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DOE OSTI2023

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Assessing correlated truncation errors in modern nucleon-nucleon potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒⁢EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒⁢EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒⁢EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒⁢EFT NN potentials.

Bayesian methods↗

DOE OSTI2023

Seeing through noise in power laws

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Inferring the Thermal History of the Intergalactic Medium from the Properties of the Hydrogen and Helium Lyα Forest

The filamentary network of intergalactic medium (IGM) gas that gives origin to the Lyα forest in the spectra of distant quasars encodes information on the physics of structure formation and the early thermodynamics of diffuse baryonic material. Here we use a massive suite of more than 400 high-resolution cosmological hydrodynamical simulations run with the Graphics Processing Unit–accelerated code Cholla to study the IGM at high spatial resolution maintained over the entire computational volume. The simulations capture a wide range of possible IGM thermal histories by varying the photoheating and photoionizing background produced by star-forming galaxies and active galactic nuclei. A statistical comparison of synthetic spectra with the observed 1D flux power spectra of hydrogen at redshifts 2.2 ≤ z ≤ 5.0 and with the helium Lyα opacity at redshifts 2.4 < z < 2.9 tightly constrains the photoionization and photoheating history of the IGM. By leveraging the constraining power of the available Lyα forest data to break model degeneracies, we find that the IGM experienced two main reheating events over 1.2 Gyr of cosmic time. For our best-fit model, hydrogen reionization completes by z R ≈ 6.0 with a first IGM temperature peak of T 0 ≃ 1.3 × 10 4 K and is followed by the reionization of He ii that completes by z R ≈ 3.0 and yields a second temperature peak of T 0 ≃ 1.4 × 10 4 K. We discuss how our results can be used to obtain information on the timing and the sources of hydrogen and helium reionization.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

A convergence metric for counting statistics in time-resolved small angle neutron scattering

Here, this work introduces a model-independent, dimensionless metric for predicting optimal measurement duration in time-resolved small-angle neutron scattering using early-time data. Built on a Gaussian process regression framework, the method reconstructs scattering profiles with quantified uncertainty, even from sparse or noisy measurements. Demonstrated on the EQ-SANS instrument at the Spallation Neutron Source, the approach generalizes to general SANS instruments with a two-dimensional detector. A key result is the discovery of a dimensionless convergence metric revealing a universal power-law scaling in profile evolution across soft matter systems. When time is normalized by a system-specific characteristic time t*, the variation in inferred profiles collapses onto a single curve with an exponent between −2 and −1. This trend emerges within the first ten time steps, enabling early prediction of measurement sufficiency. The method supports real-time experimental optimization and is especially valuable for maximizing efficiency in low-flux environments such as compact accelerator-based neutron sources.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

DOE OSTI2021

In Situ Inference for Earth System Predictability

An understanding of future evolution in precipitation extremes is critical to numerous DOE mission questions. Extreme events are by nature short time-scale events that are difficult to diagnose in available model data. Accurate modeling of extreme events necessarily requires high spatial resolution at the storm scale locally. However, the environment in which storms grow is dependent on global, remote, processes. These complex spatiotemporal relationships are impossible to diagnose at resolutions required to accurately model storms responsible for extreme precipitation. At exascale, climate simulations will produce results at fine enough resolution to investigate these relationships. However, the resulting data from these simulations will be far too large to save for post-simulation analysis. We advocate for fitting statistical models inside the simulations as they run, a context known as in situ, which will facilitate scientific investigations using the full fine-scale data stream. Figure 1 shows an example of the type of model we could consider, a Bayesian hierarchical spatial regression model. Precipitation extremes at each grid cell are modeled using extreme value distributions. Since extremes are rare, fitting models to individual grid cells can result in high variance and poor estimates. Instead, the model can be made more robust by smoothing the parameters of the extreme value model across space. Additionally, the parameters themselves can be functionally linked to other variables elsewhere in the simulation. Thus, we can use the fine-scale data to build more robust models for extremes that link extreme behavior to other climate patterns.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

KilonovaNet : Surrogate models of kilonova spectra with conditional variational autoencoders

ABSTRACT Detailed radiative transfer simulations of kilonova spectra play an essential role in multimessenger astrophysics. Using the simulation results in parameter inference studies requires building a surrogate model from the simulation outputs to use in algorithms requiring sampling. In this work, we present kilonovanet, an implementation of conditional variational autoencoders (cVAEs) for the construction of surrogate models of kilonova spectra. This method can be trained on spectra directly, removing overhead time of pre-processing spectra, and greatly speeds up parameter inference time. We build surrogate models of three state-of-the-art kilonova simulation data sets and present in-depth surrogate error evaluation methods, which can in general be applied to any surrogate construction method. By creating synthetic photometric observations from the spectral surrogate, we perform parameter inference for the observed light-curve data of GW170817 and compare the results with previous analyses. Given the speed with which kilonovanet performs during parameter inference, it will serve as a useful tool in future gravitational wave observing runs to quickly analyse potential kilonova candidates.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Methods for Explainable Artificial Intelligence

We explored ways of quantifying information in a neural network. This can be used to determine the right size of a network or to infer the way in which a network is processing information. The first year and a half was somewhat exploratory while the last half of the project focused on approaches that seemed to show the most promise. The introduce a new way of computing explainable artificial intelligence (XAI) saliency maps that is several orders of magnitude faster than methods with similar fidelity We call it FastCAM. The method works be combining a Class Activation Map (CAM) method such as GradCAM with a forward activation map computed with a statistic we call SMOE Scale. The addition of the forward activation maps to CAM methods seems to always improve their fidelity. At the same time, computational overhead is not increased by very much. While Gradients with SmoothGrad scores better on some fidelity measures, it is overall not as good and requires more than 1500 times to compute. We demonstrate two completed applications of FastCAM on tasks outside of the LDRD at LLNL. The source code for FastCAM is currently being implanted into Captum, the official XAI toolkit for the popular deep learning toolkit PyTorch. The LDRD currently has 13 publications released to the public. 10 of them are journal length.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Inference of the optical depth to reionization τ from Planck CMB maps with convolutional neural networks

The optical depth to reionization, τ, is the least constrained parameter of the cosmological Λ cold dark matter (ΛCDM) model. To date, its most precise value is inferred from large-scale polarized cosmic microwave background (CMB) power spectra from the High Frequency Instrument (HFI) aboard the Planck satellite. These maps are known to contain significant contamination by residual non-Gaussian systematic effects, which are hard to model analytically. Therefore, robust constraints on τ are currently obtained through an empirical cross-spectrum likelihood built from simulations. In this paper, we present a likelihood-free inference of τ from polarized Planck HFI maps which, for the first time, is fully based on neural networks (NNs). NNs have the advantage of not requiring an analytical description of the data and can be trained on state-of-the-art simulations, combining the information from multiple channels. By using Gaussian sky simulations and Planck SRoll2 simulations, including CMB, noise, and residual instrumental systematic effects, we trained, tested, and validated NN models considering different setups. We inferred the value of τ directly from Stokes Q and U maps at ~4° pixel resolution, without computing angular power spectra. On Planck data, we obtained τ NN = 0.0579 ± 0.0082, which is compatible with current EE cross-spectrum results but with a ~30% larger uncertainty, which can be assigned to the inherent nonoptimality of our estimator and to the retraining procedure applied to avoid biases. While this paper does not improve on current cosmological constraints on τ, our analysis represents a first robust application of NN-based inference on real data, and highlights its potential as a promising tool for complementary analysis of near-future CMB experiments, also in view of the ongoing challenge to achieve the first detection of primordial gravitational waves.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Light element ($$Z=1,2$$) production from spontaneous ternary fission of $$^{252}$$Cf

Abstract The yields of light elements ( $$Z=1,2$$ Z = 1 , 2 ) obtained from spontaneous ternary fission of $$^{252}$$ 252 Cf are treated within a nonequilibrium approach, and the contribution of unstable nuclei and excited bound states is taken into account. These light cluster yields may be used to probe dense matter, and to infer in-medium corrections such as Pauli blocking which is determined by the nucleon density. Continuum correlations are calculated from scattering phase shifts using the Beth-Uhlenbeck formula, and the effect of medium modification is estimated. The relevant distribution is reconstructed from the measured yields of isotopes. This describes the state of the nucleon system at scission and cluster formation, using only three Lagrange parameters which are the nonequilibrium counterparts of the temperature and chemical potentials, as defined in thermodynamic equilibrium. We concluded that a simple nuclear statistical equilibrium model neglecting continuum correlations and medium effects is not able to describe the measured distribution of H and He isotopes. Moreover, the freeze-out concept may serve as an important ingredient to the nonequilibrium approach using the relevant statistical operator concept.

Röpke, G.↗

DOE OSTI2025

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Extracting forces from noisy dynamics in dusty plasmas

Extracting environmental forces from noisy data is a common yet challenging task in complex physical systems. Machine learning (ML) represents a robust approach to this problem, yet is mostly tested on simulated data with known parameters. Here we use supervised ML to extract the electrostatic, dissipative, and stochastic forces acting on micron-sized charged particles levitated in an argon plasma (dusty plasma). By tracking the sub-pixel motion of particles in subsequent images, we successfully estimated these forces from their random motion. The experiments contained important sources of non-Gaussian noise, such as drift and pixel-locking, representing a data mismatch from methods used to analyze simulated data with purely Gaussian noise. Our model was trained on simulated particle trajectories that included all of these artifacts, and used more than 100 dynamical and statistical features, resulting in a prediction with 50\% better accuracy than conventional methods. Lastly, in systems with two interacting particles, the model provided non-contact measurements of the particle charge and Debye length in the plasma environment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Statistical chronometry of meteorites. I. A Test of 26 Al homogeneity and the Pb-Pb age of the solar system’s $t=0$

Here, we use rapidly cooled achondrites to test the assumption of 26 Al homogeneity in the solar nebula, by checking if there is a single value of t SS , the absolute “Pb-Pb” age of the Solar System’s t=0, that makes concordant their ages from the Al-Mg and Pb-Pb systems. We find that values t SS =4568.42 ± 0.24 Myr do make these ages concordant, and therefore the hypothesis of homogeneous 26 Al is not falsified. This age, defined to be when the solar nebula had ( 26 Al/ 27 Al) = 5.23 × 10 –5 , is significantly older than the ≈ 4567.3 Myr inferred from direct measurements of Pb-Pb ages in CAIs. Discrepancies between the Al-Mg and Pb-Pb chronometers in chondrules and CAIs have previously been interpreted as arising from heterogeneities in 26 Al, under the presumption that the Al-Mg and Pb-Pb systems in CAIs closed simultaneously. We examine this assumption and show that resetting is to be expected in CAIs. In particular, we quantitatively demonstrate that it is plausible that Pb-Pb ages of CAIs were reset at late times, without resetting the earlier Al-Mg ages, if they were transiently heated in the same manner as chondrules. We critically examine Pb-Pb isochrons, refining data and suggesting best practices for their calculation and reporting. We advocate reporting chronometry as times of formation after t=0 rather than absolute ages, as only the former is useful for astrophysical models of the solar nebula. We advocate averaging of multiple samples, rather than anchoring to individual meteorites, to improve precision.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Thermodynamics of order and randomness in dopant distributions inferred from atomically resolved imaging

Abstract Exploration of structure-property relationships as a function of dopant concentration is commonly based on mean field theories for solid solutions. However, such theories that work well for semiconductors tend to fail in materials with strong correlations, either in electronic behavior or chemical segregation. In these cases, the details of atomic arrangements are generally not explored and analyzed. The knowledge of the generative physics and chemistry of the material can obviate this problem, since defect configuration libraries as stochastic representation of atomic level structures can be generated, or parameters of mesoscopic thermodynamic models can be derived. To obtain such information for improved predictions, we use data from atomically resolved microscopic images that visualize complex structural correlations within the system and translate them into statistical mechanical models of structure formation. Given the significant uncertainties about the microscopic aspects of the material’s processing history along with the limited number of available images, we combine model optimization techniques with the principles of statistical hypothesis testing. We demonstrate the approach on data from a series of atomically-resolved scanning transmission electron microscopy images of Mo x Re 1- x S 2 at varying ratios of Mo/Re stoichiometries, for which we propose an effective interaction model that is then used to generate atomic configurations and make testable predictions at a range of concentrations and formation temperatures.

25 ENERGY STORAGE↗

DOE OSTI2026

Inference of the linear matter power spectrum at z = 0 using DESI DR1 Full-Shape data

Measurements of galaxy distributions at large cosmic distances capture clustering from the past. In this study, we use a cosmological model to translate these observations into the present-day galaxy distribution. Specifically, we reconstruct the 3D linear matter power spectrum at redshift z = 0 using Dark Energy Spectroscopic Instrument (DESI) Year 1 (DR1) galaxy clustering data and Cosmic Microwave Background (CMB) observations, assuming the ΛCDM model, and compare it to the result assuming the w 0 w a CDM model. Building on previous state-of-the-art methods, we apply Effective Field Theory (EFT) modelling of the galaxy power spectrum to account for small-scale effects in the 2-point statistics of galaxy data. Implementation of the EFT approach improves the modelling of the galaxy power spectrum, providing a more robust consistency test of the assumed cosmological model. By casting both CMB and galaxy clustering observations, spanning distinct redshift regimes, into k-space, we can identify discrepancies between the datasets of different redshifts, which would indicate potential inaccuracies in the assumed expansion history. While previous studies have shown consistency with ΛCDM, this work extends the analysis with higher-quality data to further test the expansion histories of both ΛCDM and w 0 w a CDM. Our findings show that both ΛCDM and w 0 w a CDM provide consistent fits to the linear matter power spectrum recovered from DESI DR1 data.

cosmological parameters from LSS↗

DOE OSTI2020

Inferring transmission heterogeneity using virus genealogies: estimation and targeted prevention

Spread of HIV typically involves uneven transmission patterns where some individuals spread to a large number of individuals while others to only a few or none. Such transmission heterogeneity can impact how fast and how much an epidemic spreads. Further, more efficient interventions may be achieved by taking such transmission heterogeneity into account. To address these issues, we developed two phylogenetic methods based on virus sequence data: 1) to generally detect if significant transmission heterogeneity is present, and 2) to pinpoint where in a phylogeny high-level spread is occurring. We derive inference procedures to estimate model parameters, including the amount of transmission heterogeneity, in a sampled epidemic. We show that it is possible to detect transmission heterogeneity under a wide range of simulated situations, including incomplete sampling, varying levels of heterogeneity, and including within-host genetic diversity. When evaluating real HIV-1 data from different epidemic scenarios, we found a lower level of transmission heterogeneity in slowly spreading situations and a higher level of heterogeneity in data that included a rapid outbreak, while R0 and Sackin’s index (overall tree shape statistic) were similar in the two scenarios, suggesting that our new method is able to detect transmission heterogeneity in real data. We then show by simulations that targeted prevention, where we pinpoint high-level spread using a coalescence measurement, is efficient when sequence data are collected in an ongoing surveillance system. Such phylogeny-guided prevention is efficient under both single-step contact tracing as well as iterative contact tracing as compared to random intervention.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

A 5 per cent measurement of the Hubble–Lemaître constant from Type II supernovae

ABSTRACT The most stringent local measurement of the Hubble–Lemaître constant from Cepheid-calibrated Type Ia supernovae (SNe Ia) differs from the value inferred via the cosmic microwave background radiation (Planck+ΛCDM) by ∼5σ. This so-called Hubble tension has been confirmed by other independent methods, and thus does not appear to be a possible consequence of systematic errors. Here, we continue upon our prior work of using Type II supernovae to provide another, largely independent method to measure the Hubble–Lemaître constant. From 13 SNe II with geometric, Cepheid, or tip of the red giant branch (TRGB) host-galaxy distance measurements, we derive H$_0= 75.4^{+3.8}_{-3.7}$ km s−1 Mpc−1 (statistical errors only), consistent with the local measurement but in disagreement by ∼2.0σ with the Planck+ΛCDM value. Using only Cepheids (N = 7), we find H$_0 = 77.6^{+5.2}_{-4.8}$ km s−1 Mpc−1, while using only TRGB (N = 5), we derive H$_0 = 73.1^{+5.7}_{-5.3}$ km s−1 Mpc−1. Via 13 variants of our data set, we derive a systematic uncertainty estimate of 1.5 km s−1 Mpc−1. The median value derived from these variants differs by just 0.3 km s−1 Mpc−1 from that produced by our fiducial model. Because we only replace SNe Ia with SNe II – and we do not find statistically significant difference between the Cepheid and TRGB H0 measurements – our work reveals no indication that SNe Ia or Cepheids could be the sources of the ‘H0 tension.’ We caution, however, that our conclusions rest upon a modest calibrator sample; as this sample grows in the future, our results should be verified.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Supernova-driven Turbulent Metal Mixing in High-redshift Galactic Disks: Metallicity Fluctuations in the Interstellar Medium and its Imprints on Metal-poor Stars in the Milky Way

The extent to which turbulence mixes gas in the face of recurrent infusions of fresh metals by supernovae (SN) could help provide important constraints on the local star formation conditions. This includes predictions of the metallicity dispersion among metal-poor stars, which suggests that the interstellar medium was not very well mixed at these early times. The purpose of this Letter is to help isolate, via a series of numerical experiments, some of the key processes that regulate turbulent mixing of SN elements in galactic disks. We study the gas interactions in small simulated patches of a galaxy disk with the goal of resolving the small-scale mixing effects of metals at parsec scales, which enables us to measure the turbulent diffusion coefficient in various galaxy environments. By investigating the statistics of variations of α elements in these simulations, we are able to derive constraints not only on the allowed range of intrinsic yield variations in SN explosions but also on the star formation history of the Milky Way. We argue that the observed dispersion of [Mg/Fe] in metal-poor halo stars is compatible with the star-forming conditions expected in dwarf satellites or in an early low-star-forming Milky Way progenitor. In particular, metal variations in stars that have not been phase-mixed can be used to infer the star-forming conditions of disrupted dwarf satellites.

79 ASTRONOMY AND ASTROPHYSICS↗