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DOE OSTI2025

Sensitive detection of structural dynamics using a statistical framework for comparative crystallography

Chemical and conformational changes are crucial to protein function and its pharmacological control. X-ray crystallography can reveal these changes in atomic detail, but standard analysis methods, which refine separate datasets, often overlook differences that are subtle or arise in only a subset of molecules. Direct comparison of crystallographic datasets is, in principle, more powerful, but systematic errors (“scales”) often mask changes in the crystallographic observables (“structure factors”). Machine learning algorithms that jointly estimate scales and structure factors can address this limitation. Here, we augment this approach with multivariate, structured priors derived from crystallographic theory, implemented in the variational deep learning framework Careless. Doing so strongly improves the detection of protein dynamics, element-specific anomalous signals, and the binding of drug candidates, offering a robust approach to comparative crystallography and, potentially, to detection of protein dynamics by other structure determination methods.

Hekstra, Doeke R. [Harvard Univ., Cambridge, MA (U↗

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 OSTI2025

Evaluating User Errors and Temporal Trends in Marine Fish Communities Using 360-Degree Underwater Photography

The use of environmental DNA (eDNA) sampling has been proposed as a complementary method to monitor fish species in marine environments, offering a non-invasive and potentially more efficient approach to marine species observations. eDNA monitoring could be especially useful in and around sites targeted for marine energy generation as these regions need regular monitoring that would be impractical with traditional techniques. Before we can fully rely upon eDNA, we must first verify its accuracy against other proven methods, such as the use of underwater photography. In this study, I deployed a 360-degree camera in the tidal channel of Sequim Bay once a month during several hours overlapping slack tide. I investigated how having multiple people identify and count fish on underwater images could affect the overall results. Using chi square tests in R, I compared my fish identifications and counts to those made by another intern on the same images recorded in August. I found significant differences in the number of species identified and the total individual counts between the two different datasets. I also tested the statistical differences in both Shannon diversity and Pielou evenness indices between the August, September, and November camera deployments using a Hutcheson t-test. Only one significant difference was found in the Shannon index comparisons, and none were found between the Pielou evenness comparisons. These findings show that if multiple identifiers are used to process underwater images, quality control checks must be made to reduce the potential for error. This also points toward the possibility to leverage more advanced image analysis processes, such as automated image analysis software. The findings from this study also show that the dynamics of marine fish communities can vary over a few months; however, further analysis is needed to determine the extent of the seasonal changes in Sequim Bay.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Implementation of a Three-Dimensional Planetary Boundary Layer Parameterization in a Coupled Modeling System and Evaluation of "Gray Zone" Simulations of a Wind-Wave Event Off the US California Coast Using Observations

A three-dimensional (3D) planetary boundary layer (PBL) parameterization was added to the Coupled Ocean Atmosphere Wave Sediment Transport (COAWST) model and the first coupled atmosphere/wave "gray zone" simulations were carried out using the 3D PBL parameterization. A case study of a significant wind-wave event from 4-8 November 2020 off the US west coast was examined, with a focus on the impacts of the event within an approximate 280x280 km central California coastal region covering the Bureau of Ocean Energy Management Morro Bay wind energy lease area. Simulations with both one-dimensional (1D; Yonsei University) and 3D PBL parameterizations were examined in this nest with ..delta..x=400 m. Two-way coupling was active, with near-surface winds feeding back to the wave model and bulk wave statistics feeding back to the atmospheric model. Both simulations compared favorably with buoy observations in capturing the timing and magnitude of wind speed, temperature, dewpoint, and significant wave height, as the front associated with the maritime weather system moved southward across coastal California. However, wind speed errors over land were larger. Time series of the vertical profile of winds below z=250 m from the simulations compared favorably with observations from the US Dept. of Energy Morro Bay Doppler lidar buoy. Differences between the coupled 1D and 3D PBL simulations were minor. The most notable difference was that the simulation using the 3D PBL parameterization had approximately 10 % weaker winds at the peak of the event causing 10 % lower significant wave heights. This difference was shown to be mostly due to differences in the vertical mixing treatment between the parameterizations, in particular the nonlocal downward mixing of higher momentum air in the 1D Yonsei University parameterization in convective conditions. Overall, this work demonstrates that the 3D PBL parameterization can be used in a coupled atmosphere/wave modeling framework with similar behaviors as traditional PBL parameterizations that do not provide horizontal turbulent variances and fluxes.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Atacama Cosmology Telescope: DR6 gravitational lensing and SDSS BOSS cross-correlation measurement and constraints on gravity with the 𝐸 𝐺 statistic

We derive new constraints on the 𝐸 𝐺 statistic as a test of gravity, combining the cosmic microwave background (CMB) lensing map estimated from Data Release 6 (DR6) of the Atacama Cosmology Telescope with Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (SDSS BOSS) CMASS and LOWZ galaxy data. We develop an analysis pipeline to measure the cross-correlation between CMB lensing maps and galaxy data, following a blinding policy and testing the approach through null and consistency checks. By testing the equivalence of the spatial and temporal gravitational potentials, the 𝐸 𝐺 statistic can distinguish Λ⁢ CDM from alternative models of gravity. We find 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢1$^{+0.06}_{−0.05}$ for Atacama Cosmology Telescope (ACT) and CMASS data at 68.28% confidence level, and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢9$^{+0.14}_{−0.11}$ for the ACT and LOWZ. Systematic errors are estimated to be 3% and 4%, respectively. Including CMB lensing information from Planck PR4 results in 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢4$^{+0.05}_{−0.05}$ with CMASS and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢3$^{+0.11}_{−0.09}$ with LOWZ. These are consistent with predictions for the Λ⁢ CDM model that best fits the Planck CMB anisotropy and SDSS BOSS baryon acoustic oscillations (BAO), where 𝐸$^{GR}_{𝐺⁡}$(𝑧 eff =0.555) =0.401 ± 0.005 for CMB lensing combined with CMASS and 𝐸$^{GR}_{𝐺}$⁡(𝑧 eff = 0.316) = 0.452 ± 0.005 combined with LOWZ. We also find 𝐸 𝐺 to be scale independent, with probability to exceed >5%, as predicted by general relativity. The methods developed in this work are also applicable to improved future analyses with upcoming spectroscopic galaxy samples and CMB lensing measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

MIC-DP: A Scalable Correlation-Aware Differential Privacy Framework for High-Dimensional Data

Conventional differential privacy (DP) assumes record independence, limiting effectiveness on real-world datasets with temporal, spatial, or structural correlations. These dependencies undermine privacy guarantees and degrade utility in domains like healthcare, IoT, and smart city analytics. We propose Maximum Information Correlated Differential Privacy (MIC-DP), a novel framework that dynamically calibrates noise based on statistical dependencies. MIC-DP uses the Maximum Information Coefficient (MIC) to capture both linear and nonlinear correlations without explicit modeling, enabling adaptive sensitivity adjustment and improved privacy–utility trade-offs. Evaluations on healthcare (MIMIC), demographic (ACI), and synthetic datasets show that MIC-DP reduces mean absolute error (MAE) by up to 5.2% under strict privacy budgets (ϵ≤1), with aggregate utility improvements reaching 18% across datasets and evaluation metrics. MIC-DP provides formal (ϵ,δ)-privacy guarantees, scales efficiently with feature count, and supports deployment in moderate-scale, privacy-sensitive applications. Its tunable performance and runtime efficiency make MIC-DP suitable for privacy-sensitive applications where low-latency analytics and strong privacy guarantees must coexist. These results demonstrate MIC-DP’s effectiveness as a correlation-aware solution for practical DP.

Yang, Wenjun [Univ. of Washington, Tacoma, WA (Uni↗

DOE OSTI2026

Model-observation discrepancies in Arctic moisture intrusions: causes and pathways for improved simulation

Arctic moisture intrusions (MIs), narrow filaments of strong moisture transport, are key drivers of poleward moisture flux and Arctic weather extremes, yet their representation in climate models is poorly understood. Using a new Arctic MI detection algorithm, we document persistent biases across three CMIP generations (CMIP3–CMIP6): models overestimate MI occurrence over the Pacific sector and underestimate it over the Atlantic sector. These errors stem from misrepresented midlatitude westerly jets, with an equatorward North Atlantic jet associated with too few Atlantic MIs, and a poleward, weakened North Pacific jet linked to too many Pacific MIs. Experiments that correct sea surface temperature and sea ice concentration biases and increase atmospheric resolution improve jet structure and MI statistics, while a cloud-locking simulation indicates that better high-frequency cloud–radiation–circulation interactions can yield further gains. Our results clarify pathways to reducing long-standing MI and jet biases, providing guidance for improving simulations of Arctic and midlatitude climate.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Hourly PM 2.5 Estimates across California from 2018 to 2023

This study presents a new data set of hourly PM 2.5 concentrations across California from 2018 to 2023 at a three-kilometer resolution. This data set was developed by assimilating observations from PurpleAir and the U.S. EPA Air Quality System monitors into wildfire smoke forecasts from the High-Resolution Rapid Refresh Smoke (HRRR-Smoke) model using the Gridpoint Statistical Interpolation (GSI) three-dimensional variational data assimilation framework. Archived forecasts of modeled wildfire smoke PM 2.5 from HRRR-Smoke create the background field for assimilation, which is then corrected using surface observations of total PM 2.5 . The resulting reanalysis from GSI provides an estimate of total PM 2.5 that minimizes error from both the observational and the model data. Validation results indicate strong performance, with monthly R 2 values ranging from 0.73 to 0.91 across the six-year data set, comparable to other PM 2.5 data sets. Case studies are presented for three major fire events, the 2018 Camp Fire, 2019 Kincade Fire, and 2020 Lightning Complex Fires to demonstrate the data set’s fidelity in resolving plume dynamics and local exposure patterns. Root-mean-squared error averaged over each month scales with average PM 2.5 concentrations, resulting in a low error under typical conditions but higher absolute errors during extreme smoke events. This is the first long-term, hourly PM 2.5 data set of its kind for California and enables the generation of subdaily exposure metrics, such as peak hourly concentrations, exceedance durations, and time-of-day exposure peaks. The novelty and strong validation of this data set make it a compelling resource for future studies on the impact and significance of subdaily PM 2.5 exposure.

PM2.5↗

DOE OSTI2025

Improving tropical cyclone rapid intensification forecasts with satellite measurements of sea surface salinity and calibrated machine learning

Forecasting rapid intensification (RI) of tropical cyclones (TC) is a mission known for large errors. One under-researched factor that affects TC intensification is salinity, which is important for density stratification in certain ocean regions and can affect the surface enthalpy flux under a strengthening hurricane. To investigate the impact and efficacy of using salinity information in state-of-the-art forecasting, we use a statistical model consisting of a variety of machine learning (ML) methods. For salinity data, we use satellite measurements of pre-storm sea surface salinity (SSS) as a proxy for the salinity stratification. We train and test the model on various ocean basins, including the Atlantic, eastern North Pacific and western North Pacific. A calibrator is trained on top of the ML models to correct and enhance probability forecasts. The calibrator significantly improves probability forecasts relative to recent works. The ML model performance is improved with the addition of SSS in the Eastern North Pacific, western North Pacific, and the Caribbean subregion of the North Atlantic, and the overall model performance is better than previous studies. SSS decreases model skill for a model trained on the full Atlantic basin. In the Indian Ocean, SSS is also notably correlated with RI occurrence, but the TC samples are not sufficient to train ML models.

hurricane↗

DOE OSTI2025

Time Distribution Analysis for Task Primitives to Support Dynamic Human Reliability Analysis

To support data collection for dynamic human reliability analysis (HRA), this study investigates time distributions for task primitives defined in the Goals, Operators, Methods, and Selection rules (GOMS)–Human Reliability Analysis (HRA) method and Human Reliability data EXtraction (HuREX). GOMS-HRA was developed to provide cognition-based time and human error probability (HEP) information for dynamic HRA calculations within the Human Unimodel for Nuclear Technology to Enhance Reliability (HUNTER) framework, while HuREX is a comprehensive HRA data collection method developed by the Korea Atomic Energy Research Institute (KAERI). In this paper, we examine time distributions by using experimental data collected from the Simplified Human Error Experimental Program (SHEEP) study, which proposes an HRA data collection framework to complement full-scope simulator research and gather input data for dynamic HRA by using simplified simulators such as the Rancor Microworld simulator. This paper investigates whether the time required for GOMS-HRA and HuREX task primitives fits 13 statistical distributions. Additionally, we compare and discuss the time distributions obtained from both student operators and professional operators. The result was that this study identified several time distributions for five GOMS-HRA and four HuREX task primitives. In the future, the results of this study are expected to provide objective reference data on the elapsed time for task primitives and aid in realistically simulating scenarios within dynamic HRA.

Dynamic Human Reliability Analysis↗

DOE OSTI2026

Ensemble Effects on Hydroxide Bond Dissociation Free Energies in Polyoxovanadate Clusters

Understanding structure-property relationships is foundational to numerous modern chemistries, such as proton-coupled electron transfer (PCET). However, an experimentally measured property is the result of the behavior from an ensemble of molecules. Neglecting ensemble effects, especially under complex chemical environments, may obfuscate these relationships and lead to discrepancies between theory and experiment. In this work, we demonstrate the impact of configurational entropy and local chemical environments on hydroxide bond dissociation free energies [BDFE- (O−H)] for a set of polyoxovanadate nanoclusters, at ambient conditions. The O−H bond strengths are investigated via density functional theory (DFT) coupled with statistical thermodynamic analysis and bilinear modeling, and compared with previous experimental results on the same systems, namely electrochemical solutions of: [V 6 O 13−x (OH) x (TRIOL R ) 2 ] −2 (x = 2, 4, 6; R = NO 2 , Me) and [V 6 O 11−x (OMe) 2 (OH) x (TRIOL NO 2 ) 2 ] −2 (x = 2, 4). Interestingly, we find that ensemble effects, even at room temperature, can account for a significant portion of the BDFE(O−H) trend with the degree of reduction via H atom binding, which cannot be fully captured by single-structure, static DFT calculations. Moreover, we find that the ensemble effects may be replicated statistically, requiring only enumeration of energetically accessible H-binding sites. With the ensemble effects resolved, we present a simple bilinear model to reconcile remaining biases between experiment and ensemble-informed theory, which corelate with clusterspecific electronic environment differences. The bilinear model achieves outstanding accuracy vs experiments with a root-mean squared error of 0.4 kcal/mol. Finally, based on the physicochemical characteristics of hydrogen interaction with polyoxometalates, we present a simple methodology that captures the BDFE(O−H) trend while dramatically reducing required DFT calculations by 98% and achieving accuracy within 1 kcal/mol. Overall, this work elucidates the roles and structural origins of configurational entropy and chemical effects on polyoxometalate hydroxide bond energies, with potential applicability to various atomically precise metal oxide systems. Importantly, it introduces models for rapid and highly accurate property calculations in connection with experiments.

Cluster chemistry↗

DOE OSTI2024

Observing Quantum Measurement Collapse as a Learnability Phase Transition

During a quantum measurement, superpositions of states with different observable properties probabilistically collapse into one with a sharp value of the measured observable. In macroscopic quantum systems, this collapse arises via a continuous measurement-induced phase transition (MIPT) at a critical value of the strength of interaction with the measurement apparatus. MIPTs lie outside established paradigms for equilibrium or nonequilibrium critical phenomena and delineate distinct, stable dynamical and computational phases of matter. Quantum computers enable programmable simulation of the interaction of a measurement apparatus with a dynamical quantum system, to explore MIPT phenomena over a range of system sizes while retaining quantum coherence. Yet, existing experimental protocols rely on fundamentally nonscalable postselection techniques or direct classical simulation of quantum circuits. Here, we report the scalable observation of finite-size scaling evidence for an observable-sharpening MIPT in monitored quantum circuits in a chain of Yb + 171 ions in Quantinuum’s H1-1 trapped-ion quantum processor. By leveraging an equivalent description as a statistical physics problem, we implement scalable classical algorithms to infer the value of the measured observable from a single experimental shot. This technique enables a truly scalable protocol to observe observable-sharpening MIPTs in generic classes of circuits that cannot be directly classically simulated and also provides enhanced means to detect and suppress errors in the quantum simulation. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Leveraging design of experiments to build chemometric models for the quantification of uranium (VI) and HNO3 by Raman spectroscopy

Partial least squares regression (PLSR) and support vector regression (SVR) models were optimized for the quantification of U(VI) (10–320 g L −1 ) and HNO 3 (0.6–6 M) by Raman spectroscopy with optimized calibration sets chosen by optimal design of experiments. The designed approach effectively minimized the number of samples in the calibration set for PLSR and SVR by selecting sample concentrations with a quadratic process model, despite complex confounding and covarying spectral features in the spectra. The top PLS2 model resulted in percent root mean square errors of prediction for U(VI), HNO 3 , and NO 3 − of 3.7%, 3.6%, and 2.9%, respectively. PLS1 models performed similarly despite modeling an analyte with a majority linear response (i.e., uranyl symmetric stretch) and another with more covarying vibrational modes (i.e., HNO 3 ). Partial least squares (PLS) model loadings and regression coefficients were evaluated to better understand the relationship between weaker Raman bands and covarying spectral features. Support vector machine models outperformed PLS1 models, resulting in percent root mean square error of prediction values for U(VI) and HNO 3 of 1.5% and 3.1%, respectively. The optimal nonlinear SVR model was trained using a similar number of samples (11) compared with the PLSR model, even though PLS is a linear modeling approach. The generic D-optimal design presented in this work provides a robust statistical framework for selecting training set samples in disparate two-factor systems. This approach reinforces Raman spectroscopy for the quantification of species relevant to the nuclear fuel cycle and provides a robust chemometric modeling approach to bolster online monitoring in challenging process environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Data-driven high-dimensional statistical inference with generative models

Crucial to many measurements at the LHC is the use of correlated multi-dimensional information to distinguish rare processes from large backgrounds, which is complicated by the poor modeling of many of the crucial backgrounds in Monte Carlo simulations. In this work, we introduce HI-SIGMA, a method to perform unbinned high-dimensional statistical inference with data-driven background distributions. In contradistinction to many applications of Simulation Based Inference in High Energy Physics, HI-SIGMA relies on generative ML models, rather than classifiers, to learn the signal and background distributions in the high-dimensional space. These ML models allow for interpretable inference while also incorporating model errors and other sources of systematic uncertainties. We showcase this methodology on a simplified version of a di-Higgs measurement in the bbγγ final state, where the di-photon resonance allows for background interpolation from sidebands into the signal region. We demonstrate that HI-SIGMA provides improved sensitivity as compared to standard classifier-based methods, and that systematic uncertainties can be straightforwardly incorporated by extending methods which have been used for histogram based analyses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

U-net architected deep material network training with microstructure local field information

The Deep Material Network (DMN) has recently emerged as a powerful reduced-order modeling framework for simulating the mechanical response of heterogeneous materials such as composites. Unlike most data-driven approaches that directly learn a material’s response under prescribed loading, the DMN acts as a homogenization operator, learning the kinematic constraints and mechanical interactions of the underlying microstructure. However, traditional DMN training relies exclusively on homogenized effective properties derived from Direct Numerical Simulations (DNS), discarding the rich local field data that govern microstructural interactions. In this work, we extend the DMN framework to incorporate such local field information into the offline training process. Utilizing a U-Net architecture, we augment the DMN training objective to include the first and second statistical moments of the local stress fields obtained from linear DNS. This ensures that the learned network topology not only fits the effective stiffness but also accurately reflects the internal local stress and strain partitioning of the microstructure. The results confirm that supervising the localization process during training yields a superior surrogate model, reducing local prediction errors by an order of magnitude and significantly improving generalization to unseen nonlinear constitutive behaviors compared to traditional DMNs.

36 MATERIALS SCIENCE↗

DOE OSTI2025

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↗