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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Aeroelastic oscillations of a pitching flexible wing with structural geometric nonlinearities: Theory and numerical simulation

In this paper, we focus on the derivation of an analytical model of the aeroelastic dynamics of an elastically mounted flexible wing. This equations of motion obtained serve to help understand the behaviour of the aeroelastic wind tunnel setup in question, which consists of a rectangular wing with a uniform NACA 0012 airfoil profile, whose base is free to rotate rigidly about a longitudinal axis. Of particular interest are the structural geometric nonlinearities primarily introduced by the coupling between the rigid body pitch degree-of-freedom and the continuous system. A coupled system of partial differential equations (PDEs) coupled with an ordinary differential equation (ODE) describing axial-bending-bending-torsion-pitch motion is derived using Hamilton's principle. A finite dimensional approximation of the system of coupled differential equations is obtained using the Galerkin method, leading to a system of coupled nonlinear ODEs. Subsequently, these nonlinear ODEs are solved numerically using Houbolt's method. The results that are obtained are verified by comparison with the results obtained by direct integration of the equations of motion using a finite difference scheme. Adopting a linear unsteady aerodynamic model, it is observed that the system undergoes coalescence flutter due to coupling between the rigid body pitch rotation dominated mode and the first flapwise bending dominated mode. Finally, the behaviour of the limit cycle oscillations is primarily influenced by the structural geometric nonlinear terms in the coupled system of PDEs and ODE.

42 ENGINEERING↗
DOE OSTI2024

Efficient general method for numerically modeling laser pulse propagation, overlap, and lifetime effects in amplifiers

An efficient numerical time-dependent general method is developed to address incoherent pulse overlap and lifetime effects in laser amplifiers. The alternating propagation-population laser energetics method (APPLE) has been validated against a semi-discrete coupled rate equation numerical method (SDRE) and analytic formalisms in bounding cases. APPLE is based on decoupled rates applied to a time-dependent framework where both space-time-dependent populations and pulse energetics are consistently updated in each time step. A significant advantage of APPLE lies in its conceptual simplicity, ease of implementation, and relatively small computational cost. SDRE tracks the populations through coupled rates and uses the method of lines to discretize the hyperbolic partial differential transport equations allowing for use of ordinary differential equation solvers. With reasonably sized mesh, we report both energetic and power pulse shape relative differences on the order of one percent between the models over a large range of initial conditions.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Quandary

Quandary numerically simulates and optimizes the time-evolution of open quantum systems. The underlying dynamics are modelled by Lindblad's master equation, a linear ordinary differential equation (ODE) describing quantum systems interacting with the environment. Quandary solves this ODE numerically by applying a time-stepping integration scheme, and utilizes a gradient-based optimization approach to determine optimal control pulses that drive the quantum system to a desired target state. Two optimization objectives are considered: (a) Unitary gate optimization that finds controls to realize a unitary gate transformation, and (b) optimal reset that aims to drive the quantum system to the ground states. Gradient-based optimization schemes utilizing Petsc's Tao optimization package are applied to generate control pulses that minimize the respective measure. To evaluate the gradient of the objective function, the discrete adjoint method is used while leveraging techniques from Algorithmic Differentiation to produce exact and consistent gradients. To mitigate excessive execution run times, the software can be build together with the XBraid software library which provides a parallelization strategy to distribute the time-evolution of the underlying dynamics onto multiple processor.

Petersson, NilsA.↗
DOE OSTI2022

MULTISTEP AND CONTINUOUS PHYSICS-INFORMED NEURAL NETWORK METHODS FOR LEARNING GOVERNING EQUATIONS AND CONSTITUTIVE RELATIONS

In this work, we investigate the applicability and relative merit of discrete and continuous versions of physics-informed neural network (PINN) methods for learning unknown governing equations or constitutive relations in a nonlinear dynamical system. In the case of unknown dynamics, entire right-hand-side (RHS) equations of the ordinary differential equations are unknown. In the case of unknown constitutive relations, however, the RHS equations are known up to the specification of constitutive relations (that may depend on the state of the system). We use a deep neural network to model unknown governing equations or constitutive relations. The discrete PINN approach combines classical multistep discretization methods for dynamical systems with neural-network-based machine learning methods. On the other hand, the continuous versions utilize deep neural networks to minimize the residual function for the continuous governing equations. We use the case of a fedbatch bioreactor system to study the effectiveness of these approaches and discuss conditions for their applicability. Our results indicate that the accuracy of the trained neural network models is much higher for the cases where we only have to learn a constitutive relation instead of all dynamics. This finding corroborates the well-known fact from scientific computing that building as much structural information as is available into an algorithm can enhance its efficiency and/or accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Latent Neural ODE for Integrating Multi-Timescale Measurements in Smart Distribution Grids

Under a smart grid paradigm, there has been an increase in sensor installations to enhance situational awareness. The measurements from these sensors can be leveraged for real-time monitoring, control, and protection. However, these measurements are typically irregularly sampled. These measure-ments may also be intermittent due to communication bandwidth limitations. To tackle this problem, this paper proposes a novel latent neural ordinary differential equations (LODE) approach to aggregate the unevenly sampled multivariate time-series measurements. The proposed approach is flexible in performing both imputations and predictions while being computationally efficient. Simulation results on IEEE 37 bus test systems illustrate the efficiency of the proposed approach.

multi time-scale measurements↗
DOE OSTI2022

Physics-Informed Neural Network Solution of Point Kinetics Equations for a Nuclear Reactor Digital Twin

A digital twin (DT) for nuclear reactor monitoring can be implemented using either a differential equations-based physics model or a data-driven machine learning model. The challenge of a physics-model-based DT consists of achieving sufficient model fidelity to represent a complex experimental system, whereas the challenge of a data-driven DT consists of extensive training requirements and a potential lack of predictive ability. We investigate the performance of a hybrid approach, which is based on physics-informed neural networks (PINNs) that encode fundamental physical laws into the loss function of the neural network. We develop a PINN model to solve the point kinetic equations (PKEs), which are time-dependent, stiff, nonlinear, ordinary differential equations that constitute a nuclear reactor reduced-order model under the approximation of ignoring spatial dependence of the neutron flux. The PINN model solution of PKEs is developed to monitor the start-up transient of Purdue University Reactor Number One (PUR-1) using experimental parameters for the reactivity feedback schedule and the neutron source. The results demonstrate strong agreement between the PINN solution and finite difference numerical solution of PKEs. We investigate PINNs performance in both data interpolation and extrapolation. For the test cases considered, the extrapolation errors are comparable to those of interpolation predictions. Extrapolation accuracy decreases with increasing time interval.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

PETN spark-gap detonators

The well-developed theory of Lorentz plasma that is dominated by electron–ion interactions is used to calculate the PETN arc characteristics. The spark-gap discharge current is a ramp with 10 to 25 ns rise time to peak and remaining constant subsequently. The approximate formulas for the arc channel conductivity, arc temperature, arc radius, and shock pressure from the arc are obtained from a system of nonlinear ordinary differential equations, which is the similarity solution of hydrodynamic equations similar to the Braginskii approximation. These arc parameters are given for the peak current ranging from 100 A to 1000 A and with different rise times. Representative cases are compared to the nonlinear ordinary differential equation code results. The shock pressures at the peak current are comparable to those from a typical commercial EBW bridgewire burst reported in the literature; the arc radius at the peak current is comparable to a typical bridgewire diameter of 0.0375 mm (e.g., RISI detonators, RP-1, and RP-80). The relevant Pop-Plot for low-density PETN is converted into an empirical detonation criterion, which is applicable to explosives subject to shocks of variable pressure. Finally, this criterion is then used to determine the detonation thresholds, which are comparable with test data obtained by Tucker, et al.

42 ENGINEERING↗
DOE OSTI2022

ILI Code

This R code consists of three scripts, described below. 1. ILI_LHC_sample.R The first script generate 10,000 samples from the total parameter space formed by the ranges of the following five parameters inputted into the ILI model: transmission rate (beta), per capita rate of progress from exposed to infectious state (gamma_1), per capita rate of progress through initial infectious state (gamma_2), per capita rate of progress through hospitalized state (gamma_3), and per capita rate of progress through non-hospitalized infectious state (gamma_4). The output is LHS_samples.csv, for input into the global sensitivity script, ILI_SEIR. 2. ILI_SEIR.R The second script solves a standard Susceptible-Exposed-Infected- Recovered (SEIR) model (a system of Ordinary Differential Equations (ODEs)), runs global sensitivity analyses, and generates plots showing the impact of the input variables on the response variables for each virus. 3. virus_sims.R The third script solves a standard Susceptible-Exposed-Infected- Recovered (SEIR) model (a system of Ordinary Differential Equations (ODEs)), aimed at modeling outbreaks for five common upper respiratory viruses within a contained population. The output of this code is an epidemic curve to show timing and magnitude of the epidemic peak for each virus. Note: for all three scripts, the parameter values must be hard-coded by the user or the output will not be accurate.

Spencer, Julie↗
DOE OSTI2026

Data and scripts associated with a manuscript modeling microbial regulation of priming effects

This data package is associated with the publication “Modeling Microbial Regulatory Feedback in Organic Matter Decomposition Identifies Copiotrophic Traits as Key Drivers of Positive Priming” published as a preprint on BioRXiv by Ahamed et al. (2026); https://doi.org/10.1101/2024.08.11.607483. The package contains MATLAB scripts and saved simulation outputs used to implement a cybernetic model of microbial regulation during complex organic matter (OM) decomposition governing priming effects. It includes models of (i) single microbial functional groups (copiotrophic or oligotrophic degraders) and (ii) binary consortia composed of degraders and non-degraders with contrasting or common growth traits. Simulation results were generated using Monte Carlo analyses, with randomized key model parameters across a range of environmental mixing fractions of complex and labile OM. The dataset was created to provide a transparent and reusable computational framework for systematically exploring how microbial growth traits, metabolic regulation, and community composition influence OM decomposition dynamics and priming effects. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. In addition to a readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes the variable definitions. This package includes: (1) annotated MATLAB code implementing the system of ordinary differential equations and cybernetic control laws; (2) saved output files containing data (e.g., biomass, substrates, enzyme levels, priming metrics); and (3) scripts for processing saved outputs and regenerating figures. Specifically, the data package contains three main MATLAB scripts: runPrimingModel.m, runPlotData.m, and runPlotSuppFigS1.m, along with this readme and supporting documentation. Users should begin with runPrimingModel.m, which contains the annotated code implementing the system of ordinary differential equations and cybernetic control laws. This script runs the Monte Carlo simulations of microbial OM decomposition and allows users to modify microbial trait definitions, adjust parameter distributions, or define new community configurations. Simulation outputs are automatically saved as .mat files in the folder named SavedData, which stores all pre-generated results included in this package. The second script, runPlotData.m, reads files from the SavedData folder and processes them to regenerate the figures presented in the manuscript. The third script, runPlotSuppFigS1.m, specifically generates Figure S1 in the Supplementary Material of the manuscript. The package also includes the aforementioned files in non-proprietary .txt format. If users intend to use them, they should first save the files in their respective .m or .mat formats prior to execution in MATLAB.

Biomass concentration↗
DOE OSTI2023

The role of stiffness in training and generalization of ResNets

Neural ordinary differential equations (NODEs) have recently regained popularity as large-depth limits of a large class of neural networks. In particular, residual neural networks (ResNets) are equivalent to an explicit Euler discretization of an underlying NODE, where the transition from one layer to the next is one time step of the discretization. The relationship between continuous and discrete neural networks has been of particular interest. Notably, analysis from the ordinary differential equation viewpoint can potentially lead to new insights for understanding the behavior of neural networks in general. In this work, we take inspiration from differential equations to define the concept of stiffness for a ResNet via the interpretation of a ResNet as the discretization of a NODE. Here, we then examine the effects of stiffness on the ability of a ResNet to generalize, via computational studies on example problems coming from climate and chemistry models. We find that penalizing stiffness does have a unique regularizing effect, but we see no benefit to penalizing stiffness over L 2 regularization (penalization of network parameter norms) in terms of predictive performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

CryoTRANS: predicting high-resolution maps of rare conformations from self-supervised trajectories in cryo-EM

Cryogenic electron microscopy (cryo-EM) has revolutionized structural biology, enabling efficient determination of structures at near-atomic resolutions. However, a common challenge arises from the severe imbalance among various conformations of vitrified particles, leading to low-resolution reconstructions in rare conformations due to a lack of particle images in these quasi-stable states. We introduce CryoTRANS, a method that predicts high-resolution maps of rare conformations by constructing a self-supervised pseudo-trajectory between density maps of varying resolutions. This trajectory is represented by an ordinary differential equation parameterized by a deep neural network, ensuring retention of detailed structures from high-resolution density maps. By leveraging a single high-resolution density map, CryoTRANS significantly improves the reconstruction of rare conformations and has been validated on four real-world datasets: alpha-2-macroglobulin, actin-binding protein complexes, SARS-CoV-2 spike glycoprotein, and the 70S ribosome. CryoTRANS can also predict high-resolution structures in cryogenic electron tomography maps using a high-resolution cryo-EM map.Cryogenic electron microscopy (cryo-EM) has revolutionized structural biology, enabling efficient determination of structures at near-atomic resolutions. However, a common challenge arises from the severe imbalance among various conformations of vitrified particles, leading to low-resolution reconstructions in rare conformations due to a lack of particle images in these quasi-stable states. We introduce CryoTRANS, a method that predicts high-resolution maps of rare conformations by constructing a self-supervised pseudo-trajectory between density maps of varying resolutions. This trajectory is represented by an ordinary differential equation parameterized by a deep neural network, ensuring retention of detailed structures from high-resolution density maps. By leveraging a single high-resolution density map, CryoTRANS significantly improves the reconstruction of rare conformations and has been validated on four real-world datasets: alpha-2-macroglobulin, actin-binding protein complexes, SARS-CoV-2 spike glycoprotein, and the 70S ribosome. CryoTRANS can also predict high-resolution structures in cryogenic electron tomography maps using a high-resolution cryo-EM map.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

State elimination for mixed‐integer optimal control of partial differential equations by semigroup theory

Abstract Mixed‐integer optimal control problems governed by partial differential equations (MIPDECOs) are powerful modeling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by partial differential equations that have the structure of an abstract ordinary differential equation in function space. This allows us to avoid repeated calculations of the states for all time steps, and our approach is applied only once before starting the optimization. The presentation of theoretical results is complemented by numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Exponential Time Differencing Schemes for Fuel Depletion and Transport in Molten Salt Reactors: Theory and Implementation

A numerical framework for modeling depletion and mass transport in liquid-fueled molten salt reactions is presented based on exponential time differencing. The solution method involves using the finite volume method to transform the system of partial differential equations (PDEs) into a much larger system of ordinary differential equations. The key part of this method involves solving for the exponential of a matrix. We explore six different algorithms to compute the exponential in a series of progression problems that explore physical transport phenomena in molten salt reactors. This framework shows good results for solving linear parabolic PDEs with each of the six matrix exponential algorithms. For large problems, the series solvers such as Padé and Taylor have large run times, which can be mitigated by using the Krylov subspace.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A Mathematical Model of the Dynamics of Cytokine Expression and Human Immune Cell Activation in Response to the Pathogen Staphylococcus aureus

Cell-based mathematical models have previously been developed to simulate the immune system in response to pathogens. Mathematical modeling papers which study the human immune response to pathogens have predicted concentrations of a variety of cells, including activated and resting macrophages, plasma cells, and antibodies. This study aims to create a comprehensive mathematical model that can predict cytokine levels in response to a gram-positive bacterium, S. aureus by coupling previous models. To accomplish this, the cytokines Tumor Necrosis Factor Alpha (TNF-α), Interleukin 6 (IL-6), Interleukin 8 (IL-8), and Interleukin 10 (IL-10) are included to quantify the relationship between cytokine release from macrophages and the concentration of the pathogen, S. aureus, ex vivo. Partial differential equations (PDEs) are used to model cellular response and ordinary differential equations (ODEs) are used to model cytokine response, and interactions between both components produce a more robust and more complete systems-level understanding of immune activation. In the coupled cellular and cytokine model outlined in this paper, a low concentration of S. aureus is used to stimulate the measured cellular response and cytokine expression. Results show that our cellular activation and cytokine expression model characterizing septic conditions can predict ex vivo mechanisms in response to gram-negative and gram-positive bacteria. Our simulations provide new insights into how the human immune system responds to infections from different pathogens. Novel applications of these insights help in the development of more powerful tools and protocols in infection biology.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Entropy–Preserving and Entropy–Stable Relaxation IMEX and Multirate Time–Stepping Methods

In this work, we propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods. In particular, we extend the explicit relaxation Runge–Kutta methods to IMEX–RK methods and a class of explicit second-order multirate methods for stiff problems arising from scale-separable or grid-induced stiffness in a system. The proposed approaches not only mitigate system stiffness but also fully support entropy-preserving and entropy-stability properties at a discrete level. The key idea of the relaxation approach is to adjust the step completion with a relaxation parameter so that the time-adjusted solution satisfies the entropy condition at a discrete level. The relaxation parameter is computed by solving a scalar nonlinear equation at each timestep in general; however, as for a quadratic entropy function, we theoretically derive the explicit form of the relaxation parameter and numerically confirm that the relaxation parameter works the Burgers equation. Several numerical results for ordinary differential equations and the Burgers equation are presented to demonstrate the entropy-conserving/stable behavior of these methods. We also compare the relaxation approach and the incremental direction technique for the Burgers equation with and without a limiter in the presence of shocks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Assessing Critical Conditions for Scour Near Obstructions using Bed Shear, Particle Onset of Motion Balances, and CFD-DEM Modeling of Granular Beds

Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Model-form Error Correction using Universal Differential Equations for an Agent-Based Model of Infectious Disease

This report demonstrates universal differential equations (UDEs) as an approach to bridge the gap between ordinary differential equations (ODE) models and agent-based models (ABMs). Using UDE models as surrogates for ABMs allows us to preserve the foundational ODE that represents global disease dynamics while coupling it with a neural network model to approximate functions for the local behaviors of the ABM.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Improved quantum algorithms for linear and nonlinear differential equations

We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In [1], a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices including singular matrices. The algorithm here is also exponentially faster than the bounds derived in [1] for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in [2]). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by [3], but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas [2] and [3] additionally require normality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗