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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

MatCal Users Guide: Release 1.3.0

Any continuum mechanics model will require three components: (1) a discretized geometry of the boundary value problem being studied, (2) the partial differential equations to be solved, and (3) the initial conditions and boundary conditions for the problem. To describe material behavior in these computational models, material models contribute to (2) the underlying equations and, occasionally, to (3) the initial conditions for the simulation. These material models can exhibit a mathematical form that is empirically based, based on first principles, or developed from both empirical observations and known physics. In general, these models are meant to represent a class of materials with well understood behavior. As a result, material models have parameters that must be tuned or calibrated so that the model response matches characterization data available for the specific material it is intended to represent when used to simulate a specific system. For simple models, such as isotropic, linear elastic materials in solid mechanics, this calibration process can be a simple analytical calculation directly extracting the parameters from experimental measurements. For complex models that have many inputs and require many characterization datasets to adequately identify the material behavior, the model calibration process can require an inverse problem approach where an optimization is performed to tune the model parameters to the available data.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine Learning meets Algebraic Combinatorics: A Suite of Benchmark Datasets to Accelerate AI for Mathematics Research

The use of benchmark datasets has become an important engine of progress in machine learning (ML) over the past 15 years. Recently there has been growing interest in utilizing machine learning to drive advances in research-level mathematics. However, off-the-shelf solutions often fail to deliver the types of insights required by mathematicians. This suggests the need for new ML methods specifically designed with mathematics in mind. The question then is: what benchmarks should the community use to evaluate these? On the one hand, toy problems such as learning the multiplicative structure of small finite groups have become popular in the mechanistic interpretability community whose perspective on explainability aligns well with the needs of mathematicians. While toy datasets are a useful benchmark for initial work, they lack the scale, complexity, and sophistication of many of the principal objects of study in modern mathematics. To address this, we introduce a new collection of benchmark datasets, Algebraic Combinatorics Benchmarks (ACBench), representing either classic or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. After describing the datasets, we discuss the challenges involved in constructing “good” mathematics benchmarks, describe baseline model performance, and discuss some of the insights these datasets can provide that may be of interest even to those who are not interested in mathematics research itself.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Robust Interpretation of Electrochemical Impedance Spectra Using Numerical Complex Analysis

Electrochemical Impedance Spectroscopy (EIS) is a noninvasive technique widely used for understanding charge transfer and charge transport processes in electrochemical systems and devices. Standard approaches for the interpretation of EIS data involve starting with a hypothetical circuit model for the physical processes in the device based on experience/intuition and then fitting the EIS data to this circuit model. This work explores a mathematical approach for extracting key characteristic features from EIS data by relying on fundamental principles of complex analysis. These characteristic features can suggest the presence of inductors and constant phase elements (nonideal capacitors) from impedance data and enable us to answer questions about the identifiability and nonuniqueness of equivalent circuit models. In certain scenarios such as models with only resistors and capacitors, we are able to enumerate all possible families of circuit models. Finally, we apply the mathematical framework presented here to real-world electrochemical systems and highlight results using impedance measurements from a lithium-ion battery coin cell.

charge transfer↗
DOE OSTI2025

Particle Markov Chain Monte Carlo Approach to Inference in Transient Surface Kinetics

Here, in this work, we develop a novel Bayesian approach to study the adsorption and desorption of CO onto a Pd(111) surface, a process of great importance in natural sciences. The motivation for this work comes from the recent availability of time-resolved infrared spectroscopy data and the need for model interpretability and uncertainty quantification in chemical processes. The objective is to learn the relevant parameters that characterize the process: coverage with time, rate constants, activation energies, and pre-exponential factors. Our approach consists of three main schemes: (i) a problem design and probabilistic model for the whole system, (ii) a particle Markov chain Monte Carlo sampler to learn the hidden coverages and rate constant parameters, and (iii) two Bayesian formulations to infer the activation energies and pre-exponential factors. The flexibility of the Bayesian framework allows for uncertainty quantification where possible and integration of mathematical constraints in the model to reflect the system physically. We found that our results for the activation energies and pre-exponential factor are in agreement with those reported in the experimental literature, independently, and we provide discussions on the advantages and disadvantages as well as applicability to other systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A dynamic volumetric heat source model for laser additive manufacturing

Melt pool scale models of laser powder bed fusion (LPBF) offer insights into the process-structure-property relationships in additive manufacturing (AM). These models often neglect physical phenomena such as vapor cavity formation and fluid mechanics to reduce computational demands. Instead, volumetric heat source models are used to represent the effects that these phenomena have on the predicted melt pool dimensions. Generally, the dimensions and effective absorption of the volumetric heat source are calibrated to reproduce melt pool dimensions observed in metallographic cross sections taken from single-track experiments on bare plate. However, the transient nature of LPBF often deviates the melt pool dimensions from the assumed steady-state conditions of single-track experiments, motivating the need for a volumetric heat source model that more generally considers the dynamic relationship between melt pool shape and laser-material interactions. Here, we introduce a two-parameter volumetric heat source model that integrates several existing models into a generalized mathematical expression, providing independent control over the radial heat distribution via the parameter k and the volumetric shape of the heat source via the parameter m. This parameterization enables the calibration of melt pool shape predictions through simultaneous adjustment of these parameters, while keeping the radial heat source dimensions consistent with the experimental spot size (D4σ) and constraining the heat source depth and absorption to physically derived expressions for cavities. Consequently, the proposed volumetric heat source model adapts to changes in the local melt pool conditions due to scanning strategy and part geometry by dynamically adjusting the heat source depth and absorption. We demonstrate the capabilities of the proposed model through comparisons with a collection of experiments from the Additive Manufacturing Benchmark (AMBench).

36 MATERIALS SCIENCE↗
DOE OSTI2025

Nonintrusive projection-based reduced order modeling using stable learned differential operators

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where underlying governing equations are known but the access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a glass-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov–Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through four numerical experiments: 1-D scalar advection, 1-D Burgers, 2-D scalar advection and 1-D scalar advection–diffusion–reaction equations. In conclusion, the results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.

42 ENGINEERING↗
DOE OSTI2026

Frameworks, Algorithms, and Scalable Technologies for Mathematics (FASTMath) SciDAC Institute

As computational models scale to larger computers, the rate at which they produce data has far outstripped the same computers ability to write that data and further the file systems ability to store that data. Almost all of the SciDAC applications, but especially those related to fusion solve very large scale PDEs whose scientific output his impacted by this problem. To gain access to dynamics in an exascale simulation that are not identifiable a priori and to make that dynamical data available to machine learning requires fundamental research in the area of in situ data data analytics. Here data analytics includes compression, visualization, uncertainty quantification, and machine learning. This in situ data analytics will enable on-the-fly spatial and temporal compression of solution dynamics, expose that space-time compressed field to machine learning algorithms that have been specialized to work with dynamically evolving data (existing machine learning algorithms treat data sets as static), greatly improving the opportunity for machine learning to provide feedback to the compression, all within an ongoing simulation, without the need to write data to files. The same concepts are also being applied to uncertainty quantification and multi-fidelity modeling which have similar needs for spatial and temporal compression of the ongoing exascale simulation to perform either without the typical, unacceptable writing of data to files.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Spatially Patterned Architectures to Modulate CO 2 Reduction Cascade Catalysis Kinetics

Electrochemical CO 2 reduction using renewable sources of electrical energy holds promise for converting CO 2 into fuels and chemicals. The complex interactions among chemical/electrochemical reactions and mass transport make it difficult to analyze the effect of an individual process on electrode performance based only on experimental methods. Here, we developed a generalized steady-state simulation to describe an electrode surface in which sequential cascade catalysts are patterned in a periodic trench design. If appropriately constructed, this trench geometry is hypothesized to be able to yield a higher net current density for a CO 2 reduction (CO 2 R) cascade reaction. We have used realistic experimental reaction kinetics to investigate the role of trench geometry in mass transport, local microenvironments, and selectivity for a model CO 2 R cascade reaction. The model considers local concentration gradients of bicarbonate species at quasi-equilibrium and catalytic surface reactions based on concentration-dependent Butler–Volmer kinetics. Our results suggest that varying the spatial distribution of active sites plays a significant role in facilitating effective mass transport between active sites, modulating selectivity for the cascade reaction, and enhancing the yield of desirable cascade products. Moreover, we observe that this trench geometry significantly alters the cascade reaction rate by affecting the local pH, which can cause inadvertent depletion of available aqueous CO 2 to limit the CO 2 R cascade kinetics and modest suppression of the hydrogen evolution reaction (HER). The results highlight the trade-offs between mass transport, pH, and reaction kinetics that become apparent only when considering the coupled physics of all processes at the electrode surface. Here, this model can thus serve as a primary tool to build more selective and efficient patterned architectures for the CO 2 R cascade catalysis.

CO2 reduction↗
DOE OSTI2025

Exact Ground State of Interacting Electrons in Magic Angle Graphene

One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi-θ$${\theta }$$ and Weierstrass-℘$${\wp }$$ functions.

Becker, Simon↗
DOE OSTI2026

Ensemble Kalman filter for data assimilation coupled with low-resolution computations techniques applied in fluid dynamics

This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.

Data Assimilation↗
DOE OSTI2025

Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets

We present a model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm produces DFBSs suitable for accurate robust DF approximation of 2-particle interactions in mean-field and correlated electronic structures. The algorithm is designed to (a) saturate the OBS product space by a large regularized set of primitive solid-harmonic Gaussian shells with nonuniform distribution of exponents, followed by (b) pruning of the shells according to their contributions to the 2- body energy of a correlated atomic ensemble. Building the DFBS generator model almost exclusively on mathematical and physical principles allows one to limit the number of parameters that control the density fitting error to three, with a single set of parameters sufficient for computations with all basis cardinal numbers, with and without correlation of core electrons, with and without scalar and spin-dependent relativistic effects, spanning almost all of the Periodic Table. Performance assessment included basis sets up to quadruple-ζ quality from several major basis set families, using molecules composed of main-group, d-block, and f-block elements. The resulting DF errors in Hartree−Fock and second-order MP2 energies (with relativistic all-electron treatments, when appropriate) were on the order of 20 and 10 μE h per electron, respectively.

Approximation↗
DOE OSTI2024

Nonlinear Sigma model amplitudes to all loop orders are contained in the Tr ( Φ 3 ) theory

Scattering amplitudes for the simplest theory of colored scalar particles—the Tr ( Φ 3 ) theory—have recently been the subject of active investigations. In this work we describe an unanticipated wider implication of this work: the Tr ( Φ 3 ) theory secretly contains nonlinear sigma model (NLSM) amplitudes to all loop orders. The NLSM amplitudes are obtained from Tr ( Φ 3 ) amplitudes by a unique shift of kinematic variables. We show that this shifted kinematics produces amplitudes for a cubic theory with a linear term in the potential, with extrema spontaneously breaking U ( N ) → U ( N − k ) × U ( k ) . The Goldstone amplitudes for this theory coincide with those of pions in the U ( N ) × U ( N ) → U ( N ) chiral Lagrangian to all orders in the planar limit. We also give a purely on-shell understanding of this correspondence, showing that integrands defined by the kinematic shifts have the correct residues on poles and appropriately produce the Adler zero. Finally, we discuss how similar kinematic shifts produce certain infinite classes of mixed amplitudes of pions and Tr ( Φ 3 ) scalars, most of which are not interpretable from the Lagrangian description. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

ChatGPT and Other Large Language Models for Cybersecurity of Smart Grid Applications

Cybersecurity breaches targeting electrical substations constitute a significant threat to the integrity of the power grid, necessitating comprehensive defense and mitigation strategies. Any anomaly in information and communication technology (ICT) should be detected for secure communications between devices in digital substations. This paper proposes large language models (LLMs), e.g., ChatGPT, for the cybersecurity of IEC 61850-based communications. Multi-cast messages such as generic object oriented system events (GOOSE) and sampled values (SV) are used for case studies. The proposed LLM-based cybersecurity framework includes, for the first time, data pre-processing of communication systems and human-in-the-loop (HITL) training (considering the cybersecurity guidelines recommended by humans). The results show a comparative analysis of detected anomaly data carried out based on the performance evaluation metrics for different LLMs. A hardware-in-the-loop (HIL) testbed is used to generate and extract a dataset of IEC 61850 communications.

ChatGPT↗
DOE OSTI2026

Semi-analytic solutions to the Noh problem with a black box EoS

The objective of this paper is to derive a method of constructing semi-analytic solutions to the Noh problem when the equation of state is a black box. Such solutions can be used for verification tests of hydrodynamics codes. We present the underlying theory, the method for finding solutions, and several examples of derived semi-analytic solutions. We end by performing a classic verification convergence test comparing numerical results from a hydrodynamics code against a non-trivial semi-analytic solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Modeling the Enceladus dust plume based on in situ measurements performed with the Cassini Cosmic Dust Analyzer

We analyzed data recorded by the Cosmic Dust Analyzer on board the Cassini spacecraft during Enceladus dust plume traversals. Our focus was on profiles of relative abundances of grains of different compositional types derived from mass spectra recorded with the Dust Analyzer subsystem during the Cassini flybys E5 and E17. The E5 profile, corresponding to a steep and fast traversal of the plume, has already been analyzed. In this paper, we included a second profile from the E17 flyby involving a nearly horizontal traversal of the south polar terrain at a significantly lower velocity. Additionally, we incorporated dust detection rates from the High Rate Detector subsystem during flybys E7 and E21. We derived grain size ranges in the different observational data sets and used these data to constrain parameters for a new dust plume model. This model was constructed using a mathematical description of dust ejection implemented in the software package DUDI. Further constraints included published velocities of gas ejection, positions of gas and dust jets, and the mass production rate of the plume. Our model employs two different types of sources: diffuse sources of dust ejected with a lower velocity and jets with a faster and more colimated emission. From our model, we derived dust mass production rates for different compositional grain types, amounting to at least 28 kg s –1 . Previously, salt-rich dust was believed to dominate the plume mass based on E5 data alone. The E17 profile shows a dominance of organic-enriched grains over the south polar terrain, a region not well constrained by E5 data. By including both E5 and E17 profiles, we find the salt-rich dust contribution to be at most 1% by mass. This revision also results from an improved understanding of grain masses of various compositional types that implies smaller sizes for salt-rich grains. Our new model can predict grain numbers and masses for future mission detectors during plume traversals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Fully implicit crystal plasticity models representing orientations with modified Rodrigues parameters

Here, this work describes a crystal plasticity formulation combining several mathematical, numerical, and implementation choices to produce a highly efficient model. Specifically, the key choices in the implementation are (1) representing orientations with modified Rodrigues parameters, (2) implementing a fully coupled implicit time integration for the elastic stretch, the crystal orientations, and the model internal variables, (3) implementing the model in the NEML2 constitutive modeling framework, based on PyTorch, to vectorize the calculations and port the computation to GPUs and other hardware accelerators, and (4) an exact implementation of the consistent tangent matrix, even for arbitrary coupling to other field variables beyond the displacements, like temperature, neutron fluence, etc. The first two features of the model are, to our knowledge, novel. The paper considers each of these choices individually as well as the final model as a whole. This includes a full description of modified Rodrigues parameters, their advantages over other representations of orientations, the mathematical formulae and tools required to implement a model with modified Rodrigues parameters, and a detailed description of the geometry of the space of modified Rodrigues parameters (in an appendix). It also includes a description of a fully implicit time integration scheme for the orientations and the advantages in representing orientations with modified Rodrigues parameters in implementing such a model. The work then assess, via numerical examples, the advantages of fully coupled implicit time integration versus more common decoupled and explicit time integration schemes. These studies demonstrate the computational advantages of fully coupled integration versus other time integration algorithms, though the performance of the competing models depends on the complexity of the underlying single crystal model. The study concludes by demonstrating that the choice of time integration method affects the sharpness of the predicted texture, with explicit methods for integrating the orientations overestimating texture sharpness and implicit methods underestimating texture sharpness.

Crystal plasticity↗
DOE OSTI2024

Adaptive Online Model Update Algorithm for Predictive Control in Networked Systems

In this article, we introduce an adaptive on-line model update algorithm designed for predictive control applications in networked systems, particularly focusing on power distribution systems. Unlike traditional methods that depend on historical data for offline model identification, our approach utilizes real-time data for continuous model updates. This method integrates seamlessly with existing online control and optimization algorithms and provides timely updates in response to real-time changes. This methodology offers significant advantages, including a reduction in the communication network bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt after disturbances. Furthermore, our algorithm is tailored for non-linear convex models, enhancing its applicability to practical scenarios. The efficacy of the proposed method is validated through a numerical study, demonstrating improved control performance using a synthetic IEEE test case.

data-driven model predictive control↗