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Results for “generation equation”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Superfield Generating Equation of Field-Antifield Formalism

A simple quantum superfield generating equation of the field-antifield formalism is proposed. The Schroedinger equation with the Hamiltonian having Δ-exact form is derived. An Sp(2) symmetric extension to the main construction, with specific features caused by the principal fact that all basic equations become Sp(2) vector-valued ones, is presented. A principal role of quantum antibrackets in formulation of the Heisenberg equations of motion is shown.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Optimization to Generate Equations of State for Hydrogen Production

On a high level, the larger project in question, HydroGEN, aims to develop software used for finding equations of state (EOS) to optimize catalyst configuration for H 2 production through water splitting. In particular, this summer project focused on solving the nonlinear equations used in fitting the equations. This problem involved using Python to solve a linear system with nonlinear constraints. In order for this to be achieved, Pyomo was used to build a model and the solver Ipopt, interior point optimizer, was used. Pyomo is a Python-based language developed at Sandia; it is an optimization modeling language. Rather than solving the entire problem at once, a toy problem was created, simplifying the problem down to the most important focus. This problem had a known solution, comparable to the calculated solution to assess accuracy and as progress was made towards finding solutions, complexity was gradually added to the problem. After building and solving the toy problem, it was found that it gave reasonably accurate solutions, better compared to the two existing solvers previously used with this project in terms of functionality. The solver is now ready for implementation into the project’s main software.

08 HYDROGEN↗
DOE OSTI2020

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Derivation of physical equations for high-speed laser welding using large language models

It is challenging to formulate complex physical phenomena that occur in a manufacturing process, particularly when the available data are limited, rendering conventional data-driven approaches ineffective. This study aims to predict humping onset in high-speed laser welding by introducing a novel framework, namely text-to-equations generative pre-trained transformer (T2EGPT). This method leverages the capabilities of large language models (LLMs), in combination with sparse experimental data and enriched literature data, to derive an interpretable and generalizable equation for predicting humping initiation. By capturing key correlations among physical parameters, T2EGPT generates a compact and dimensionless expression that accurately predicts hump formation. The equation reveals that humping arises from the interplay between inertia-driven backward melt flow and capillary-driven surface stabilization, where inertial forces drive molten metal backward and capillary forces resist surface deformation. Furthermore, compared to traditional data-driven models, T2EGPT demonstrates enhanced predictive accuracy and cross-material transferability. More broadly, this study highlights the potential of LLMs to integrate textual information with data-driven discovery, enabling the extraction of physical laws in data-scarce scientific domains.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Univariate Prediction of Hammett Parameters and Select Relative Reaction Rates Using Loewdin Atomic Charges

Loewdin charges from density functional theory calculations were used here to obtain general, univariate linear correlations for the prediction of experimental Hammett parameters and relative reaction rates. While previous studies have established that Hirshfeld and CM5 charges perform strongly as univariate predictors, the near-ubiquitous Loewdin charges have not yet been evaluated. To this end, we assess the predictive capability of Loewdin charges for three chemical systems. First, we show that Loewdin charges outperform Hirshfeld and CM5 charges for Hammett parameter prediction. Second, we see that Loewdin charges generally perform comparably to Hirshfeld charges for predicting the relative rates of olefin cleavage by photoexcited nitroarenes. The single case of poor correlation, between relative rates and the Loewdin charges on nitrogen sites, is ameliorated when considering the net charge on the NO 2 group. Third, we show that Loewdin, Hirshfeld, and CM5 charges all perform very well for generating correlations for relative reaction rates for C–H activation of 9-(4-X-phenyl)-9H-fluorene substrates by a transition metal catalyst. The equations generated throughout the study enable the prediction of Hammett parameters and relative reaction rates. Finally, these tools can accelerate synthetic and experimental studies by enabling the in silico prediction of uncharacterized chemical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning

Various modeling techniques are used to predict the capacity fade of Li-ion batteries. Algebraic reduced-order models, which are inherently interpretable and computationally fast, are ideal for use in battery controllers, technoeconomic models, and multi-objective optimizations. For Li-ion batteries with graphite anodes, solid-electrolyte-interphase (SEI) growth on the graphite surface dominates fade. This fade is often modeled using physically informed equations, such as square-root of time for predicting solvent-diffusion limited SEI growth, and Arrhenius and Tafel-like equations predicting the temperature and state-of-charge rate dependencies. In some cases, completely empirical relationships are proposed. However, statistical validation is rarely conducted to evaluate model optimality, and only a handful of possible models are usually investigated. This article demonstrates a novel procedure for automatically identifying reduced-order degradation models from millions of algorithmically generated equations via bi-level optimization and symbolic regression. Identified models are statistically validated using cross-validation, sensitivity analysis, and uncertainty quantification via bootstrapping. On a LiFePO 4 /Graphite cell calendar aging data set, automatically identified models utilizing square-root, power law, stretched exponential, and sigmoidal functions result in greater accuracy and lower uncertainty than models identified by human experts, and demonstrate that previously known physical relationships can be empirically "rediscovered" using machine learning.

25 ENERGY STORAGE↗
DOE OSTI2020

Herbicide, fertilization, and planting density effects on intensively managed loblolly pine early stand development

Production forestry in the southeast US has been partially transitioned to intensively managed short rotations (~10 years), in which multiple silvicultural interventions are performed during forest development. Understanding the responses to silvicultural practices and continued refinement of site-specific recommendations is critical to sustainably maximize forest production. We evaluated the effects of silvicultural practices (herbicide, fertilization, and planting density) on growth, stand homogeneity, and above- and belowground biomass accumulation and partitioning of loblolly pine (Pinus taeda) throughout early stand development (age 5 years) in the southeastern US. Five treatments with eight replications each were tested: no herbicide and no fertilization (C); herbicide only (H); herbicide and half-reduced fertilization rate (R); herbicide and full fertilization (F); and increased stand density (60+ %; 1346 vs. 2152 trees per hectare) with herbicide and full fertilization rate (D). Allometric equations generated from destructive harvests were applied to annual diameter measurements to estimate plot-level biomass and allocation. Herbicide was crucial to promote stand uniformity and increase yield (~600+ % stem biomass compared with C at age 5). Aboveground biomass was similar in R and F treatments, which was ~25% higher than in H at age 5. Increasing planting density along with multiple herbicide and fertilizer applications yielded higher biomass without compromising individual tree size (diameter and height). There was little effect of silviculture practices on allocation patterns. Our results parallel what was found for fertilization with herbicide from a number of loblolly stands under similar conditions and indicate a ~28% volume gain with fertilization during early stand development. Similarly, our results were consistent with other studies implementing similar differences in planting density and suggest a ~26% volume gain through early stand development with an initial 60% increase in planting density. Furthermore, our study helps to understand complex relationships between production and silvicultural practices during early stand development and demonstrates that silvicultural prescriptions can be optimized to increase sustainability of production forestry

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

A methodology for decay heat characterization in molten salt reactors

Accurate decay heat prediction in molten salt reactors (MSRs) faces dual challenges: complex operational uncertainties and the need for interpretable models compatible with engineering workflows. This work presents a hybrid machine learning and segmented polynomial methodology that addresses both requirements through three key innovations. First, a modular data architecture encodes MSR-specific operational parameters (power density: 1-100 W cm -3 , humidity: 0-0.1 wt %, air ingress: 0-0.1 mol %) with uncertainty-aware temporal discretization spanning 15 orders of magnitude. Second, region-optimized machine learning models achieve 92.3 % root mean square error (RMSE) reduction over conventional polynomials while maintaining physical interpretability through automated piecewise equation generation. Third, dual front-end interfaces accelerate safety analyses — a Jupyter environment enables researchers to explore 10,000+ parameter combinations via interactive widgets, while a Streamlit web application reduces design iteration cycles through production-grade visualization tools. Operational deployment demonstrates prediction times of only a couple hundred milliseconds for 10 4 years decay profiles, enabling real-time optimization of spent fuel container designs.

42 - ENGINEERING↗
DOE OSTI2024

Physics informed neural network can retrieve rate and state friction parameters from acoustic monitoring of laboratory stick-slip experiments

Various machine learning (ML) and deep learning (DL) techniques have been recently applied to the forecasting of laboratory earthquakes from friction experiments. The magnitude and timing of shear failures in stick-slip cycles are predicted using features extracted from the recorded ultrasonic or acoustic emission (AE) signals. In addition, the Rate and State Friction (RSF) constitutive laws are extensively used to model the frictional behavior of faults. In this work, we use data from shear experiments coupled with passive acoustic (variance, kurtosis, and AE rate) interleaved with active source ultrasonic monitoring (transmitted wave amplitude) to develop physics-informed neural network (PINN) models incorporating the RSF law and AE rate generation equation with wave amplitude serving as a proxy for friction state variable. This PINN framework allows learning RSF parameters from stick-slip experiments rather than measuring them through a series of velocity step experiments. We observe that when the stick-slip cycles are irregular, the PINN models outperform the data-driven DL models. Transfer learning (TL) PINN models are also developed by pre-training on data collected at one normal stress level followed by forecasting shear failures and retrieving RSF parameters at other stress levels (i.e., with different recurrence intervals) after retraining on a limited amount of new data. Our findings suggest that TL models perform better compared to standalone models. Both standalone and TL PINN-estimated RSF parameters and their ground truth values show excellent agreements thus demonstrating that RSF parameters can be retrieved from laboratory stick-slip experiments using the corresponding acoustic data and that the transmitted wave amplitude provides a good representation of the evolving frictional state during stick-slips.

58 GEOSCIENCES↗
DOE OSTI2024

Towards Exascale Astrophysics of Mergers and Supernovae (TEAMS)

The major goals of the TEAMS project are (i) to improve the modeling of many of the suggested astrophysical sites of the r‐process, as well as some potential p‐process sites, (ii) to use our models to support and guide the experimental efforts at FRIB and similar facilities, and (iii) to use our tools to cement our understanding of the roles that massive stars play in galactic chemical evolution. As part of the TEAMS project, Mezzacappa (UTK, Reddy (UW), Surman (ND), and Steiner (UTK) are (i) generating equations of state and neutrino opacities for simulations of core‐collapse supernovae and neutron star mergers which are more faithful to current understanding of the nucleon‐nucleon interaction, (ii) integrating those new equations of state and neutrino opacities into new simulation codes being developed, (iii) performing detailed nuclear reaction network post‐processing to determine abundances from simulations and (iv) quantifying the impact of nuclear physics uncertainties on r‐process abundances.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Gaussian-process generative model for the QCD equation of state

We develop a generative model for the nuclear matter equation of state at zero net baryon density using the Gaussian process regression method. We impose first-principles theoretical constraints from lattice quantum chromodynamics and hadron resonance gas at high- and low-temperature regions, respectively. By allowing the trained Gaussian process regression model to vary freely near the phase transition region, we generate random smooth crossover equations of state with different speeds of sound that do not rely on specific parametrizations. Here, we explore a collection of experimental observable dependencies on the generated equations of state, which paves the groundwork for future Bayesian inference studies to use experimental measurements from relativistic heavy-ion collisions to constrain the nuclear matter equation of state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Systems and methods for optimizing component placement in a battery design

Systems, computer readable media, and method concern determining operational parameters of an inventory of components to be included in a battery. The components can include storage components and electrical components. The method includes generating a system of equations that describe suitable combinations of components in locations in a battery design layout for the battery, the system of equations being generated based at least partially on rules and constraints, and includes analyzing the system of equations using integer optimization. The integer optimization can optimizes, based at least partially on the operational parameters, one or more objective functions in the system of equations to determine at least one solution for the battery design layout, and the at least one solution can include a set of the components for the locations in the battery design layout for the battery. The method includes providing, via an interface, the at least one solution.

Cox, Kelsea↗
DOE OSTI2023

Optimal mitigation and control over power system dynamics for stochastic grid resilience

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the western system coordinating council 9-bus test system using synthetic multi-device outage scenarios.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2022

Dynamics Informed Optimization for Resilient Energy Systems

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the Western System Coordinating Council (WSCC) 9-bus test system using synthetic multi-device outage scenarios. Towards integrating our modeling framework with real threats and more realistic power systems, we explore applying hybrid dynamics to power systems. Our work is applied to basic RL circuits with the ultimate goal of using the methodology to model protective tripping schemes in the grid. Finally, we survey mitigation techniques for HEMP threats and describe a GIS application developed to create threat scenarios in a grid with geographic detail.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Radiative properties of quantum emitters in boron nitride from excited state calculations and Bayesian analysis

Abstract Point defects in hexagonal boron nitride (hBN) have attracted growing attention as bright single-photon emitters. However, understanding of their atomic structure and radiative properties remains incomplete. Here we study the excited states and radiative lifetimes of over 20 native defects and carbon or oxygen impurities in hBN using ab initio density functional theory and GW plus Bethe-Salpeter equation calculations, generating a large data set of their emission energy, polarization and lifetime. We find a wide variability across quantum emitters, with exciton energies ranging from 0.3 to 4 eV and radiative lifetimes from ns to ms for different defect structures. Through a Bayesian statistical analysis, we identify various high-likelihood charge-neutral defect emitters, among which the native V N N B defect is predicted to possess emission energy and radiative lifetime in agreement with experiments. Our work advances the microscopic understanding of hBN single-photon emitters and introduces a computational framework to characterize and identify quantum emitters in 2D materials.

Chemistry↗