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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Hybrid particle-spectral method for kinetic plasma simulations

A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ~1/$\sqrt{N_p}$ with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly nonequilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Using ARM Observations to Evaluate Process-Interactions in MCS Simulations Across Scales (Final Progress Report)

This project, funded by DOE Atmospheric System Research (DE-SC0020050), focused on improving the representation of mesoscale convective systems (MCSs) in numerical weather and climate models by leveraging high-resolution observations from the DOE Atmospheric Radiation Measurement (ARM) program. The research aimed to evaluate model sensitivities to grid spacing, microphysics, and planetary boundary layer (PBL) schemes, with a particular emphasis on improving convection parameterization for high-resolution modeling. Findings from this work highlight several key advancements. Model validation against ARM radar wind profiler data from the Southern Great Plains (SGP) and Manaus (MAO) sites revealed systematic biases in simulated convective mass flux profiles, leading to the development of an observationally constrained evaluation framework for diagnosing and improving model performance. Sensitivity analyses demonstrated that the representation of Amazonian MCSs was highly dependent on PBL scheme selection, while mid-latitude MCSs were more strongly influenced by microphysics parameterizations. A series of high-resolution WRF simulations, ranging from 4 km to 125 m grid spacing, provided insight into the behavior of convective drafts across scales. While updraft properties converged at sub-kilometer resolutions, biases in downdraft intensity persisted even at the finest resolution tested, emphasizing the need for further refinements in model physics. Additionally, comparisons of MCS vertical structures between mid-latitude and tropical environments revealed stronger updrafts and larger mass flux in mid-latitude MCSs, providing critical insights for improving climate model representations of storm-scale dynamics. The project’s findings have already contributed to advancing numerical modeling capabilities, particularly in WRF, MPAS, ICON, and DOE’s SCREAM model, by refining how convective processes are represented in high-resolution climate simulations. Results were disseminated through peer-reviewed publications, conference presentations, and ARM/ASR Research Highlights, engaging the broader scientific community. The project also provided valuable training opportunities for two postdoctoral researchers, who played central roles in model development, analysis, and dissemination of results. Their work contributed to several publications and conference presentations, helping prepare them for careers in atmospheric modeling. By improving the simulation of MCSs, this research directly supports the development of next-generation climate models capable of more accurately representing extreme precipitation and convective processes. The insights gained will inform future improvements in convective parameterization and guide the design of high-resolution weather and climate simulations, ultimately enhancing the reliability of climate projections and weather forecasts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Comparative verification of hydro-mechanical fracture behavior: Task G of international research project DECOVALEX–2023

Numerical simulations become a necessity when experimental approaches cannot cover the required physical and time scale of interest. One of such area is a simulation of long-term host rock behaviors for nuclear waste disposal and simulation tools involved in the assessment must go through rigorous validation tests. The DECOVALEX project (Development of COupled models and their VAlidation against EXperiments) is dedicated to this purpose by international participants. This work is part of the ongoing phase DECOVALEX–2023 (D–2023, Task G) particularly aiming to simulate fracture behaviors under various conditions. Here, in this study, we cross-verified a variety of numerical methods including continuous and discontinuous approaches against four benchmark exercises with emphasis on numerical accuracy and parameterization of the various numerical approaches. The systematic inter-comparisons of test cases highlight advantages and disadvantages of the different numerical models. Numerical details on discretization effects (e.g. mesh density and orientation) and domain size were investigated in detail for practical applications. It became evident that meticulous attention to mesh resolution and domain size is imperative for achieving accurate numerical simulations, even for static cracks. Moreover, when comparing numerical methods to closed-form solutions for static cracks, all models successfully reproduced the maximum crack opening but encountered challenges near the crack tips. Finally, the paper discusses how to convert between and therefore compare parameters of various numerical approaches. Our benchmark studies reveal that each model necessitates a distinct number of parameters, even in simple scenarios like static crack aperture benchmarks. It is generally more practical to employ fewer parameters to mitigate model over-parameterization and enhance experimental feasibility.

58 GEOSCIENCES↗
DOE OSTI2022

Data-driven causal model discovery and personalized prediction in Alzheimer's disease

Abstract With the explosive growth of biomarker data in Alzheimer’s disease (AD) clinical trials, numerous mathematical models have been developed to characterize disease-relevant biomarker trajectories over time. While some of these models are purely empiric, others are causal, built upon various hypotheses of AD pathophysiology, a complex and incompletely understood area of research. One of the most challenging problems in computational causal modeling is using a purely data-driven approach to derive the model’s parameters and the mathematical model itself, without any prior hypothesis bias. In this paper, we develop an innovative data-driven modeling approach to build and parameterize a causal model to characterize the trajectories of AD biomarkers. This approach integrates causal model learning, population parameterization, parameter sensitivity analysis, and personalized prediction. By applying this integrated approach to a large multicenter database of AD biomarkers, the Alzheimer’s Disease Neuroimaging Initiative, several causal models for different AD stages are revealed. In addition, personalized models for each subject are calibrated and provide accurate predictions of future cognitive status.

Zheng, Haoyang (ORCID:0000000168358242)↗
DOE OSTI2023

Revealing the dynamics of ultrarelativistic non-equilibrium many-electron systems with phase space tomography

The description of physical processes with many-particle systems is a key approach to the modeling of numerous physical systems. For example in storage rings, where ultrarelativistic particles are agglomerated in dense bunches, the modeling and measurement of their phase-space distribution is of paramount importance: at any time the phase-space distribution not only determines the complete space-time evolution but also provides fundamental performance characteristics for storage ring operation. Here, we demonstrate a non-destructive tomographic imaging technique for the 2D longitudinal phase-space distribution of ultrarelativistic electron bunches. For this purpose, we utilize a unique setup, which streams turn-by-turn near-field measurements of bunch profiles at MHz repetition rates. To demonstrate the feasibility of our method, we induce a non-equilibrium state and show that the phase-space distribution microstructuring as well as the phase-space distribution dynamics can be observed in great detail. Our approach offers a pathway to control ultrashort bunches and supports, as one example, the development of compact accelerators with low energy footprints.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Tracing the Mott-Hubbard transition in one-dimensional Hubbard models without Umklapp scattering

Here we apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction U equals the bandwidth U c = W, where the single-particle gap opens linearly, Δ(U ≥ W) = U - W. The simple nature of the elementary excitations permits us to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution $n_k$ at the Fermi wave number $k_F$ = 0 cannot be used to locate accurately U c from finite-size systems. However, the slope of $n_k$ at the band edges $k_B$ = ±π, reveals the formation of a single-particle bound state which can be used to determine U c reliably from $n_k$ using accurate finite-size data.

1-dimensional systems↗
DOE OSTI2026

Reformulating a Gurson-based dynamic damage model and demonstrating improved predictive power and numerical robustness

The original Tepla (TEnsile PLAsticity) ductile damage model, based on the Gurson yield surface, has long been used to model damage evolution and material failure under dynamic loading. Unfortunately, Tepla suffered from mesh sensitivity, numerical instability, and limited predictive capability. Here, we theoretically reformulate Tepla to address these issues. We especially focus on the prediction of porosity, which is the key state variable used for modeling ductile damage, as compared to more easily measured surface velocities, which are at best an indirect measure of damage. Key model changes include separating the viscosity during volumetric void growth from underlying shear strength behavior and switching to an iterative bisection solver. The new Tepla is then calibrated on incipient spall experiments on half-hard copper and tantalum, which demonstrate its ability to simultaneously fit the model to recovered porosity distributions and measured surface velocities, a stringent test. Improved numerical behavior, such as greatly reduced mesh sensitivity, is also shown in those simulations. Finally, the new Tepla model is applied to several high-explosive loaded, sweeping wave experiments, showing the ability of the model to predict behavior on tests with significantly different loading conditions and histories than the calibration data.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Numerical simulations of membrane distillation systems with actively heated membranes

Membrane distillation (MD) is a thermal desalination process that is gaining attention for treating hypersaline brines. One recent approach uses composite membranes with a thermally conductive layer that delivers heat to the membrane–feed interface, where it drives evaporation. Though this increases single-pass recovery, it comes with the challenge of promoting lateral heat conduction through the thin membrane. Herein, we develop a 3D, computational fluid dynamics (CFD) model that simulates conjugate heat, mass, and momentum transport in the feed channel and composite membrane. We then use the CFD to verify a simpler numerical model that approximates the feed velocity field analytically. We validate the numerical model experimentally, and use it to investigate the impacts of the conductive layer thickness, feed channel geometry, and operating conditions on temperature and concentration polarization, permeate production, and specific energy consumption. Overall, we find that lateral heating increases permeate production at the expense of increased concentration polarization. In extreme cases, the concentration increases more than four-fold along the membrane surface. Furthermore, we show however, that the feed flow rate and conductive layer thickness can be tailored to mitigate concentration polarization, for only a small reduction in permeate production.

42 ENGINEERING↗
DOE OSTI2019

Numerical Simulation of the Three-Phase Flow of a Bubble Interacting with the Steel–Slag Interface During the Secondary Refining Process

Gas stirring is an effective method for the secondary refining process of steel. The microphenomena among the phases of an argon bubble floating in steel and motion across the steel–slag interface were simulated and discussed with a sharp interface tracking method. A water-model experiment was set to validate the numerical model, and the experimental results showed agreement with the numerical model. A critical size for bubbles to pass the interface was found using the model.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Modeling framework for evaluating the impacts of hydrodynamic pressure on hydrologic exchange fluxes and residence time for a large-scale river section over a long-term period

Quantifying hydrologic exchange fluxes (HEF) at the river and subsurface interface and their residence times (RT) in subsurface are important for managing the water quality and ecosystem health in dynamic river corridor systems. In this study, a modeling framework is developed for coupling the three-dimensional (3D) multi-phase surface, subsurface flow transport, and numerical tracer model for RT in a large-scale river section over a long period. The framework is utilized to evaluate the impacts of hydrodynamic pressure on HEFs and RT for a 30 km section of the Columbia River in Washington State over a three-year period. Based on comparisons between model simulations with and without considering hydrodynamic pressure, we found that hydrodynamic pressure increases the net HEFs by 7% with river gaining water from the subsurface domain, and leads to slight reduction of RT.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Opportunities and Challenges of Computational Electromagnetics Methods for Superconducting Circuit Quantum Device Modeling: A Practical Review

High-fidelity numerical methods that model the physical layout of a device are essential for the design of many technologies. For methods that characterize electromagnetic effects, these numerical methods are referred to as computational electromagnetics (CEM) methods. Although the CEM research field is mature, emerging applications can still stress the capabilities of the techniques in use today. The design of superconducting circuit quantum devices falls in this category due to the unconventional material properties and important features of the devices covering nanometer to centimeter scales. Such multiscale devices can stress the fundamental properties of CEM tools which can lead to an increase in simulation times, a loss in accuracy, or even cause no solution to be reliably found. While these challenges are being investigated by CEM researchers, knowledge about them is limited in the broader community of users of these CEM tools. This review is meant to serve as a practical introduction to the fundamental aspects of the major CEM techniques that a researcher may need to choose between to model a device, as well as provide insight into what steps they may take to alleviate some of their challenges. Our focus is on highlighting the main concepts without rigorously deriving all the details, which can be found in many textbooks and articles. After covering the fundamentals, we discuss more advanced topics related to the challenges of modeling multiscale devices with specific examples from superconducting circuit quantum devices. We conclude with a discussion on future research directions that will be valuable for improving the ability to successfully design increasingly more sophisticated superconducting circuit quantum devices. Although our focus and examples are taken from this area, researchers from other fields will still benefit from the details discussed here.

Elkin, Samuel T. [Virginia Tech., Blacksburg]↗
DOE OSTI2023

A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed here by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An experimentally validated mesoscale model for the effective thermal conductivity of U-Zr fuels

An experimentally validated mesoscale model was developed to simulate the effective thermal conductivity (ETC) of metallic U and U–Zr nuclear fuels. The effects of microstructure, temperature, composition, and interfacial thermal resistance (ITR) were investigated. Companion experiments were conducted to validate the model. The numerical simulations clearly demonstrate that accounting for the interface (Kapitza) thermal resistance and Zr precipitation is necessary to improve the model predictions. The dependence of the effective Kapitza resistance of depleted-U and U-10Zr on temperature was determined. Finally, for both materials, the largest difference between the model calculations and the experimental data was about 4.5%, which is within the precision of the experimental measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Self-Supervised and Interpretable Anomaly Detection Using Network Transformers

Machine learning and deep neural networks (DNNs) have been proposed as a tool to identify anomalies in computer network communications. However, due the obfuscated nature of off-the-shelf machine learning models, their output often does not provide enough information to isolate the source of the anomaly to take corrective measures. In this article, we introduce the network transformer (NeT), a DNN model for anomaly detection that incorporates the graph structure of the communication network in order to improve interpretability. Further, the presented approach has the following advantages: first, enhanced interpretability by incorporating the graph structure of computer networks; second, provides a hierarchical set of features that enables analysis at different levels of granularity; second, self-supervised training that does not require labeled data. The NeT model was evaluated on a set of anomalous scenarios executed in a real industrial control system. The presented approach successfully identified the anomalies, the devices affected, and the specific connections causing the anomalies, providing a data-driven hierarchical approach to analyze the behavior of a cyber network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Progress Report on An Exascale Computational Simulation Capability for Pervasive Fracture & Failure

How does a structure fail in an explosion? Is there an engineering design opportunity to mitigate the effects of a blast? These are questions that may be addressed with simulation; however, a computational simulation capability to answer these questions must include developments in material physics modeling and numerical algorithms that we believe are possible, but do not yet exist. This LDRD project proposes to develop the physics models and computational approaches to create a computational simulation approach to answer these physics and engineering questions.

42 ENGINEERING↗
DOE OSTI2019

Application of Machine Learning and Artificial Intelligence in Proxy Modeling for Fluid Flow in Porous Media

Reservoir simulation models are the major tools for studying fluid flow behavior in hydrocarbon reservoirs. These models are constructed based on geological models, which are developed by integrating data from geology, geophysics, and petro-physics. As the complexity of a reservoir simulation model increases, so does the computation time. Therefore, to perform any comprehensive study which involves thousands of simulation runs, a very long period of time is required. Several efforts have been made to develop proxy models that can be used as a substitute for complex reservoir simulation models. These proxy models aim at generating the outputs of the numerical fluid flow models in a very short period of time. This research is focused on developing a proxy fluid flow model using artificial intelligence and machine learning techniques. In this work, the proxy model is developed for a real case CO2 sequestration project in which the objective is to evaluate the dynamic reservoir parameters (pressure, saturation, and CO2 mole fraction) under various CO2 injection scenarios. The data-driven model that is developed is able to generate pressure, saturation, and CO2 mole fraction throughout the reservoir with significantly less computational effort and considerably shorter period of time compared to the numerical reservoir simulation model.

Amini, Shohreh↗