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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Data-Driven Learning of Nonautonomous Systems

In this work, we present a numerical framework for recovering unknown nonautonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the nonautonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Efficient Interdependent Systems Recovery Modeling with DeepONets

Modeling the recovery of interdependent critical infrastructure is a key component of quantifying and optimizing societal resilience to disruptive events. However, simulating the recovery of large-scale interdependent systems under random disruptive events is computationally expensive. Therefore, we propose the application of Deep Operator Networks (DeepONets) in this paper to accelerate the recovery modeling of interdependent systems. DeepONets are ML architectures which identify mathematical operators from data. The form of governing equations DeepONets identify and the governing equation of interdependent systems recovery model are similar. Therefore, we hypothesize that DeepONets can efficiently model the interdependent systems recovery with little training data. We applied DeepONets to a simple case of four interdependent systems with sixteen states. DeepONets, overall, performed satisfactorily in predicting the recovery of these interdependent systems for out of training sample data when compared to reference results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Analytic model of dislocation density evolution in fcc polycrystals accounting for dislocation generation, storage, and dynamic recovery mechanisms

Here, an analytic model of the evolution of dislocation density in fcc polycrystals is described. The evolution equations approximately account for most known dislocation storage, dynamic recovery, and dislocation generation mechanisms in fcc polycrystals. Specifically, the model incorporates network (forest) and grain boundary storage, mobile-network and mobile–mobile annihilation, screw–screw annihilation via athermal and thermal single cross-slip, generation by double cross-slip (Koehler mechanism, including dipole formation), Frank-Read sources, grain boundary nucleation, and mobile–immobile dislocation nucleation due to shock loading. Single cross-slip is assumed to proceed through the Friedel–Escaig (FE) mechanism; the corresponding activation energy is calculated using a modified FE model. The activation energy for double cross-slip is calculated for the first time by extending the FE model. The exact evolution equations are integro-differential equations, and as such are difficult to implement in a code; hence, the evolution equations are simplified by making several approximations. Preliminary results on copper are presented, including comparisons to experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Molecular-Scale Considerations of Enhanced Oil Recovery in Shale

With only less than 10% recovery, the primary production of hydrocarbon from shale reservoirs has redefined the energy equation in the world. Similar to conventional reservoirs, Enhanced Oil Recovery (EOR) techniques could be devised to enhance the current recovery factors. However, shale reservoirs possess unique characteristics that significantly affect the fluid properties. Therefore, we are adopting a molecular simulation approach that is well-suited to account for these effects to evaluate the performance of three different gases, methane, carbon dioxide and nitrogen, to recover the hydrocarbons from rough pore surfaces. Our hydrocarbon systems consists of either a single component (decane) or more than one component (decane and pentane). We simulated cases where concurrent and countercurrent displacement is studied. For concurrent displacement (injected fluids displace hydrocarbons towards the production region), we found that nitrogen and methane yielded similar recovery; however nitrogen exhibited a faster breakthrough. On the other hand, carbon dioxide was more effective in extracting the hydrocarbons when sufficient pressure was maintained. For countercurrent displacement (gases are injected and hydrocarbons are produced from the same direction), methane was found to be more effective, followed by carbon dioxide and nitrogen. In all cases, confinement reduced the recovery factor of all gases. This work provides insights to devise strategies to improve the current recovery factors observed in shale reservoirs.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2026

Nonlinear optimal recovery in Hilbert spaces

Here, this paper investigates solution strategies for nonlinear problems in Hilbert spaces, such as nonlinear partial differential equations (PDEs) in Sobolev spaces, when only finite measurements are available. We formulate this as a nonlinear optimal recovery problem, establishing its well-posedness and proving its convergence to the true solution as the number of measurements increases. However, the resulting formulation might not have a finite-dimensional solution in general. We thus present a sufficient condition for the finite dimensionality of the solution, applicable to problems with well-defined point evaluation measurements. To address the broader setting, we introduce a relaxed nonlinear optimal recovery and provide a detailed convergence analysis. An illustrative example is given to demonstrate that our formulations and theoretical findings offer a comprehensive framework for solving nonlinear problems in infinite-dimensional spaces with limited data.

convergence↗
DOE OSTI2022

Adaptive workflow for simulation of RF heaters

Accurate RF (Radio Frequency) simulations of fusion systems like ITER require the definition of high-fidelity analysis geometries that include detailed antenna, reactor wall, and physics regions. Here, this paper will describe a workflow for the execution of adaptive high-performance simulations of RF fusion systems. In this workflow, the simulation input consists of a CAD model attributed with the needed analysis attributes. The analysis mesh is automatically generated and the analysis steps are executed using the time-harmonic Maxwell's equations solved using high-order Nédélec finite elements. A patch recovery-based error estimator is used to drive a conforming mesh adaptation procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A modified Susceptible-Infected-Recovered model for observed under-reported incidence data

Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

MBMS1.0: An Open-Source Code for Modeling and Simulation of Membrane-Based Dehumidification and Energy Recovery

Membrane-based dehumidification is currently being considered as a promising solution for the building application due to its low cost and very limited energy consumption. Developing a simple and efficient open-source code simulation tool is important for boosting the optimization and evaluation of such device in HVAC community. This paper reports a first-order physics based model which accounts for the fundamental heat and mass transfer of humid-air vapor at feed side to flow stream at permeate side. The current model comprises two membrane mass transfer submodels (i.e. microstructure model and performance map model); and it adopts a segment-by-segment methodology for discretizing heat and mass transfer governing equations. The model is capable of simulating both dehumidifiers and energy recovery ventilators with parallel-flow cross-flow, and counter-flow configurations. The model was validated with the measurements at appropriate device. The practices in dehumidification and energy recovery exchangers are also discussed. The model and open-source codes are expected to become a solid fundament for developing a more comprehensive and accurate membrane-based dehumidification in the future.

Gao, Zhiming↗
DOE OSTI2026

Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.

Dirichlet-to-Neumann map↗
DOE OSTI2022

Dynamic properties of FeCrMnNi, a high entropy alloy

The goal of this paper was to assess the dynamic properties of a new class of materials, High entropy alloys (HEAs). Specifically, gas gun experiments coupled with recovery were performed on a specific HEA, FeCrMnNi, to measure its equation of state (EOS) and its spall strength, which is a measure of the stress required to nucleate voids under shock loading conditions. While there has been a plethora of work performed to assess the mechanical properties of these HEAs under uniaxial stress conditions as a function of strain rate, investigation of its properties in dynamic extremes remains rare. The current work fills this gap in knowledge for this novel class of materials. Our results show that the measured EOS for this material at one velocity was in reasonable agreement with an estimated Hugoniot. Furthermore, while the spall strength for this material was found to be ~1.9 GPa, with some variation based on sample location, the main failure mode was brittle. This brittle failure leading to formation of cracks in the material is different than the ductile failure observed in pure iron and its alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Dynamic properties of FeCrMnNi, a High Entropy Alloy

The goal of this paper was to assess the dynamic properties of a new class of materials, High entropy alloys (HEAs). Specifically, gas gun experiments coupled with recovery were performed on a specific HEA, FeCrMnNi, to measure its equation of state (EOS) and its spall strength, which is a measure of the stress required to nucleate voids under shock loading conditions. While there has been a plethora of work performed to assess the mechanical properties of these HEAs under uniaxial stress conditions as a function of strain rate, investigation of its properties in dynamic extremes remains rare. The current work fills this gap in knowledge for this novel class of materials. Our results show that the measured EOS for this material at one velocity was in reasonable agreement with an estimated Hugoniot. Furthermore, while the spall strength for this material was found to be ~1.9 GPa, with some variation based on sample location, the main failure mode wasbrittle. This brittle failure leading to formation of cracks in the material is different than the ductile failure observed in pure iron and its alloys. DOE/NV/03624--1298

36 MATERIALS SCIENCE↗
DOE OSTI2021

Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics

The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be computationally demanding for applications involving sophisticated microphysics models, such as those required to calculate accurate gravitational wave signals in numerical relativity simulations of binary neutron stars. This work explores the use of machine learning methods to speed up the recovery of primitives in relativistic hydrodynamics. Artificial neural networks are trained to replace either the interpolations of a tabulated equation of state or directly the conservative-to-primitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equation-of-state and multi-dimensional interpolations. In particular, the neural networks for the conservative-to-primitive map accelerate the variable recovery by more than an order of magnitude over standard methods while maintaining accuracy. Neural networks are thus an interesting option to improve the speed and robustness of relativistic hydrodynamics algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Impact of nuclear reactor radiation on the performance of AlN/sapphire surface acoustic wave devices

The performance of an AlN/sapphire surface acoustic wave (SAW) delay line device was characterized in real time under irradiation inside a nuclear reactor. Both its resonant frequency and transmission efficiency were observed to respond to a change in reactor power. The response follows an exponentially saturating behavior after a step power increase, followed by an exponentially decaying recovery after reactor shutdown. A sensitivity analysis based on the governing electro-mechanical equations shows that the frequency shift can be attributed to the softening of sapphire’s elastic constants under neutron radiation. Additionally, a kinetic rate equation is adopted to interpret device response and describe its microstructural evolution. These results suggest that the AlN/sapphire SAW device remains functional under irradiation, is sensitive to neutron and gamma ray fluxes, and offers an opportunity for remote sensing and in-situ measurement of material properties when exposed to nuclear reactor environment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Methane mass transfer in mesoporous silica saturated with liquid hydrocarbons

Mass transfer across gas/liquid interfaces plays a central role in many industrial applications. In particular, gas dissolution and diffusion in liquid hydrocarbon mixtures, confined in nanometer-sized pores, is an essential mechanism during enhanced oil recovery (EOR) from unconventional formations. In this work, we have measured methane (C 1 ) diffusion in n-decane (C 10 ), n-hexadecane (C 16 ), and mixtures of C 10 + C 16 in a mesoporous material with an average pore size of 4 nm at 50 °C and ~ 8 MPa of gas pressure. A key conclusion of this work is that the diffusivities, measured in the bulk phase, for the relevant binary systems, are sufficient to predict the diffusion behavior of the corresponding multicomponent systems in the porous medium by using Wilke’s equation for the evaluation of effective component diffusivities, combined with an accurate equation of state (EOS) representation of the (bulk) phase behavior. This observation can facilitate accurate prediction of recovery processes in unconventional formations and, potentially, guide other applications that entail gas-liquid interface mass transfer in mesoporous materials.

42 ENGINEERING↗
DOE OSTI2023

Exploring the working range of automated standard dilution analysis of nutrient elements in foods by inductively coupled plasma optical emission spectrometry

Inductively coupled plasma optical emission spectrometry (ICP-OES) is an important tool for measuring nutrient elements in food. ICP-OES methods typically determine analytical concentrations using external standard calibration but can be susceptible to matrix effects. The method of standard additions does not suffer from matrix effects but is time consuming and labor intensive. Automated standard dilution analysis (SDA) allows for online matrix matched calibration without preparing individual standard additions for each sample matrix. This approach may solve both time and matrix issues and has been described in the literature as an attractive alternative to standard additions. The working range of the method for nutrient elements, however, is an understudied feature of SDA that may be a potential drawback to routine analysis of foods. We evaluated automated SDA performance through the analysis of 10 reference materials and four fortified (i.e., spiked) foods spanning the AOAC food triangle. We evaluated the working range, accuracy, and precision for analyses of nutrient elements in foods. Accepted accuracy (80–120% recovery) was achieved for 10 nutrient elements, Ca, Cu, Fe, K, Mg, Mn, Na, P, S, and Zn, when the analytical solution concentration to standard concentration ratio was less than 10. This equates to a working range for each element spanning at least two orders of magnitude. Removing outliers, Z scores (n = 95) ranged from –1.8 to 0.88, and the average recovery (n = 85) from fortification experiments was 97 ± 12% (2σ). Therefore, automated SDA applied to ICP-OES may be used for nutrient elemental analyses in samples with difficult matrices such as foods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Conceptual and Mathematical Foundation for the FE/NETL CO 2 Prophet Model for Simulating CO 2 Enhanced Oil Recovery, Version 2

The United States (U.S.) Department of Energy (DOE) Office of Fossil Energy (FE) at the National Energy Technology Laboratory (NETL) has developed the FE/NETL CO 2 Prophet Model, which is Version 2 of CO 2 Prophet. This document describes the mathematical foundation for the FE/NETL CO 2 Prophet Model. CO 2 Prophet was originally developed in the 1990s by Texaco Exploration and Production and Technology Department for DOE. The FE/NETL CO 2 Prophet Model is an oil reservoir simulator that is suitable for simulating water floods and supercritical carbon dioxide (CO 2 ) enhanced oil recovery (EOR). The FE/NETL CO 2 Prophet Model uses a number of assumptions to simplify the equations describing the flow of oil, water (or brine), and CO 2 in the oil reservoir.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗