shear from four hydrodynamical simulations that have different extremes of baryonic parameters as mock data and run a likelihood analysis comparing the residual bias on Ωm and σ8 of our method and the HMCode for an LSST-like survey. We use different modelling of the theoretical error covariance matrix to test the robustness of the method. We show that it is possible to reduce the bias in the determination of the tested cosmological parameters at the price of a modest decrease in the precision.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Bias on tensor-to-scalar ratio inference with estimated covariance matrices

ABSTRACT We investigate simulation-based bandpower covariance matrices commonly used in cosmological parameter inferences such as the estimation of the tensor-to-scalar ratio r. We find that upper limits on r can be biased low by tens of per cent. The underestimation of the upper limit is most severe when the number of simulation realizations is similar to the number of observables. Convergence of the covariance-matrix estimation can require a number of simulations an order of magnitude larger than the number of observables, which could mean $\mathcal {O}(10\ 000)$ simulations. This is found to be caused by an additional scatter in the posterior probability of r due to Monte Carlo noise in the estimated bandpower covariance matrix, in particular, by spurious non-zero off-diagonal elements. We show that matrix conditioning can be a viable mitigation strategy in the case that legitimate covariance assumptions can be made.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Evaluating quenching in cosmological simulations of galaxy formation with spectral covariance in the optical window

ABSTRACT Cosmological hydrodynamical simulations provide valuable insights on galaxy evolution when coupled with observational data. Comparisons with real galaxies are typically performed via scaling relations of the observables. Here, we follow an alternative approach based on the spectral covariance in a model-independent way. We build upon previous work by Sharbaf et al. that studied the covariance of high-quality SDSS (Sloan Digital Sky Survey) continuum-subtracted spectra in a relatively narrow range of velocity dispersion ($\sigma \in [100,150]$ km s$^{-1}$). Here, the same analysis is applied to synthetic data from the eagle and IllustrisTNG100 simulations, to assess the ability of these runs to mimic real galaxies. The real and simulated spectra are consistent regarding spectral covariance, although with subtle differences that can inform the implementation of subgrid physics. Spectral fitting done a posteriori on stacks segregated with respect to latent space reveals that the first principal component (PC1) is predominantly influenced by the stellar age distribution, with an underlying age–metallicity degeneracy. Good agreement is found regarding star formation prescriptions but there is disagreement with active galactic nucleus (AGN) feedback, that also affects the subset of quiescent galaxies. We show a substantial difference in the implementation of the AGN subgrid prescriptions, regarding central black hole seeding, that could lead to the mismatch. Differences are manifest between these two simulations in the star formation histories stacked with respect to latent space. We emphasize that this methodology only relies on the spectral covariance to assess whether simulations provide a true representation of galaxy formation.

Sharbaf, Z. (ORCID:0009000450545946)↗
DOE OSTI2022

Analytic Gaussian covariance matrices for galaxy N-point correlation functions

Here, we derive analytic covariance matrices for the N-point correlation functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary N and projected onto the isotropic basis functions given by spherical harmonics and Wigner 3j symbols. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a nonuniform window function. Our result is recently shown to facilitate NPCF analysis on a realistic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Whisper Use of Nuclear Data Covariances [Slides]

Whisper is statistical analysis code using sensitivity/uncertainty-based methods to determine baseline upper subcritical limit (USL) for nuclear criticality safety. Features of Whisper 1.1 include: GLLS method implemented to compute adjusted covariance based on current benchmark suite (1,100+ ICSBEP models), BLO “low-fidelity” covariance data used (44 energy groups), adjusted covariance is pre-computed and saved, and adjusted cross sections are NOT computed. Potential future efforts include: an extension to include angular distributions in benchmark selection and in GLLS adjustment, a move toward more modern covariance data (ENDF/B-VIII.0) and different group structure, and compute and store adjusted cross sections (trivial).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

From Quantum Time to Manifestly Covariant QFT: On the Need for a Quantum-Action-Based Quantization

In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather than being hidden as in the standard canonical formulation. We address this question by proposing a second-quantized approach in which the elementary particle is the QT particle itself, leading naturally to the notion of spacetime field algebras and of quantum action. We show, however, that a naive many-body construction runs into inconsistencies. To pinpoint their origin we introduce a classical counterpart of the second-quantized formalism, spacetime classical mechanics (SCM), and prove a no-go theorem: Dirac quantization of SCM collapses back to standard QFT and therefore hides covariance. We circumvent this problem by presenting a quantum-action-based quantization that yields a spacetime version of quantum mechanics (SQM), making covariance manifest for (interacting) QFTs. Finally, we show that this resolution is tied to a genuine spacetime generalization of the notion of a quantum state, required by causality and closely connected to recent “states over time” proposals and, in dS/CFT–motivated settings, to microscopic notions of timelike entanglement and emergent time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Wake-Resolving Acoustic Tomography: Advances through Numerical Covariance Methods

Acoustic tomography offers path-integrated measurements of atmospheric velocity and temperature fluctuations with high spatial resolution. Classical implementations of time-dependent stochastic inversion rely on homogeneous, isotropic covariance models that are poorly suited to the anisotropic structure of wind turbine wakes. By directly estimating heterogeneous covariances from large-eddy simulations (LESs) into the time-dependent stochastic inversion operator, we relax implicit assumptions in the analytical models used historically. Retrievals using these LES-informed models improve agreement with true fields in variance, turbulent kinetic energy, and spectral content compared to analytical and precursor-based covariance models. The results indicate that LES-informed covariance models can enhance the accuracy of acoustic tomography retrievals in complex, anisotropic flows such as wind turbine wakes in some cases and highlight instances where analytical models still offer competitive performance, despite their simplifying assumptions.

17 WIND ENERGY↗
DOE OSTI2025

Better practices for inferring ecosystem water use strategy from eddy covariance data

Eddy covariance data are critical for inferring ecosystem water use strategies. Yet, such inferences are sensitive to a range of assumptions applied across studies, hindering our understanding of water use strategies within and across eddy covariance sites. A recent analysis across 151 FLUXNET2015 and AmeriFlux-FLUXNET datasets found that poor model performance was the key driver of non-robust inferences of ecosystem water use strategies. Here, we leverage this previous analysis to (i) identify the specific assumptions that improve inference model performance across most sites, (ii) explain the mechanisms behind the performance improvements, and (iii) check whether better performance improves water use inference. We find that the common practice of fitting a model to canopy conductance (G c ) derived from the evapotranspiration (ET) observations, rather than to observed ET itself, artificially amplifies data errors and degrades the model performance. Next, accounting for vegetation dynamics by applying a growing season filter or incorporating satellite LAI data improves performance, but the former practice may remove soil water stress periods. Lastly, using the leaf-to-air vapor pressure deficit (VPD l ) derived from ET observations as a model input may artificially inflate performance. Based on these results, we recommend selecting observed ET (rather than derived G c ) as the response variable, carefully accounting for vegetation dynamics, and avoiding derived VPD l as a model input; these best practices improve model performance by c. 20% and robustness by c. 80% across all eddy covariance sites. Nevertheless, the performance improvements do not always correspond to more robust inference of water use strategies, as model parameter selection and surface energy budget closure corrections still strongly influence the ecosystem water use parameter estimation in a site-specific manner.

AmeriFlux↗
DOE OSTI2023

Upscaling Wetland Methane Emissions From the FLUXNET–CH4 Eddy Covariance Network (UpCH4 v1.0): Model Development, Network Assessment, and Budget Comparison

Wetlands are responsible for 20%–31% of global methane (CH 4 ) emissions and account for a large source of uncertainty in the global CH 4 budget. Data-driven upscaling of CH 4 fluxes from eddy covariance measurements can provide new and independent bottom-up estimates of wetland CH 4 emissions. Here, we develop a six-predictor random forest upscaling model (UpCH4), trained on 119 site-years of eddy covariance CH 4 flux data from 43 freshwater wetland sites in the FLUXNET-CH4 Community Product. Network patterns in site-level annual means and mean seasonal cycles of CH 4 fluxes were reproduced accurately in tundra, boreal, and temperate regions (Nash-Sutcliffe Efficiency ~0.52–0.63 and 0.53). UpCH4 estimated annual global wetland CH 4 emissions of 146 ± 43 TgCH 4 y –1 for 2001–2018 which agrees closely with current bottom-up land surface models (102–181 TgCH 4 y –1 ) and overlaps with top-down atmospheric inversion models (155–200 TgCH 4 y –1 ). However, UpCH4 diverged from both types of models in the spatial pattern and seasonal dynamics of tropical wetland emissions. We conclude that upscaling of eddy covariance CH 4 fluxes has the potential to produce realistic extra-tropical wetland CH 4 emissions estimates which will improve with more flux data. To reduce uncertainty in upscaled estimates, researchers could prioritize new wetland flux sites along humid-to-arid tropical climate gradients, from major rainforest basins (Congo, Amazon, and SE Asia), into monsoon (Bangladesh and India) and savannah regions (African Sahel) and be paired with improved knowledge of wetland extent seasonal dynamics in these regions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Distinguishing the XUV-induced Coulomb explosion dynamics of iodobenzene using covariance analysis

The primary and secondary fragmentation dynamics of iodobenzene following its ionization at 120 eV were determined using three-dimensional velocity map imaging and covariance analysis. Site-selective iodine 4d ionization was used to populate a range of excited polycationic parent states, which primarily broke apart at the carbon-iodine bond to produce I+ with phenyl or phenyl-like cations (C n H x + or C n H, with n = 1 – 6 and x = 1 – 5). The molecular products were produced with varying degrees of internal excitation and dehydrogenation, leading to stable and unstable outcomes. This further allowed the secondary dynamics of C 6 H x 2+ intermediates to be distinguished using native-frame covariance analysis, which isolated these processes in their own centre-of-mass reference frames. Furthermore, the mass resolution of the imaging mass spectrometer used for these measurements enabled the primary and secondary reaction channels to be specified at the level of individual hydrogen atoms, demonstrating the ability of covariance analysis to comprehensively measure the competing fragmentation channels of aryl cations, including those involving intermediate steps.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Updates from the Covariance Session Committee [Slides]

The CSEWG covariance session template paper was submitted on June 8, 2021 to journal. CSEWG will not publish adjusted VIII.1, but there is interest in adjustment results from the community. Other focus points for the release for VIII.1 include stringent testing of covariances before their release and missing covariances.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

Nuclear Criticality Safety Integral Experiment Covariance Determination

Integral benchmarks for criticality safety and nuclear data validation require expensive uncertainty quantification studies. Commonly, the uncertainty quantification ignores correlations between experiments that share components. Experiments such as the TEX (Thermal/Epithermal eXperiments) campaigns consist of many shared parts between experiments, such as fuel, which creates a strong correlation in their errors. While these correlations are known to exist, they are often not estimated due to the complexity of such calculations. This paper describes a software package that uses an intuitive method of determining the covariance for each of the experimental components, providing a correlation matrix for each family of parts across the multiple cases examined within a benchmark. The code uses the TEX-HEU campaign as a proof of concept, and we show that the correlations can be calculated with information commonly found in ICSBEP (International Criticality Safety Benchmark Evaluation Project) benchmarks. The estimated covariances are used in χ 2 trending studies to evaluate their impact on nuclear data validation. The covariance determination code can be easily integrated into current benchmark evaluations as well as reevaluating legacy benchmark uncertainties. Uncertainty correlation calculations should become the baseline for criticality safety integral experiment benchmarks and can now be easily calculated with the described software package.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches

Abstract In complex systems with multiple variables monitored at high‐frequency, variables are not only temporally autocorrelated, but they may also be nonlinearly related or exhibit nonstationarity as the inputs or operation changes. One approach to handling such variables is to detrend them prior to monitoring and then apply control charts that assume independence and stationarity to the residuals. Monitoring controlled systems is even more challenging because the control strategy seeks to maintain variables at prespecified mean levels, and to compensate, correlations among variables may change, making monitoring the covariance essential. In this paper, a vector autoregressive model (VAR) is compared with a multivariate random forest (MRF) and a neural network (NN) for detrending multivariate time series prior to monitoring the covariance of the residuals using a multivariate exponentially weighted moving average (MEWMA) control chart. Machine learning models have an advantage when the data's structure is unknown or may change. We design a novel simulation study with nonlinear, nonstationary, and autocorrelated data to compare the different detrending models and subsequent covariance monitoring. The machine learning models have superior performance for nonlinear and strongly autocorrelated data and similar performance for linear data. An illustration with data from a reverse osmosis process is given.

Weix, Derek↗
DOE OSTI2021

Helicity, spin, and infra-zilch of light: A Lorentz covariant formulation

Highlights: • Spin and orbital parts of angular momentum. • The helicity tensor contains the helicity, spin and infra-zilch currents. • The helicity tensor is a Noether current for a duality-symmetric action. • Symmetry generator for the helicity tensor. • The helicity tensor is conserved in Lorenz gauge. In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced in Maxwell theory. The conservation of the helicity tensor expresses the conservation laws contained in the helicity array, introduced by Cameron et al. (2012), including helicity, spin, as well as the spin-flux or infra-zilch. The Lorentz covariance of the helicity tensor is in contrast to previous formulations of the helicity hierarchy of conservation laws, which required the non-Lorentz covariant transverse gauge. The helicity tensor is shown to arise as a Noether current for a variational symmetry of a duality-symmetric Lagrangian for Maxwell theory. This symmetry transformation generalizes the duality symmetry and includes the symmetry underlying the conservation of the spin part of the angular momentum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Two-Dimensional Projected-Momentum Covariance Mapping for Coulomb Explosion Imaging

We introduce projected-momentum covariance mapping, an extension of recoil-frame covariance mapping for 2D ion imaging studies. By considering the two-dimensional projection of the ion momenta as recorded by the detector, one opens the door to a complex suite of analysis tools adapted from three-dimensional momentum imaging studies. This includes the use of different frames of reference to unravel the dynamics of fragmentation and the application of fragment momentum constraints to isolate specific fragmentation channels. The technique is demonstrated on data from a two-dimensional ion imaging study of the Coulomb explosion of the cis and trans isomers of 1,2-dichloroethene, following strong-field ionization by an intense near-infrared femtosecond laser pulse. Classical simulations are used to guide the interpretation of projected-momentum covariance maps. The results offer a detailed insight into the distinct Coulomb explosion dynamics for this pair of isomers and lay the groundwork for future time-resolved studies of photoisomerization dynamics in this molecular system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Semi-analytical covariance matrices for two-point correlation function for DESI 2024 data

We present an optimized way of producing the fast semi-analytical covariance matrices for the Legendre moments of the two-point correlation function, taking into account survey geometry and mimicking the non-Gaussian effects. We validate the approach on simulated (mock) catalogs for different galaxy types, representative of the Dark Energy Spectroscopic Instrument (DESI) Data Release 1, used in 2024 analyses. We find only a few percent differences between the mock sample covariance matrix and our results, which can be expected given the approximate nature of the mocks, although we do identify discrepancies between the shot-noise properties of the DESI fiber assignment algorithm and the faster approximation (emulator) used in the mocks. Importantly, we find a close agreement (≤ 8% relative differences) in the projected errorbars for distance scale parameters for the baryon acoustic oscillation measurements. This confirms our method as an attractive alternative to simulation-based covariance matrices, especially for non-standard models or galaxy sample selections, making it particularly relevant to the broad current and future analyses of DESI data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Covariance matrices for variance-suppressed simulations

ABSTRACT Cosmological N-body simulations provide numerical predictions of the structure of the Universe against which to compare data from ongoing and future surveys, but the growing volume of the Universe mapped by surveys requires correspondingly lower statistical uncertainties in simulations, usually achieved by increasing simulation sizes at the expense of computational power. It was recently proposed to reduce simulation variance without incurring additional computational costs by adopting fixed-amplitude initial conditions. This method has been demonstrated not to introduce bias in various statistics, including the two-point statistics of galaxy samples typically used for extracting cosmological parameters from galaxy redshift survey data, but requires us to revisit current methods for estimating covariance matrices of clustering statistics for simulations. In this work, we find that it is not trivial to construct covariance matrices analytically for fixed-amplitude simulations, but we demonstrate that ezmock (Effective Zel’dovich approximation mock catalogue), the most efficient method for constructing mock catalogues with accurate two- and three-point statistics, provides reasonable covariance matrix estimates for such simulations. We further examine how the variance suppression obtained by amplitude-fixing depends on three-point clustering, small-scale clustering, and galaxy bias, and propose intuitive explanations for the effects we observe based on the ezmock bias model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Kronecker-structured covariance models for multiway data

Many applications produce multiway data of exceedingly high dimension. Modeling such multi-way data is important in multichannel signal and video processing where sensors produce multi-indexed data, e.g. over spatial, frequency, and temporal dimensions. We will address the challenges of covariance representation of multiway data and review some of the progress in statistical modeling of multiway covariance over the past two decades, focusing on tensor-valued covariance models and their inference. We will illustrate through a space weather application: predicting the evolution of solar active regions over time.

97 MATHEMATICS AND COMPUTING↗