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DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

The miniJPAS survey quasar selection – I. Mock catalogues for classification

In this series of papers, we employ several machine learning (ML) methods to classify the point-like sources from the miniJPAS catalogue, and identify quasar candidates. Since no representative sample of spectroscopically confirmed sources exists at present to train these ML algorithms, we rely on mock catalogues. In this first paper, we develop a pipeline to compute synthetic photometry of quasars, galaxies, and stars using spectra of objects targeted as quasars in the Sloan Digital Sky Survey . To match the same depths and signal-to-noise ratio distributions in all bands expected for miniJPAS point sources in the range 17.5 ≤ r < 24, we augment our sample of available spectra by shifting the original r-band magnitude distributions towards the faint end, ensure that the relative incidence rates of the different objects are distributed according to their respective luminosity functions, and perform a thorough modelling of the noise distribution in each filter, by sampling the flux variance either from Gaussian realizations with given widths, or from combinations of Gaussian functions. Finally, we also add in the mocks the patterns of non-detections which are present in all real observations. Although the mock catalogues presented in this work are a first step towards simulated data sets that match the properties of the miniJPAS observations, these mocks can be adapted to serve the purposes of other photometric surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Utilizing machine learning to improve the precision of fluorescence imaging of cavity-generated spin squeezed states

We present a supervised learning model to calibrate the photon collection rate during the fluorescence imaging of cold atoms. The linear regression model finds the collection rate at each location on the sensor such that the atomic population difference equals that of a highly precise optical cavity measurement. This 192 variable regression results in a measurement variance 27% smaller than our previous single variable regression calibration. The measurement variance is now in agreement with the theoretical limit due to other known noise sources. This model efficiently trains in less than a minute on a standard personal computer's CPU and requires less than 10 min of data collection. Furthermore, the model is applicable across a large change in population difference and across data collected on different days.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Data-driven discovery of dynamics from time-resolved coherent scattering

Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex dynamics is often limited by one or more factors—the ability to visualize dynamics in real space, computational cost of high-fidelity simulations, and effectiveness of approximate or phenomenological models. In this work, we develop a data-driven framework to uncover mechanistic models of dynamics directly from time-resolved CXS measurements without solving the phase reconstruction problem for the entire time series of diffraction patterns. Our approach uses neural differential equations to parameterize unknown real-space dynamics and implements a computational scattering forward model to relate real-space predictions to reciprocal-space observations. This method is shown to recover the dynamics of several computational model systems under various simulated conditions of measurement resolution and noise. Moreover, the trained model enables estimation of long-term dynamics well beyond the maximum observation time, which can be used to inform and refine experimental parameters in practice. Finally, we demonstrate an experimental proof-of-concept by applying our framework to recover the probe trajectory from a ptychographic scan. Our proposed framework bridges the wide existing gap between approximate models and complex data.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Prediction of curing kinetics of resorcinol‐added resole phenolic resins using differential scanning calorimetry for the fabrication of carbon/carbon composites

Phenolic resins are commonly used as carbon precursors for the fabrication of carbon/carbon composites due to their high carbon yield and aromatic nature. To decrease curing times, acid catalysts are generally used, but the addition of resorcinol was found to have a similar effect while being incorporated into the resin matrix with no contamination or corrosion issues. In this work, the curing kinetics of pure, 10, 20, and 30 wt% resorcinol-added phenolic resins were investigated through differential scanning calorimetry. Heating rates of 0.5, 1, 2.5, and 5°C min -1 were used with several curing models to predict isothermal curing. Averaged mean absolute error (MAE) for the isoconversional mathematical approaches namely Kissinger–Akahira–Sunose (MAE = 12.9 min), Flynn–Wall–Ozawa (15.8 min), and Vyazovkin (14 min) show that these methods provide the best predictions, attributed to their adoption of an activation energy that depends on the extent of cure (E a (α)). The Kissinger method (MAE = 36 min), which depends only on peak temperature with a constant activation energy assumption, and the data noise sensitive Friedman model (MAE = 1144.7 min) provide the least accurate results. Thermogravimetric analysis revealed that resorcinol decreases the curing times by up to 71% without lowering carbon yield.

36 MATERIALS SCIENCE↗

DOE OSTI2025

DESI DR1 Lyα 1D power spectrum: the optimal estimator measurement

The one-dimensional power spectrum P 1D of Lyα forest offers rich insights into cosmological and astrophysical parameters, including constraints on the sum of neutrino masses, warm dark matter models, and the thermal state of the intergalactic medium. We present the measurement of P 1D using the optimal quadratic maximum likelihood estimator applied to over 300,000 Lyα quasars from Data Release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI) survey. This sample represents the largest to date for P 1D measurements and is larger than the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) by a factor of 1.7. We conduct a meticulous investigation of instrumental and analysis systematics and quantify their impact on P 1D . This includes the development of a cross-exposure estimator that eliminates the need to model the pipeline noise and has strong potential for future P 1D measurements. We also present new insights into metal contamination through the 1D correlation function. Using a fitting function we measure the evolution of the Lyα forest bias with high precision: b F (z) = (-0.218 ± 0.002) × ((1 + z)/4) 2.96±0.06 . In a companion validation paper, we substantially extend our previous suite of CCD image simulations to quantify the pipeline's exquisite performance accurately. In another companion paper, we present DR1 P 1D measurements using the Fast Fourier Transform (FFT) approach to power spectrum estimation. These two measurements produce a forest bias parameter that differs by 2.2 sigma. However, our model is simplistic, so this disagreement will be investigated in future work.

Lyman alpha forest↗

DOE OSTI2023

Many but not all deep neural network audio models capture brain responses and exhibit correspondence between model stages and brain regions

Models that predict brain responses to stimuli provide one measure of understanding of a sensory system and have many potential applications in science and engineering. Deep artificial neural networks have emerged as the leading such predictive models of the visual system but are less explored in audition. Prior work provided examples of audio-trained neural networks that produced good predictions of auditory cortical fMRI responses and exhibited correspondence between model stages and brain regions, but left it unclear whether these results generalize to other neural network models and, thus, how to further improve models in this domain. We evaluated model-brain correspondence for publicly available audio neural network models along with in-house models trained on 4 different tasks. Most tested models outpredicted standard spectromporal filter-bank models of auditory cortex and exhibited systematic model-brain correspondence: Middle stages best predicted primary auditory cortex, while deep stages best predicted non-primary cortex. However, some state-of-the-art models produced substantially worse brain predictions. Models trained to recognize speech in background noise produced better brain predictions than models trained to recognize speech in quiet, potentially because hearing in noise imposes constraints on biological auditory representations. The training task influenced the prediction quality for specific cortical tuning properties, with best overall predictions resulting from models trained on multiple tasks. The results generally support the promise of deep neural networks as models of audition, though they also indicate that current models do not explain auditory cortical responses in their entirety.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Investigation of the effects of turbulence modeling on the prediction of compression-ignition combustion unsteadiness

Adverse effects of global warming due to the greenhouse gas emissions is changing the actual paradigm for the use energy resources. In the absence of a mid-term solution for reducing these emissions in transportation, internal combustion (IC) engines are going to coexist in the social spheres in the foreseeable future. Therefore, the study of other IC engine-related problems remains relevant to ensuring the health of the society. In this investigation, a numerical methodology for comprehensive understanding of Noise, Vibration and Harshness in internal combustion engines is proposed. Due to its inherent complexity and lack of awareness, the main objective is to evaluate the impact of the turbulence modeling framework on the in-cylinder acoustic field recreation. Modal decomposition methods have been applied to isolate the coherent flow structures and to analyze how they change with the turbulence approach. Results demonstrate that the choice of the turbulence model is a critical aspect for noise modeling. Unsteady Reynolds-Averaged Navier-Stokes schemes predict a raw estimation of the internal acoustic field with the added value of being computationally less expensive. However, the use of more complex turbulence approaches such us large eddy simulation offers an accurate prediction of the acoustic structures and their cyclic dispersion.

Broatch, A.↗

DOE OSTI2021

Perspectives on the Calibration of CNN Energy Reconstruction in Highly Granular Calorimeters

We present a study which shows encouraging stability of the response linearity for a simulated high granularity calorimeter module reconstructed by a CNN model to miscalibration, bias, and noise effects. Our results also show an intuitive, quantifiable relationship between these factors and the calibration parameters. We trained a CNN model to reconstruct energy in the calorimeter module using simulated single-pion events; we then observed the response of the model under various miscalibration, bias, and noise conditions that affected the model input. From these data, we estimated linear response models to calibrate the CNN. We also quantified the relationship between these factors and the calibration parameters by regression analysis.

Akchurin, Nural↗

DOE OSTI2024

The Shortwave Cloud-SST Feedback Amplifies Multi-Decadal Pacific Sea Surface Temperature Trends: Implications for Observed Cooling

Climate models struggle to produce sea surface temperature (SST) gradient trends in the tropical Pacific comparable to those seen recently in nature. Here, we find that the magnitude of the cloud-SST feedback in the subtropical Southeast Pacific is correlated across models with the magnitude of Eastern Pacific multi-decadal SST variability. A heat-budget analysis reveals coupling between cloud-radiative effects, circulation, and SST gradients in driving multi-decadal variability in the Eastern Pacific. Using this relationship and observed feedback estimates, we find that internal Eastern Pacific SST variability is underestimated in most models. Adjusting for model bias increases the likelihood of generating a cooling trend at least as large as observations in preindustrial control simulations by ~56% on average. If models underestimate climate “noise,” as our results suggest, this bias should be accounted for when attributing the relative importance of forced versus unforced changes in the climate.

58 GEOSCIENCES↗

DOE OSTI2023

De novo design of high-affinity binders of bioactive helical peptides

Many peptide hormones form an α-helix on binding their receptors, and sensitive methods for their detection could contribute to better clinical management of disease. De novo protein design can now generate binders with high affinity and specificity to structured proteins. However, the design of interactions between proteins and short peptides with helical propensity is an unmet challenge. Here we describe parametric generation and deep learning-based methods for designing proteins to address this challenge. We show that by extending RFdiffusion to enable binder design to flexible targets, and to refining input structure models by successive noising and denoising (partial diffusion), picomolar-affinity binders can be generated to helical peptide targets by either refining designs generated with other methods, or completely de novo starting from random noise distributions without any subsequent experimental optimization. The RFdiffusion designs enable the enrichment and subsequent detection of parathyroid hormone and glucagon by mass spectrometry, and the construction of bioluminescence-based protein biosensors. The ability to design binders to conformationally variable targets, and to optimize by partial diffusion both natural and designed proteins, should be broadly useful.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Accuracy of power spectra in dissipationless cosmological simulations

Abstract We exploit a suite of large N-body simulations (up to N = 40963) performed with abacus, of scale-free models with a range of spectral indices n, to better understand and quantify convergence of the matter power spectrum. Using self-similarity to identify converged regions, we show that the maximal wavenumber resolved at a given level of accuracy increases monotonically as a function of time. At 1 per cent level it starts at early times from a fraction of $k_\Lambda$, the Nyquist wavenumber of the initial grid, and reaches at most, if the force softening is sufficiently small, ${\sim}2{-}3 k_\Lambda$ at the very latest times we evolve to. At the $5{{\ \rm per\ cent}}$ level, accuracy extends up to wavenumbers of order $5k_\Lambda$ at late times. Expressed as a suitable function of the scale-factor, accuracy shows a very simple n-dependence, allowing a extrapolation to place conservative bounds on the accuracy of N-body simulations of non-scale-free models like LCDM. We note that deviations due to discretization in the converged range are not well modelled by shot noise, and subtracting it in fact degrades accuracy. Quantitatively our findings are broadly in line with the conservative assumptions about resolution adopted by recent studies using large cosmological simulations (e.g. Euclid Flagship) aiming to constrain the mildly non-linear regime. On the other hand, we remark that conclusions about small-scale clustering (e.g. concerning the validity of stable clustering) obtained using PS data at wavenumbers larger than a few $k_\Lambda$ may need revision in light of our convergence analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Stochastic hydrodynamics and hydro-kinetics: Similarities and differences

The hydro-kinetic formalism has been used as a complementary approach to solving the Stochastic Differential Equations (SDE) corresponding to noisy hydrodynamics. The hydro-kinetic formalism consists of a deterministic set of relaxation type equations that tracks the evolution of 2-point correlation functions of stochastic hydrodynamic quantities. Hence they are comparatively easier to solve than the SDEs, which are computationally intensive and need to deal with arbitrarily large gradients. This work compares the two approaches for the propagation and diffusion of conserved charge fluctuations in the Bjorken hydrodynamic model. For white noise, the two approaches agree. For colored Catteneo noise, which is causal, the two approaches diverge. This is because white noise only induces two-point correlations, while Catteneo noise also induces higher-order correlations. Furthermore, this difference is quantified from the effects of causal evolution and influence from higher-order correlations induced by the Catteneo noise.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Numerically modeling stochastic inflation in slow-roll and beyond

In this work, we present a complete numerical treatment of inflationary dynamics under the influence of stochastic corrections from sub-Hubble modes. We discuss how to exactly model the stochastic noise terms arising from the sub-Hubble quantum modes that give rise to the coarse-grained inflaton dynamics in the form of stochastic differential equations. The stochastic differential equations are solved event by event on a discrete time grid. We then compute the power spectrum of curvature perturbations that can be compared with the power spectrum computed in the traditional fashion using the Mukhanov-Sasaki equation by canonically quantizing the inflaton fluctuations. Our numerical procedure helps us to easily extend the formalism to ultra slow-roll inflation and study the possibility of primordial black hole formation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

NASA’s Pandora SmallSat Mission: Simulating the Impact of Stellar Photospheric Heterogeneity and Its Correction

Stellar photospheric heterogeneity is a dominant astrophysical systematic impacting exoplanet transmission spectroscopy. NASA’s Pandora SmallSat Mission is designed to address this challenge through contemporaneous visible-band photometry and near-infrared spectroscopy of exoplanet host stars. Here, we present an end-to-end simulation study quantifying Pandora’s ability to infer stellar photospheric properties and correct stellar contamination using out-of-transit observations. We construct eight representative stellar activity scenarios and generate 160 simulated Pandora datasets, incorporating time-dependent stellar spectra, instrument response, and noise. Given accurate models, Bayesian retrievals of joint visible photometry (0.4–0.7 μm) and near-infrared spectroscopy (0.9–1.6 μm, R ≈ 120) recover photospheric temperatures with typical uncertainties of ≈30 K, with no significant bias. Models with two spectral components (i.e., a quiescent photosphere and spots) are strongly favored in 95% of cases; one-component models are preferred when true spot filling factors fall below a detection threshold of ≈0.3%. We propagate the true and inferred stellar parameters to compute true, inferred, and residual contamination signals under physically motivated spot geometries. For simple spot distributions, contamination signals of 10 2 –10 3 ppm are reduced to ≲10 ppm—well below Pandora’s expected transmission spectroscopy precision (30–100 ppm). For more complex spot distributions, geometric degeneracies limit deterministic corrections, leaving residual contamination at the 10 3 ppm level that must be mitigated using additional constraints, such as spot-crossing events and joint stellar–planetary retrievals of transmission spectra. These results define regimes in which stellar contamination can be corrected from stellar observations alone and show how Pandora stellar observations can identify cases where additional information is required.

Astronomy and AstroPhysics↗

DOE OSTI2026

Differential Privacy in Grid Kitchen: Implementation & Software Documentation

Sharing of power grid feeder models faces significant challenges due to the potential risk of exposing sensitive operational information. Traditional anonymization techniques have shown notable limitations in other sensitive domains, as evidenced by documented re-identification attacks that combine supposedly anonymized datasets with auxiliary information, raising concerns that similar vulnerabilities could affect power grid data. Consequently, there is a pressing need for a more rigorous privacy protection strategy that not only delivers formal mathematical guarantees but also preserves the analytical value of the shared models. To address this challenge, we have enhanced the Grid Kitchen framework by implementing differential privacy mechanisms within the distribution model dehydration pipeline. This implementation carefully calibrates and applies noise to sensitive attributes in feeder models according to configurable privacy levels—low, moderate, and high—each offering different balances between data utility and privacy protection. Our approach uses established noise functions (Gaussian for continuous data and Discrete Laplace for integer values) with parameters carefully calibrated so that the impact of individual data points is effectively masked in the final output. The integration leverages our Noise Catalog, which we developed to categorize feeder model properties by component type, data type, and sensitivity. This catalog guides the application of appropriate noise functions and privacy parameters ($\varepsilon$ and $\delta$) to each attribute, ensuring consistent privacy protection across the model while maintaining its structural integrity and analytical usefulness. This implementation also includes evaluation tools that allow model owners to assess the impact of privacy-preserving transformations before sharing data with external parties. This report provides documentation for the differential privacy capabilities added to the Grid Kitchen project. It includes a primer on differential privacy concepts and their importance in modern data sharing, details the architecture of our implementation, explains the privacy modes and parameter configurations, and offers practical guidance on using the code for applying differential privacy to grid feeder models. Through examples and code snippets, we demonstrate the effective application of these privacy-enhancing technologies, enabling utility operators and researchers to confidently share grid data while protecting sensitive information.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Optimal Client Sampling in Federated Learning with Client-level Heterogeneous Differential Privacy

Federated Learning with client-level differential privacy (DP) provides a promising framework for collaboratively training models while rigorously protecting clients’ privacy. However, classic approaches like DP-FedAvg struggle when clients have heterogeneous privacy requirements, as they must uniformly enforce the strictest privacy level across all clients, leading to excessive DP noise and significant degradation in model utility. Existing methods to improve the model utility in such heterogeneous privacy settings often assume a trusted server and are largely heuristic, resulting in suboptimal performance and lacking strong theoretical foundations. Here, in this work, we address these challenges under a practical attack model where both clients and the server are honest-but-curious. We propose GDPFed, which partitions clients into groups based on their privacy budgets and achieves client-level DP within each group to reduce the privacy budget waste and hence improve the model utility. Based on the privacy and convergence analysis of GDPFed, we find that the magnitude of DP noise depends on both model dimensionality and the per-group client sampling ratios. To further improve the performance of GDPFed, we introduce GDPFed+, which integrates model sparsification to eliminate unnecessary noise and optimizes per-group client sampling ratios to minimize convergence error. Extensive empirical evaluations on multiple benchmark datasets demonstrate the effectiveness of GDPFed+, showing substantial performance gains compared with state-of-the-art methods.

Xu, Jiahao [Univ. of Nevada, Reno, NV (United Stat↗

DOE OSTI2024

Graph-learning approach to combine multiresolution seismic velocity models

SUMMARY The resolution of velocity models obtained by tomography varies due to multiple factors and variables, such as the inversion approach, ray coverage, data quality, etc. Combining velocity models with different resolutions can enable more accurate ground motion simulations. Toward this goal, we present a novel methodology to fuse multiresolution seismic velocity maps with probabilistic graphical models (PGMs). The PGMs provide segmentation results, corresponding to various velocity intervals, in seismic velocity models with different resolutions. Further, by considering physical information (such as ray path density), we introduce physics-informed probabilistic graphical models (PIPGMs). These models provide data-driven relations between subdomains with low (LR) and high (HR) resolutions. Transferring (segmented) distribution information from the HR regions enhances the details in the LR regions by solving a maximum likelihood problem with prior knowledge from HR models. When updating areas bordering HR and LR regions, a patch-scanning policy is adopted to consider local patterns and avoid sharp boundaries. To evaluate the efficacy of the proposed PGM fusion method, we tested the fusion approach on both a synthetic checkerboard model and a fault zone structure imaged from the 2019 Ridgecrest, CA, earthquake sequence. The Ridgecrest fault zone image consists of a shallow (top 1 km) high-resolution shear-wave velocity model obtained from ambient noise tomography, which is embedded into the coarser Statewide California Earthquake Center Community Velocity Model version S4.26-M01. The model efficacy is underscored by the deviation between observed and calculated traveltimes along the boundaries between HR and LR regions, 38 per cent less than obtained by conventional Gaussian interpolation. The proposed PGM fusion method can merge any gridded multiresolution velocity model, a valuable tool for computational seismology and ground motion estimation.

Geochemistry & Geophysics↗