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At least 91 records · Page 5

Earth System Reanalysis in Support of Climate Model Improvements

Recent climate model developments, established through increased model resolution, have led to substantial improvements in model simulations of the time-evolving, coupled Earth system and its subcomponents. However, regardless of resolution, climate models will always produce climate features and variability that differ from the real world and will be prone to biases. This is due to many remaining uncertainties, such as in parametric and structural model uncertainty, in the initial conditions prescribed, and in the prescribed (scenario) forcing which varies on decadal to centennial timescales. Further model improvements are expected to arise specifically from improved representation of physical processes realized through model-data fusion. This will create an unprecedented opportunity to better exploit a large array of Earth observations, from in situ measurements to weather radars and satellite observations, as the resolved scales of the models approach those of the observations. For this, climate DA will be the central tool to bring models and observations into consistency, by improving initial conditions, inferring uncertain model parameters and structure, and quantifying uncertainty. Generally, there will be advantages and complementarities of adjoint-based smoother approaches, ensemble-based filter approaches, or new ML-inspired approaches. Yet, the ever-increasing model resolution will present growing challenges arising from computational cost, calling for new ways of performing data assimilation and model optimization. Using the complementarity in a hybrid approach, blending tools and concepts from variational, ensemble and ML methods might be what is required in the future. In this context ML could be important to handle non-linear responses, and to better approximate non-Gaussian distributions.

54 ENVIRONMENTAL SCIENCES↗

Constraining the Dense Matter Equation of State with Joint Analysis of NICER and LIGO/Virgo Measurements

The Neutron Star Interior Composition Explorer collaboration recently published a joint estimate of the mass and the radius of PSR J0030+0451, derived via X-ray pulse-profile modeling. Raaijmakers et al. explored the implications of this measurement for the dense matter equation of state (EOS) using two parameterizations of the high-density EOS: a piecewise-polytropic model, and a model based on the speed of sound in neutron stars (NSs). In this work we obtain further constraints on the EOS following this approach, but we also include information about the tidal deformability of NSs from the gravitational wave signal of the compact binary merger GW170817. Further, we compare the constraints on the EOS to those set by the recent measurement of a 2.14 Me pulsar, included as a likelihood function approximated by a Gaussian, and find a small increase in information gain. To show the flexibility of our method, we also explore the possibility that GW170817 was a NS–black hole merger, which yields weaker constraints on the EOS.

79 ASTRONOMY AND ASTROPHYSICS↗

Bayesian Monte Carlo Evaluation Framework for Imperfect Data and Models [Abstract]

Nuclear data evaluation methods conventionally make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate for minimization of a cost function (even for non-linear models); and that both the model (of, e.g., neutron cross section) and experimental data (including their covariance data) are perfect. These assumptions are inherent to the well-known generalized linear least squares (GLLS) minimization method commonly used for evaluations of resolved resonance region (RRR) neutron cross sections. However, these assumptions are often not justified due to the presence of non-normal PDFs, non-linear models (e.g. R -matrix formalism), and inherent imperfections in data and models (e.g. discrepant data sets, discrepancies between the previous evaluation and newly measured data, or imperfect covariance data). We remove the said assumptions in a mathematical framework of Bayes’ theorem, and implement it using the Metropolis-Hastings Monte Carlo method. Parameters of a new kind are introduced to parameterize inherent imperfections, e.g. , any discrepancies between the theoretical model and measured data. These new parameters enable evaluators to quantify their expert judgement about any discrepancies or imperfections in a reproducible manner. We demonstrate the framework with an ongoing evaluation of 233 U in the eV region using the ENDF-B/VIII library and transmission data measured by Guber, et al. , and compare the posterior parameters to those obtained by conventional evaluation methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Physics↗

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Data Analysis, Statistics and Probability (physics↗

Dark Energy Survey Year 3 results: Measurement of the baryon acoustic oscillations with three-dimensional clustering

The three-dimensional correlation function offers an effective way to summarize the correlation of the large-scale structure even for imaging galaxy surveys. We have applied the projected three-dimensional correlation function, ξ p to measure the baryonic acoustic oscillations (BAO) scale on the first-three years Dark Energy Survey data. The sample consists of about 7 million galaxies in the redshift range 0.6< z p < 1.1 over a footprint of 4108 deg 2 . Our theory modeling includes the impact of realistic true redshift distributions beyond Gaussian photo-z approximation. ξ p is obtained by projecting the three-dimensional correlation to the transverse direction. To increase the signal-to-noise of the measurements, we have considered a Gaussian stacking window function in place of the commonly used top-hat. ξ p is sensitive to D M (z eff )/r s , the ratio between the comoving angular diameter distance and the sound horizon. Using the full sample, D M (z eff )/r s is constrained to be19.00 ± 0.67 (top-hat) and 19.15 ± 0.58 (Gaussian) at z eff = 0.835. The constraint is weaker than the angular correlation w constraint 18.84 ± 0.50), and we trace this to the fact that the BAO signals are heterogeneous across redshift. While ξ p responds to the heterogeneous signals by enlarging the error bar, w can still give a tight bound on D M s in this case. When a homogeneous BAO-signal subsample in the range 0.7 < z p <1.0 (z eff = 0.845) is considered, ξp yields 19.80 ± 0.67 (top-hat) and 19.84 ± 0.53 (Gaussian). The latter is mildly stronger than the w constraint (19.86 ± 0.55). We find that the ξ p results are more sensitive to photo-z because ξ p keeps the three-dimensional clustering information causing it to be more prone to photo-z noise. The Gaussian window gives more robust results than the top-hat as the former is designed to suppress the low signal modes. ξ p and the angular statistics such as w have their own pros and cons, and they serve an important crosscheck with each other.

79 ASTRONOMY AND ASTROPHYSICS↗

Clustering with general photo- z uncertainties: application to Baryon Acoustic Oscillations

ABSTRACT Photometric data can be analysed using the 3D correlation function ξp to extract cosmological information via e.g. measurement of the Baryon Acoustic Oscillations (BAO). Previous studies modeled ξp assuming a Gaussian photo-z approximation. In this work we improve the modeling by incorporating realistic photo-z distribution. We show that the position of the BAO scale in ξp is determined by the photo-z distribution and the Jacobian of the transformation. The latter diverges at the transverse scale of the separation s⊥, and it explains why ξp traces the underlying correlation function at s⊥, rather than s, when the photo-z uncertainty σz/(1+ z) ≳ 0.02. We also obtain the Gaussian covariance for ξp. Due to photo-z mixing, the covariance of ξp shows strong off-diagonal elements. The high correlation of the data causes some issues to the data fitting. None the less, we find that either it can be solved by suppressing the largest eigenvalues of the covariance or it is not directly related to the BAO. We test our BAO fitting pipeline using a set of mock catalogs. The data set is dedicated for Dark Energy Survey Year 3 (DES Y3) BAO analyses and includes realistic photo-z distributions. The theory template is in good agreement with mock measurement. Based on the DES Y3 mocks, ξp statistic is forecast to constrain the BAO shift parameter α to be 1.001 ± 0.023, which is well consistent with the corresponding constraint derived from the angular correlation function measurements. Thus, ξp offers a competitive alternative for the photometric data analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

Nonlinear sparse Bayesian learning for physics-based models

This paper addresses the issue of overfitting while calibrating unknown parameters of over-parameterized physics-based models with noisy and incomplete observations. Here, a semi-analytical Bayesian framework of nonlinear sparse Bayesian learning (NSBL) is proposed to identify sparsity among model parameters during Bayesian inversion. NSBL offers significant advantages over machine learning algorithm of sparse Bayesian learning (SBL) for physics-based models, such as 1) the likelihood function or the posterior parameter distribution is not required to be Gaussian, and 2) prior parameter knowledge is incorporated into sparse learning (i.e. not all parameters are treated as questionable). NSBL employs the concept of automatic relevance determination (ARD) to facilitate sparsity among questionable parameters through parameterized prior distributions. The analytical tractability of NSBL is enabled by employing Gaussian ARD priors and by building a Gaussian mixture-model approximation of the posterior parameter distribution that excludes the contribution of ARD priors. Subsequently, type-II maximum likelihood is executed using Newton's method whereby the evidence and its gradient and Hessian information are computed in a semi-analytical fashion. We show numerically and analytically that SBL is a special case of NSBL for linear regression models. Subsequently, a linear regression example involving multimodality in both parameter posterior pdf and model evidence is considered to demonstrate the performance of NSBL in cases where SBL is inapplicable. Next, NSBL is applied to identify sparsity among the damping coefficients of a mass-spring-damper model of a shear building frame. These numerical studies demonstrate the robustness and efficiency of NSBL in alleviating overfitting during Bayesian inversion of nonlinear physics-based models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mock data sets for the Eboss and DESI Lyman-α forest surveys

We present a publicly-available code to generate sets of mock Lyman-α (Lyα) forest data that have realistic large-scale correlations including those due to the Baryonic Acoustic Oscillations (BAO). The primary purpose of these mocks is to test the analysis procedures of the Extended Baryon Oscillation Survey (eBOSS) and the Dark Energy Spectroscopy Instrument (DESI) surveys. The transmitted flux fraction, F(λ), of background quasars due to Lyα absorption in the intergalactic medium (IGM) is simulated using the Fluctuating Gunn-Petterson Approximation (FGPA) applied to Gaussian random fields produced through the use of fast Fourier transforms (FFT). The output includes the IGM-Lyα transmitted flux fraction along quasar lines of sight and a catalog of high-column-density systems appropriately placed at high-density regions of the IGM. This output serves as input to additional code that superimposes the IGM tranmission on realistic quasar spectra, adds absorption by high-column-density systems and metals, and simulates instrumental transmission and noise. Redshift space distortions (RSD) of the flux correlations are implemented by including the large-scale velocity-gradient field in the FGPA resulting in a correlation function of F(λ) that can be accurately predicted. One hundred realizations have been produced over the 14,000 deg 2 DESI survey footprint with 100 quasars per deg 2 . The analysis of these realizations shows that the correlations of F(λ) follows the prediction within the accuracy of eBOSS survey. Here, the most time-consuming part of the mock production occurs before application of the FGPA, and the existing pre-FGPA forests can be used to easily produce new mock sets with modified redshift-dependent bias parameters or observational conditions.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermal conductivity of a laser plasma

Here, we present a model of the electron thermal conductivity of a laser-produced plasma. The model, supported by Vlasov–Fokker–Planck simulations, predicts that laser absorption reduces conductivity by forcing electrons out of a Maxwell–Boltzmann equilibrium, which results in depletion of both low-velocity bulk electrons and high-velocity tail electrons. We show that both the bulk and tail electrons approximately follow super-Gaussian distributions, but with distinct exponents that each depend on the laser intensity and wavelength through the parameter a = Zv$^{2}_{E}$/v$^{2}_{T}$. For a value of a = 0.5, tail depletion reduces the thermal conductivity to half its zero-intensity value. We present our results as simple analytic fits that can be readily implemented in any radiation-hydrodynamics code or used to correct the local limit of non-local conduction models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Covariance operator estimation: Sparsity, lengthscale, and ensemble Kalman filters

This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of the covariance and the expected supremum of the field. We prove that thresholded estimators enjoy an exponential improvement in sample complexity compared with the standard sample covariance estimator if the field has a small correlation lengthscale. As an application of the theory, we study thresholded estimation of covariance operators within ensemble Kalman filters.

Covariance operator estimation↗

Minimizing Timing Jitter’s Impact on Ground-Penetrating Radar Array Coupling Signals

This article presents a novel investigation into the effect of receiver timing jitter on the quality of imaging of ground-penetrating radar systems. We explicitly show the impact of timing jitter throughout an entire example processing pipeline. The process of coupling removal in systems whose receivers have a random Gaussian-distributed jitter with a high standard deviation leaves randomly distributed residue in the radar image. This residue, called jitter-induced coupling noise, extends even into the expected target domain which may cause false alarms. This residue approximately follows a sum of Gaussian and Gamma distributions based on the higher order derivatives of the coupling signal. Once migrated to create an image, the coupling residue is best described by a Weibull distribution. We show that simple filtering does not remove enough residue and propose two preventative design specifications called the linear slope and migrated probability specifications. Antenna and system designers should use these specifications to assess the true severity of coupling signals in a given jitter environment.

47 OTHER INSTRUMENTATION↗

GPR_calculator: An on-the-fly surrogate model to accelerate massive nudged elastic band calculations

We present GPR_calculator, a package based on Python and C++ programming languages to build an on-the-fly surrogate model using Gaussian Process Regression (GPR) to approximate computationally expensive electronic structure calculations. The key idea is to dynamically train a GPR model during the simulation that can accurately predict energies and forces with uncertainty quantification. When the uncertainty is high, the costly electronic structure calculation is performed to obtain the ground truth data, which is then used to update the GPR model. To illustrate the effectiveness of GPR_calculator, we demonstrate its application in Nudged Elastic Band (NEB) simulations of surface diffusion and reactions, achieving 3-10 times acceleration compared to pure ab initio calculations. The source code is available at https://github.com/MaterSim/GPR_calculator.

Gaussian process regression↗

Statistical Behavior of Low-Amplitude Power System Point-on-Wave Measurements

The power grid is undergoing massive changes to ensure resiliency and reliability in a more decentralized world. Distributed energy resources are becoming a prominent source of generation, potentially leading to a lack of centralized generation sources. Due to these new behaviors and system topologies, it is important to install measurement devices that are 1) accurate and 2) self-aware of their measurement quality. In this paper, a residential-scale microgrid is used to generate voltage and current waveforms, captured by Verivolt and National Instruments measurement equipment. A least-squares approach is used to separate the “clean” signals from the noise. Finally, Gaussian mixture modeling is used to approximate noise distributions, and it is shown these higher-order distribution estimates are a better fit to voltage and current noise profiles than single-mode Gaussian estimates.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Gaussian process hydrodynamics

Abstract We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and Navier-Stokes (NS) equations. Similar to smoothed particle hydrodynamics (SPH), GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow. However, these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow. Closure is achieved by placing a divergence-free GP prior ξ on the velocity field and conditioning it on the vorticity at the particle locations. Known physics (e.g., the Richardson cascade and velocity increment power laws) is incorporated into the GP prior by using physics-informed additive kernels. This is equivalent to expressing ξ as a sum of independent GPs ξ l , which we call modes, acting at different scales (each mode ξ l self-activates to represent the formation of eddies at the corresponding scales). This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes, and enables us to analyze coarse-grain turbulence statistically rather than deterministically. Because GPH is formulated by using the vorticity equations, it does not require solving a pressure equation. By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel, GPH requires significantly fewer particles than SPH. Because GPH has a natural probabilistic interpretation, the numerical results come with uncertainty estimates, enabling their incorporation into an uncertainty quantification (UQ) pipeline and adding/removing particles (quanta of information) in an adapted manner. The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss. Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability. Because the proposed approach uses a Bayesian interpretation, it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

Mathematics↗

Optimizing qubit control pulses for state preparation

In the burgeoning field of quantum computing, the precise design and optimization of quantum pulses are essential for enhancing qubit operation fidelity. This study focuses on refining the pulse engineering techniques for superconducting qubits, employing a detailed analysis of square and Gaussian pulse envelopes under various approximation schemes. We evaluated the effects of coherent errors induced by naive pulse designs. Furthermore, we identified the sources of these errors in the Hamiltonian model’s approximation level. We mitigated these errors through adjustments to the external driving frequency and pulse durations, thus implementing a pulse scheme with stroboscopic error reduction. Our results demonstrate that these refined pulse strategies improve performance and reduce coherent errors. Moreover, the techniques developed herein are applicable across different quantum architectures, such as ion-trap, atomic, and photonic systems.

Chirp modulation↗

Uncertainty propagation in feed-forward neural network models

We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the probability density function (PDF) of the neural network output and its statistical moments as a function of the input uncertainty and the parameters of the network, i.e., weights and biases. A key finding is that an appropriate linearization of the leaky ReLU activation function yields accurate statistical results even for large perturbations in the input vectors. This can be attributed to the way information propagates through the network. We also propose new analytically tractable Gaussian copula surrogate models to approximate the full joint PDF of the neural network output. To validate our theoretical results, we conduct Monte Carlo simulations and a thorough error analysis on a multi-layer neural network representing a nonlinear integro-differential operator between two polynomial function spaces. Our findings demonstrate excellent agreement between the theoretical predictions and Monte Carlo simulations.

MLP networks↗

Marginal unbiased score expansion and application to CMB lensing

Here, we present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces, yielding Gaussianized asymptotically unbiased and near-optimal constraints on global parameters of interest. It is computationally much cheaper than exact alternatives like Hamiltonian Monte Carlo (HMC), excelling on funnel problems which challenge HMC, and does not require any problem-specific user supervision like other approximate methods such as variational inference or many simulation-based inference methods. MUSE makes possible the first joint Bayesian estimation of the delensed Cosmic Microwave Background (CMB) power spectrum and gravitational lensing potential power spectrum, demonstrated here on a simulated data set as large as the upcoming South Pole Telescope 3G 1500 deg 2 survey, corresponding to a latent dimensionality of ~6 million and of order 100 global bandpower parameters. On a subset of the problem where an exact but more expensive HMC solution is feasible, we verify that MUSE yields nearly optimal results. We also demonstrate that existing spectrum-based forecasting tools which ignore pixel-masking underestimate predicted error bars by only ~10%. This method is a promising path forward for fast lensing and delensing analyses which will be necessary for future CMB experiments such as SPT-3G, Simons Observatory, or CMB-S4, and can complement or supersede existing HMC approaches. The success of MUSE on this challenging problem strengthens its case as a generic procedure for a broad class of high-dimensional inference problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗