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DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A machine learning pipeline for membrane segmentation of cryo-electron tomograms

We describe how to use several machine learning techniques organized in a learning pipeline to segment and identify cell membrane structures from cryo electron tomograms. These tomograms are difficult to analyze with traditional segmentation tools. The learning pipeline in our approach starts from supervised learning via a special convolutional neural network trained with simulated data. It continues with semi-supervised reinforcement learning and/or a region merging technique that tries to piece together disconnected components belonging to the same membrane structure. A parametric or non-parametric fitting procedure is then used to enhance the segmentation results and quantify uncertainties in the fitting. Domain knowledge is used in generating the training data for the neural network and in guiding the fitting procedure through the use of appropriately chosen priors and constraints. We demonstrate that the approach proposed here works well for extracting membrane surfaces in two real tomogram datasets.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

NaroNet: Discovery of tumor microenvironment elements from highly multiplexed images

Understanding the spatial interactions between the elements of the tumor microenvironment -i.e. tumor cells. fibroblasts, immune cells- and how these interactions relate to the diagnosis or prognosis of a tumor is one of the goals of computational pathology. We present NaroNet, a deep learning framework that models the multi-scale tumor microenvironment from multiplex-stained cancer tissue images and provides patient-level interpretable predictions using a seamless end-to-end learning pipeline. Trained only with multiplex-stained tissue images and their corresponding patient-level clinical labels, NaroNet unsupervisedly learns which cell phenotypes, cell neighborhoods, and neighborhood interactions have the highest influence to predict the correct label. To this end, NaroNet incorporates several novel and state-of-the-art deep learning techniques, such as patch-level contrastive learning, multi-level graph embeddings, a novel max-sum pooling operation, or a metric that quantifies the relevance that each microenvironment element has in the individual predictions. We validate NaroNet using synthetic data simulating multiplex-immunostained images where a patient label is artificially associated to the -adjustable- probabilistic incidence of different microenvironment elements. We then apply our model to two sets of images of human cancer tissues: 336 seven-color multiplex-immunostained images from 12 high-grade endometrial cancer patients; and 382 35-plex mass cytometry images from 215 breast cancer patients. In both synthetic and real datasets, NaroNet provides outstanding predictions of relevant clinical information while associating those predictions to the presence of specific microenvironment elements.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Yield strength prediction of high-entropy alloys using machine learning

Yield strength at high temperature is an important parameter in the design and application of high entropy alloys (HEAs). However, the experimental measurement of yield strength at high temperature is quite costly, complicated, and time-consuming. Therefore, it is essential to identify and apply a robust method for the accurate prediction of yield strength at high temperature from the available experimental and simulation data. In this study, for the first time, a machine learning (ML) method based on the regression technique of random forest (RF) regressor is used to predict the yield strength of HEAs at the desired temperature. Further, the yield strengths of MoNbTaTiW and HfMoNbTaTiZr at 800 °C and 1200 °C, are predicted using the RF regressor model. We find that the results are consistent with the experimental reports, showing that the RF regressor model predicts the yield strength of HEAs at the desired temperatures with high accuracy.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Numerical integration of detector response functions via Monte Carlo simulations

Calculations of detector response functions are complicated because they include the intricacies of signal creation from the detector itself as well as a complex interplay between the detector, the particle-emitting target, and the entire experimental environment. As such, these functions are typically only accessible through time-consuming Monte Carlo simulations. Furthermore, the output of thousands of Monte Carlo simulations can be necessary in order to extract a physics result from a single experiment. Here we describe a method to obtain a full description of the detector response function using Monte Carlo simulations. We also show that a response function calculated in this way can be used to create Monte Carlo simulation output spectra a factor of ~1000× faster than running a new Monte Carlo simulation. A detailed discussion of the proper treatment of uncertainties when using this and other similar methods is provided as well. Here, this method is demonstrated and tested using simulated data from the Chi-Nu experiment, which measures prompt fission neutron spectra at the Los Alamos Neutron Science Center.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2018

Investigation of Compton scattering for gamma beam intensity measurements and perspectives at ELI-NP

Compton γ-ray sources have been used for over 30 years with new facilities being under construction or proposed. The gamma beam system under implementation at the Extreme Light Infrastructure - Nuclear Physics facility in Romania will deliver brilliant γ-ray beams with energies up to 19.5 MeV. Several instruments for measuring the parameters of the γ-ray beam are under development at ELI-NP. One of these instruments based on a High Purity Germanium detector is typically used for beam energy measurements at other facilities. Here we investigate the use of a High Purity Germanium detector to continuously monitor the intensity of the ELI-NP gamma beam by measuring the inelastic scattering of photons. This technique relies on both experimental and simulated data and it has been successfully tested during a recent experiment at the High Intensity γ-ray Source facility.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Unsupervised domain adaptation for radioisotope identification in gamma spectroscopy

Training machine learning models for radioisotope identification using gamma spectroscopy remains an elusive challenge for many practical applications, largely stemming from the difficulty of acquiring and labeling large, diverse experimental datasets. Simulations can mitigate this challenge, but the accuracy of models trained on simulated data can deteriorate substantially when deployed to an out-of-distribution operational environment. In this study, we demonstrate that unsupervised domain adaptation (UDA) can improve the ability of a model trained on synthetic data to generalize to a new testing domain, provided unlabeled data from the target domain are available. Conventional supervised techniques are unable to utilize this data because the absence of isotope labels precludes defining a supervised classification loss. Instead, we first pretrain a spectral classifier using labeled synthetic data and subsequently leverage unlabeled target data to align the learned feature representations between the source and target domains. We compare a range of different UDA techniques, finding that minimizing the maximum mean discrepancy (MMD) between source and target feature vectors yields the most consistent improvement to testing scores. For instance, using a custom transformer-based neural network, we achieved a testing accuracy of $0.904 \pm 0.022$ on an experimental LaBr test set after performing unsupervised feature alignment via MMD minimization, compared to $0.754 \pm 0.014$ before alignment. Overall, our results highlight the potential of using UDA to adapt a radioisotope classifier trained on synthetic data for real-world deployment.

Lalor, Peter W.↗

DOE OSTI2026

Rapid neutron and gamma-ray source localization using machine learning

Rapid localization of radiation sources is critical for applications including nuclear emergency response, safeguards, and security. However, conventional imaging systems such as neutron scatter cameras and Compton cameras depend on rare coincidence events, which often result in long acquisition times. In this work, we address the challenge of rapid source localization by developing a machine learning approach to predict the direction of a single radiation source using only count rates from an array of neutron and gamma-ray detectors. The proposed model is a fully connected neural network (FCNN) trained using Monte Carlo simulation data from a 252 Cf source. The model hyperparameters are optimized with a small set of routine 252 Cf measurements. We benchmarked the performance of the trained and optimized machine learning model using additional 252 Cf , 137 Cs , and PuBe measurements under laboratory conditions with varying source-detector configurations. For these measurements, the machine learning model achieved a mean localization error smaller than 30° with 3 x 10 3 system counts, corresponding to 8 s measurement time for the imaging system used in this work. In this low-statistics regime, the method outperformed traditional scatter-based imaging by more than 75% in localization accuracy for the evaluated measurement configurations. These results demonstrate that a machine learning-based approach can significantly reduce the time required for accurate single-source localization, providing a robust and computationally efficient alternative to traditional imaging systems in time-critical nuclear security and emergency response scenarios.

Gamma-ray imaging↗

DOE OSTI2022

Development and assessment of a reactor system prognosis model with physics-guided machine learning

Autonomous control systems provide recommendations to help operators in decision-making during plant operations ranging from normal operation to accident management. An important step of autonomous control is prognosis. In nuclear engineering domain, prognosis is the process of predicting future conditions of a system or equipment based on present signs and symptoms of a fault. The prognosis model allows predicting future reactor states for possible candidate control strategies so that the outcomes can be evaluated to determine the best control strategy. The prognosis model requires representing direct relationships between the symptoms and the predictions. In nuclear engineering, computational simulations are approximate representations of the operation of the real system. However, prognosis with computational simulations requires high computation power and time due to possible large number of scenarios. Necessary computation resources can be reduced with machine learning (ML) approach for fast predictions by building a surrogate function using the simulation data. A critical issue is, ML models are ignorant of physical knowledge, and these models approximate statistical relationships between the system variables. This ignorance can produce results that are inconsistent with physical laws, even if an optimal result is achieved from a mathematical point of view. Physics-guided machine learning (PGML) is an approach to tackle this issue. Here, this work formulates and illustrates a framework to guide development and assessment of the ML-based prognosis model for autonomous control systems. The development of the prognosis model considers the training of a ML model which consists of optimizing many aspects of the ML approach. The assessment of the prognosis model considers training data limitations and uncertainties of the ML approach. Prognosis models with standalone ML and PGML are developed and assessed on the loss-of-flow scenario of Experimental Breeder Reactor II. The results indicate that PGML based prognosis model has the best performance compared to other prognosis models.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Development and assessment of models for turbulent Rayleigh-Taylor mixing using the macroscopic forcing method

Reynolds-Averaged Navier Stokes (RANS) simulations are a popular method for designing ICF experiments, and accurate mixing models are crucial for these simulations to give good predictions. To this end, the present work seeks to demonstrate the Macroscopic Forcing Method (MFM) as a tool for both improving existing RANS models as well as assessing RANS model forms. First, MFM analysis from Lavacot et al. (Phys. Rev. Fluids, 2025) is used to develop the k–L–F model, an extension of the k–L model of Dimonte and Tipton (Phys. Fluids, 2006) that incorporates nonlocality through addition of a turbulent species flux transport equation. MFM is then applied to the k–L–F model along with the k–L and BHR–4 models to assess their forms and compare the model-implied eddy diffusivity moments to those measured from high-fidelity simulations. Furthermore, the analysis reveals that models incorporating nonlocality (k–L–F and BHR–4) match the high-fidelity simulation data better than purely local models (k–L), both in terms of mean fields and eddy diffusivity moments. However, all of the considered RANS models struggle to match temporal moments at high Atwood numbers, highlighting the importance of temporal nonlocality in these regimes and the need for additional improvement even among models incorporating nonlocality.

general physics↗

DOE OSTI2022

Probing criticality with deep learning in relativistic heavy-ion collisions

Systems with different interactions could develop the same critical behavior due to the underlying symmetry and universality. Using this principle of universality, we can embed critical correlations modeled on the 3D Ising model into the simulated data of heavy-ion collisions, hiding weak signals of a few inter-particle correlations within a large particle cloud. Employing a point cloud network with dynamical edge convolution, we are able to identify events with critical fluctuations through supervised learning, and pick out a large fraction of signal particles used for decision-making in each single event.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Experimental validation of scintillator detector response to correlated neutrons with MCNP and associated packages

Time, energy, and angle correlated neutrons are emitted in nuclear fission. New, physics-based fission event generators that capture these correlations have been incorporated into MCNP6.2 because correlations can impact nuclear non-proliferation and safeguards systems response. DRiFT is a detector response code that takes MCNP outputs and reproduces laboratory analogous detector quantities. Previous work has compared DRiFT to single detector experiment data and has discussed recent updates to DRiFT specific to correlated fission experiments. In this work, we demonstrate a validation of recent updates to DRiFT for organic scintillator response in correlated fission neutron experiments using a 252Cf source. Furthermore, outputs from MCNP with the FREYA fission event generator were post-processed with DRiFT and compared to experiment data. Simulation and experiment results are in reasonably good agreement for multiple correlated neutron quantities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2016

Assessment of HRA method predictions against operating crew performance: Part III: Conclusions and achievements

This is the last in a series of three papers documenting two large-scale human reliability analysis (HRA) empirical studies – the International HRA Empirical Study and the US HRA Empirical Study. The goal of the two studies was to develop an empirically-based understanding of the performance, strengths, and weaknesses of HRA methods by comparing HRA method predictions against actual operator performance in simulated accident scenarios on nuclear power plant (NPP) simulators. This paper first addresses areas where there is convergence between the two studies and where differences lie. Then it summarizes the combined insights and conclusions, including key findings on HRA in general through lessons learned about the HRA methods assessed in the studies and specific recommendations for improving guidance, practice and methods. Then it discusses the relevance and usefulness of simulator data for HRA in general. Finally, it presents the key achievements and overall conclusions of the two studies taken together.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. Furthermore, the Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

How we compute N matters to estimates of mixing in stratified flows

We know that most commonly used models for turbulent mixing in the ocean rely on a background stratification against which turbulence must work to stir the fluid. While this background stratification is typically well defined in idealized numerical models, it is more difficult to capture in observations. Here, a potential discrepancy in ocean mixing estimates due to the chosen calculation of the background stratification is explored using direct numerical simulation data of breaking internal waves on slopes. There are two different methods for computing the buoyancy frequency $N$ , one based on a three-dimensionally sorted density field (often used in numerical models) and the other based on locally sorted vertical density profiles (often used in the field), are used to quantify the effect of $N$ on turbulence quantities. It is shown that how $N$ is calculated changes not only the flux Richardson number $R_{f}$ , which is often used to parameterize turbulent mixing, but also the turbulence activity number or the Gibson number $Gi$ , leading to potential errors in estimates of the mixing efficiency using $Gi$ -based parameterizations.

42 ENGINEERING↗

DOE OSTI2024

Numerical validation of scaling laws for stratified turbulence

Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective Péclet number of the flow. Two types of asymptotic models have been proposed, which yield measurably different predictions for the characteristic vertical velocity and length scale of the turbulent eddies in both diffusive and non-diffusive regimes. The first, termed a ‘single-scale model’, is designed to describe flow structures having large horizontal and small vertical scales, while the second, termed a ‘multiscale model’, additionally incorporates flow features with small horizontal scales, and reduces to the single-scale model in their absence. By comparing predicted vertical velocity scaling laws with direct numerical simulation data, we show that the multiscale model correctly captures the properties of strongly stratified turbulence within regions dominated by small-scale isotropic motions, whose volume fraction decreases as the stratification increases. Meanwhile its single-scale reduction accurately describes the more orderly, layer-like, quiescent flow outside those regions.

Mechanics↗

DOE OSTI2017

Topologically Guided, Automated Construction of Metal–Organic Frameworks and Their Evaluation for Energy-Related Applications

Metal-organic frameworks (MOFs) are promising materials for a range of energy and environmental applications. Here we describe in detail a computational algorithm and code to generate MOFs based on edge-transitive topological nets for subsequent evaluation via molecular simulation. This algorithm has been previously used by us to construct and evaluate 13 512 MOFs of 41 different topologies for cryo-adsorbed hydrogen storage. Grand canonical Monte Carlo simulations are used here to evaluate the 13 512 structures for the storage of gaseous fuels such as hydrogen and methane and nondistillative separation of xenon/krypton mixtures at various operating conditions. MOF performance for both gaseous fuel storage and xenon/krypton separation is influenced by topology. In conclusion, simulation data suggest that gaseous fuel storage performance is topology-dependent due to MOF properties such as void fraction and surface area combining differently in different topologies, whereas xenon/krypton separation performance is topology-dependent due to how topology constrains the pore size distribution.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Learning Coarse-Grained Potentials for Binary Fluids

Even though atomistic and CG models have been used to simulate liquid nanodroplets in vapor, very few rigorous studies of the liquid-liquid interface structure are available, and most of them are limited to planar interfaces. In this work, we evaluate several existing force fields (FF)s, including two atomistic and three CG FFs, with respect to modeling the interface structure and thermodynamic properties of the water-hexane interface. Both atomistic FFs are able to quantitatively reproduce the interfacial tension and the coexisting densities of the experimentally-observed planar interface. We use the atomistic FFs to model water droplets in hexane and use these simulations to test the CG FFs. We found that the tested CG FFs cannot reproduce the interfacial tensions of planar and/or curved interfaces. Finally, we propose a new approach for learning coarse-grained (CG) potentials within the CG SDK (Shinoda-DeVane- Klein) FF framework from atomistic simulation data. We demonstrate that the new potential significantly improves the prediction of both the interfacial tension and structure of water-hexane planar and curved interfaces.

Gao, Peiyuan↗