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DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗

DOE OSTI2025

Moist Energy Constraints on Surface Temperature Variance Under Climate Warming

Understanding the factors controlling surface temperature variance is crucial for predicting temperature extremes. Previous investigations have examined individual impacts of temperature advection and surface turbulent fluxes on temperature fluctuations. Here, we explore the constraints on temperature variance from the moist static energy (MSE) balance and introduce a new scaling relation that connects the generation of temperature variance through moist energy transport with its dissipation due to the net energetic forcing of the atmosphere. This theory is evaluated in an idealized aquaplanet model. We find that surface temperature variance is influenced by eddy (sensible) heat flux, MSE gradient, and the Clausius‐Clapeyron relation for evaporative cooling. Under global warming, the reduced temperature variance in the aquaplanet model is dominated by the weakening in eddy heat flux, but it is also affected by changes in evaporative cooling and MSE gradient, which may be more important in realistic, moisture‐limited regions over land.

Eddy heat flux↗

DOE OSTI2026

A hybrid Monte Carlo-deterministic second moment method with efficient variance reduction

In this work, we present a hybrid method that combines Monte Carlo with deterministic finite element methods to solve a linear Boltzmann transport equation. Our hybrid method runs orders of magnitude faster than Monte Carlo, without sacrificing accuracy, for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material. We believe that this is the first demonstration of a hybrid Second Moment Method in more than one spatial dimension, the first to consider more than one material, and the first to use variance reduction. Our variance reduction approach arises from an asymptotic analysis in which we show that the magnitude of the scattering source grows without bound. We transform the problem to compute the deviation of the radiation intensity from isotropy. The magnitude of the source in the transformed problem is bounded, and the quality of the hybrid method solution is dramatically improved by a substantial reduction in the variance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Suppressing the sample variance of DESI-like galaxy clustering with fast simulations

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM. Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit. We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance. Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively. We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k 2 = 2k 1 = 0.2 h Mpc -1 by a factor of 1.6. With smaller sample variance on galaxy clustering, we are able to constrain the baryon acoustic oscillations (BAO) scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordial non-Gaussianity (NG).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Variance reduction in lattice QCD observables via normalizing flows

Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables involving gluonic operator insertions in the SU(3) Yang-Mills theory and two-flavor QCD in four space-time dimensions. Variance reduction by factors of 10–60 is achieved in glueball correlation functions and in gluonic matrix elements related to hadron structure, with demonstrated computational advantages. The observed variance reduction is found to be approximately independent of the lattice volume, so volume transfer can be utilized to minimize training costs.

Abbott, Ryan [Columbia U.; MIT, Cambridge, CTP; IA↗

DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗

DOE OSTI2026

Allan Variance is Bootstrap Aggregation for Spectral Estimation

Characterization of clocks and inertial sensors, such as accelerometers and gyroscopes, typically includes Allan variance analysis. Allan variance is ubiquitous in timing and navigation communities which may appear niche compared with generalized spectral analysis. This note provides some motivation for Allan Variance for audiences more familiar with spectral analysis.

Walker, Michael Ray [Sandia National Laboratories ↗

DOE OSTI2025

The Bias-Variance-Correlation Tradeoff and Its Implications for ML Applications in HEP

The bias-variance tradeoff is a well-recognized phenomenon in statistics and machine learning. In this talk, I will discuss an extension, dubbed the bias-variance-correlation tradeoff. Roughly speaking, as the flexibility of a model decreases, the correlations in the outputs of a trained model for different inputs increases. Such correlations have implications for several applications of machine learning in high energy physics, e.g., the use generative models for event generation. In particular, I will argue that claims in the literature of data amplification by generative models stem from ignoring important correlations between the model's outputs for different inputs.

Shyamsundar, Prasanth [Fermilab] (ORCID:0000000227↗

DOE OSTI2025

Godiva IV Thermal Neutron Dosimetry Modeling and Variance Reduction

The transfer of the Godiva IV experiment from the Los Alamos Critical Experiments Facility (LACEF) to the National Critical Experiments Research Center (NCERC) introduced a vastly different experiment room return to the neutron flux. The contribution of the background to the burst neutron energy spectrum is significant in the thermal and epithermal neutron energies. Target materials may be placed in various locations in the Godiva room, or outside of the room, for thermal neutron activation. Modeling of this dosimetry problem in Monte Carlo N-Particle (MCNP) presented a novel challenge compared to previous Godiva IV glory hole irradiation simulations. An advanced dosimetry modeling framework for high efficiency calculations in locations far from the Godiva IV fission source was desired. The mesh-based weight windows and point detector advanced variance reduction techniques in MCNP were implemented and tested using adaptations of the critical experiment benchmark model of the Godiva IV problem. The models were validated against measured activations of Nickel, Indium, Scandium, and Cobalt foils at locations 2 meters from the Godiva IV core. Dosimetry measurements were performed in collaboration with Sandia National Laboratory. The weight windows and point detector variance reduction coupled method resulted in the highest problem efficiency.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Variance Preserving Spectral Subsampling

Generating statistically faithful short-duration gamma-ray spectra from a single long measurement is essential in nuclear safeguards, supporting tasks such as algorithm development and machine-learning applications, especially when list-mode data are unavailable. Existing subsampling methods often distort the statistical characteristics of genuine short-duration measurements, leading to biased or unreliable analytical outcomes and thereby undermining downstream tasks. In this work, we compare five subsampling approaches using a benchmark set of 156 genuine replicate spectra collected with a high-purity germanium detector. We evaluate each method with respect to run-to-run variance, channel-to-channel variance, and preservation of total counts (losslessness). Across a wide range of subsampling ratios, only binomial subsampling without replacement consistently reproduces the statistical properties of genuine short-duration spectra, maintaining proper dispersion even in sparse spectral regions and perfectly preserving total counts. These results provide a mathematically principled and practically validated framework for generating synthetically shortened spectra when true short-duration measurements are unavailable.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2026

The DREAMS Project: Disentangling the Impact of Halo-to-halo Variance and Baryonic Feedback on Milky Way Dark Matter Density Profiles

In this work, we utilize a new suite of Milky Way–mass halos from the DREAMS Project, simulated with cold dark matter (CDM), to quantify the influence of baryon feedback and intrinsic halo-to-halo variance on dark matter density profiles. Our suite of 1024 halos varies over supernova and black hole feedback parameters from the IllustrisTNG model, as well as variations in two cosmological parameters. We find that, for the DREAMS parameter variations, Milky Way–mass dark matter density profiles in the IllustrisTNG model are largely insensitive to astrophysics and cosmology variations, with the dominant source of scatter instead arising from halo-to-halo variance. However, most of the (comparatively minor) feedback-driven variations come from the changes to supernova prescriptions. By comparing to dark-matter-only simulations, we find that the strongest supernova wind energies are so effective at preventing galaxy formation that the halos are nearly entirely collisionless dark matter. Finally, regardless of physics variation, all of the DREAMS halos are roughly consistent with a halo contracting adiabatically from the presence of baryons, unlike models that have bursty stellar feedback. This work represents a step toward assessing the uncertainty in Milky Way dark matter profiles, with direct implications for dark matter searches where systematic uncertainty in the density profile remains a major challenge.

Garcia, Alex M. [University of Virginia, Charlotte↗

DOE OSTI2026

The DREAMS Project: Disentangling the Impact of Halo-to-Halo Variance and Baryonic Feedback on Milky Way Dark Matter Speed Distributions

Dark matter direct detection experiments require information about the local dark matter speed distribution to produce constraints on dark matter candidates, or infer their properties in the event of a discovery. In this paper, we analyze how the uncertainty in the dark matter speed distribution near the Sun is affected by baryonic feedback, halo-to-halo variance, and halo mass. To do so, we harness the statistical power of the new DREAMS cold dark matter simulation suite, which is comprised of 1024 zoom-in Milky Way–mass halos with varied initial conditions as well as cosmological and astrophysical parameters. Applying a normalizing flows emulator to these simulations, we find that the uncertainty in the local dark matter speed distribution is dominated by halo-to-halo variance and, to a lesser extent, uncertainty in host halo mass. Uncertainties in supernova and black hole feedback (from the IllustrisTNG model in this case) are negligible in comparison. Using the DREAMS suite, we present a state-of-the-art prediction for the dark matter speed distribution in the Milky Way. Although the standard halo model is contained within the uncertainty of this prediction, individual galaxies may have distributions that differ from it. Lastly, we apply our DREAMS results to the XENON1T experiment and demonstrate that the astrophysical uncertainties are comparable to the experimental ones, solidifying previous results in the literature obtained with a smaller sample of simulated Milky Way–mass halos.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Evaluating downscaled products with expected hydroclimatic co-variances

Abstract. There has been widespread adoption of downscaled products amongst practitioners and stakeholders to ascertain risk from climate hazards at the local scale (e.g., ∼ 5 km resolution). Such products must nevertheless be consistent with physical laws to be credible and of value to users. Here we evaluate statistically and dynamically downscaled products by examining local co-evolution of downscaled temperature and precipitation during convective and frontal precipitation events (two mechanisms testable with just temperature and precipitation). We find that two widely used statistical downscaling techniques (Localized Constructed Analogs version 2, LOCA2, and Seasonal Trends and Analysis of Residuals Empirical Statistical Downscaling Model, STAR-ESDM) generally preserve expected co-variances during convective precipitation events over the historical and future projected intervals as compared to European Centre for Medium-Range Weather Forecasts Reanalysis v5 (ERA5) and two observation-based data products (Livneh and nClimGrid-Daily). However, both techniques dampen future intensification of frontal precipitation that is otherwise robustly captured in global climate models (i.e., prior to downscaling) and with process-based dynamical downscaling across five different regional climate models. In the case of LOCA2, this leads to appreciable underestimation of future frontal precipitation event intensity. This study is one of the first to quantify a likely ramification of the stationarity assumption underlying statistical downscaling methods and identify a phenomenon where projections of future change diverge depending on data production method employed. Finally, our work proposes expected co-variances during convective and frontal precipitation as useful evaluation diagnostics that can be universally applied to a wide range of statistically downscaled products.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Learning the generating functional for variance reduction in lattice QCD

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

Abbott, Ryan [Columbia U.] (ORCID:0000000258778005↗

DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗

DOE OSTI2026

UV-Induced Degradation and Associated Metastability in TOPCon Photovoltaic Modules: Understanding Kinetics and Cell Variance

Tunnel oxide passivated contact (TOPCon) silicon photovoltaic (PV) modules are dominating the PV market, but they may be susceptible to degradation under ultraviolet (UV)-containing light. Quantifying the impacts of UV-induced degradation (UVID) is complicated by an associated metastability causing further degradation under dark storage and rapid recovery under sunlight. Here, we study modules that have -2.3% to -3.2% nonrecoverable UVID loss after 60 kWh/m2 dose of 340 nm light and additional recoverable loss under dark storage. We use in situ electroluminescence (EL) imaging to characterize the post-UVID metastability at the module level. The cell-by-cell dark degradation and recovery kinetics span a wide range from +6% to -70% changes in EL intensity after 520 h of dark storage, which returns to +- 4% of the initial post-UVID EL intensity after illumination. The kinetics follow double exponential rates with dark storage degradation time constants of 345 and 45 h, and UV light recovery time constants of 5 min and 36 s. We propose that this is consistent with prior reports of kinetics for light-soaking metastability in Al2O3 passivation. Finally, we further show that cells having high UVID also have injection-dependent effective carrier lifetimes and significant intra-cell variance, suggesting possible origins of processing inconsistency.

14 SOLAR ENERGY↗

DOE OSTI2025

Numerical simulation of asteroid geometry variance on airburst threat

For an atmospheric airburst the primary source of concern when assessing uncertainty is the size and velocity. Determining these properties provides the basis for threat assessment, as the total energy of the asteroid may then be estimated, and the threat investigated thoroughly. Even with clarity as to how much energy an asteroid may deposit, a great deal of uncertainty still exists for the actual energy deposition process. One such source of uncertainty is the geometry of the incoming asteroid. The geometry of an asteroid will alter the stress distribution during entry, which adds uncertainty to when fracture will occur. Here, in this study, we use Smoothed Particle Hydrodynamics to model the atmospheric airburst of Tunguska-scale asteroids with varying geometric profiles, including a sphere, ellipsoid, binary and superellipsoid. Each asteroid is modeled as a homogenous structure with strength. We assess uncertainty through a series of planar 2D simulation cases for each geometry, comparing the source of stochasticity across geometries. A single 3D airburst simulation for each geometry is also analyzed. Additionally, the 3D cases are compared to the highly uncertain Tunguska event, predicting variance in burst height across geometries, but all bounded by theoretical burst heights proposed for Tunguska.

Airburst↗