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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Loop-by-loop differential equations for dual (elliptic) Feynman integrals

We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an ε-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of q-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known ε-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a “good” loop-by-loop basis at three-loop.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fitting Matérn smoothness parameters using automatic differentiation

The Mat$\acute{e}$rn covariance function is ubiquitous in the application of Gaussian processes to spatial statistics and beyond. Perhaps the most important reason for this is that the smoothness parameter $\nu$ gives complete control over the mean-square differentiability of the process, which has significant implications for the behavior of estimated quantities such as interpolants and forecasts. Unfortunately, derivatives of the Mat$\acute{e}$rn covariance function with respect to $\nu$ require derivatives of the modified second-kind Bessel function $K$ $\nu$ with respect to $\nu$. While closed form expressions of these derivatives do exist, they are prohibitively difficult and expensive to compute. For this reason, many software packages require fixing $\nu$ as opposed to estimating it, and all existing software packages that attempt to offer the functionality of estimating $\nu$ use finite difference estimates for $\partial$ $\nu$ $K$ $\nu$ . In this work, we introduce a new implementation of $K$$\nu$ that has been designed to provide derivatives via automatic differentiation (AD), and whose resulting derivatives are significantly faster and more accurate than those computed using finite differences. Here, we provide comprehensive testing for both speed and accuracy and show that our AD solution can be used to build accurate Hessian matrices for second-order maximum likelihood estimation in settings where Hessians built with finite difference approximations completely fail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

Physics-informed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute isolated roots of polynomial systems, and propose a new deep learning framework, named homotopy physics-informed neural networks (HomPINNs), for solving multiple solutions of nonlinear elliptic differential equations. The implementation of an HomPINN is a homotopy process that is composed of the training of a fully connected neural network, named the starting neural network, and training processes of several PINNs with different tracking parameters. The starting neural network is to approximate a starting function constructed by the trivial solutions, while other PINNs are to minimize the loss functions defined by boundary condition and homotopy functions, varying with different tracking parameters. These training processes are regraded as different steps of a homotopy process, and a PINN is initialized by the well-trained neural network of the previous step, while the first starting neural network is initialized using the default initialization method. Finally, several numerical examples are presented to show the efficiency of our proposed HomPINNs, including reaction-diffusion equations with a heart-shaped domain.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2025

JuTrack: A Julia package for auto-differentiable accelerator modeling and particle tracking

Efficient accelerator modeling and particle tracking are key for the design and configuration of modern particle accelerators. In this work, we present JuTrack, a nested accelerator modeling package developed in the Julia programming language and enhanced with compiler-level automatic differentiation (AD). With the aid of AD, JuTrack enables rapid derivative calculations in accelerator modeling, facilitating sensitivity analyses and optimization tasks. Here we demonstrate the effectiveness of AD-derived derivatives through several practical applications, including sensitivity analysis of space-charge-induced emittance growth, nonlinear beam dynamics analysis for a synchrotron light source, and lattice parameter tuning of the future Electron-Ion Collider (EIC). Through the incorporation of automatic differentiation, this package opens up new possibilities for accelerator physicists in beam physics studies and accelerator design optimization.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

HFBTHO-AD: Differentiation of a nuclear energy density functional code

The HFBTHO code implements a nuclear energy density functional solver to model the structure of atomic nuclei. HFBTHO has previously been used to calibrate energy functionals and perform sensitivity analysis by using derivative-free methods. To enable derivative-based optimization and uncertainty quantification approaches, we must compute the derivatives of HFBTHO outputs with respect to the parameters of the energy functional, which are a subset of all input parameters of the code. Here, we use the algorithmic/automatic differentiation (AD) tool Tapenade to differentiate HFBTHO. We compare the derivatives obtained using AD against finite-difference approximation and examine the performance of the derivative computation.

Algorithmic differentiation↗
DOE OSTI2022

Ca-isotopes as a robust tracer of magmatic differentiation

The large mass difference (~10%) between the two most abundant isotopes of calcium, 40 Ca and 44 Ca, gives Ca great potential in tracking mass-dependent fractionation during magmatic processes. Resolvable Ca-isotope fractionation during fractional crystallization of magma, particularly by feldspar in evolved melts, has been theoretically inferred but not robustly tested in nature. To further explore the effects of magmatic differentiation on Ca-isotope systematics, we studied the late-Permian alkaline igneous suite of the Øyangen Caldera, Oslo Rift, Norway, consisting of volcanic and intrusive units ranging from basanitic to rhyolitic compositions. Major and trace element variations and modeling demonstrate that the main series of samples (N = 21), including basanites, ring-dyke syenites, and central-dome syenites, likely documents a co-genetic and closed-system fractional crystallization sequence. Our data show minimal δ 44/40 Ca variation (< 0.05 ‰) in the intermediate magma and a marked increase in δ 44/40 Ca in the felsic magma of the Øyangen Caldera (from 0.62 ± 0.02 ‰ to 1.15 ± 0.03 ‰ relative to Ca standard, SRM915a). The systematic increase is best explained by equilibrium isotopic fractionation dominated by alkali feldspar in the fractionating mineral assemblage. This is further supported by strong correlations between δ 44/40 Ca, CaO, and Eu/Eu* in the main-series samples. Implementing a Monte Carlo approach, isotopic modeling of the liquid line of descent using Rayleigh fractionation is highly consistent with the observed Ca-isotope evolution. For the first time, we confirm prominent Ca stable isotope fractionation in felsic-stage differentiation of alkaline magma and constrain the isotope fractionation factors of plagioclase and K-feldspar. Integrated with extant estimations on mineral fractionation factors from the literature, our results suggest increasing fractionation effects of rock-forming minerals with decreasing Ca content. Finally, the affirmation of significant Ca-isotope fractionation in alkaline magma by feldspar empowers the application of Ca as a versatile tracer of crustal evolution, allowing further tests in other magmatic conditions across various planetary objects.

58 GEOSCIENCES↗
DOE OSTI2022

Evaluation of assumptions made by Hygroscopic Tandem Differential Mobility Analyzer inversion routines

The Hygroscopic Tandem Differential Mobility Analyzer (H-TDMA) measures the hygroscopicity of atmospheric particles, and many atmospheric processes that change this hygroscopicity also change the atmospheric size distribution. Two assumptions made during H-TDMA inversion create spurious hygroscopic trends as a function of the changing inlet size distribution. These two assumptions—that the particles exiting the first Differential Mobility Analyzer (DMA1) are singly charged and that the inlet size distribution has a slope of zero (flat)— generate Multi-Charge Dispersion (MCD) bias and Slope bias, respectively. First, we use a model, named TAO, to show that the inlet size distribution could theoretically change the measured ammonium sulfate hygroscopicity by 10%–20% as a function of diameter or experimental time with no change in relative humidity. Secondly, we show experimentally that aerosol emitted from the flaming combustion of grass creates MCD bias. Here, in this experiment, we measure the CPC response of the first three charges and invert these responses using a new routine named Junior. Junior's inversion of each charge shows that one growth factor distribution describes all measured diameters (no growth dependence on diameter). As in the modeling study above, previous publications of this aerosol system, using traditional inversion assumptions, report a decrease in hygroscopicity as DMA1 diameter increases. Unlike traditional inversions, Junior's inversion does not assume the particles are singly charged nor does it make the flat inlet size distribution assumption. Instead, both the inlet size distribution and each charge's CPC response are measured quantities. Thus, the discrepancy between our inversion results and previous publications is likely due to the traditional inversion routine assumptions. This underscores the importance for accounting for Slope and MCD bias during inversions. Experimental results should be carefully analyzed when reporting hygroscopic trends with respect to diameter or experimental time when using the traditional inversion assumptions.

42 ENGINEERING↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Neutron elastic and inelastic scattering differential cross sections on carbon

Elastic and inelastic neutron scattering angular distributions were measured on natural carbon samples to confirm existing experimental data and evaluations in the fast neutron region and to guide improvements in resonance parameters, where needed. Sixty-four (n,n') differential cross section measurements were performed at 45 incident neutron energies between 0.5 and 8.0 MeV. Experimental angle-integrated elastic scattering cross sections are consistent with ENDF/B-VIII.0 values with the exception of the region from 3.2 to 4.0 MeV where our results are ~3% higher. In the 3.4 to 3.6 MeV region our differential cross sections are slightly lower at forward angles and somewhat higher at backward angles than the ENDF/B-VIII.0 calculations; however, our results are consistent with measured data from other research groups. The first- through fourth-order elastic scattering Legendre coefficients from fits to these experimental data are consistent with ENDF/B-VIII.0 values across this range of incident neutron energies. Inelastic scattering cross sections were measured at 12 incident neutron energies between 5.6 and 7.8 MeV. Angle-integrated cross sections agree well with the 1978 Perey and ENDF/B-VIII.0 values; however, the angular-distribution shapes deviate somewhat from the ENDF/B-VIII.0 calculations. These data will allow refinement of the resonance parameter description in this difficult energy region.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Progress in end-to-end optimization of fundamental physics experimental apparata with differentiable programming

In this article we examine recent developments in the research area concerning the creation of end-to-end models for the complete optimization of measuring instruments. The models we consider rely on differentiable programming methods and on the specification of a software pipeline including all factors impacting performance — from the data-generating processes to their reconstruction and the inference on the parameters of interest — along with the careful specification of a utility function well aligned with the end goals of the experiment. Building on previous studies originated within the MODE Collaboration, we focus specifically on applications involving instruments for particle physics experimentation, as well as industrial and medical applications that share the detection of radiation as their data-generating mechanism. This report illustrates the most recent advancements in the area, and outlines, for each of the discussed applications as well as for automatic differentiation itself, ongoing and future work.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Comprehensive analysis of differentially expressed mRNA and circRNA in Ankylosing spondylitis patients’ platelets

Highlights: • 4996 mRNAs and 2942 circRNAs were identified differentially expressed in platelets of AS patients. • Several platelet-derived immune mediators were upregulated to regulate the interaction between platelets and immune cells. • Two downregulated circRNA were identified, and the corresponding circRNA-miRNA-mRNA regulatory network was constructed. • mRNAs and circRNAs found herein could be used as diagnostic biomarkers or new therapeutic targets. Ankylosing spondylitis (AS) is a chronic inflammatory disease significantly decreasing the quality of life. Platelets play an important and active role in the development of AS. Accumulating evidence demonstrated platelets contain diverse RNA repository inherited from megakaryocytes or microvesicles. Platelet RNAs are dynamically affected by pathological conditions and could be used as diagnostic or prognostic biomarkers. However, the role of the platelet RNAs in AS is elusive. In this study, we compared mRNA and circRNA profiles in platelets between AS patients and healthy controls using RNA sequencing and bioinformatic analysis, and found 4996 mRNAs and 2942 circRNAs were differently expressed. The significantly over-expressed mRNAs in AS patients are involved in platelet activity, gap junction, focal adhesion, rap1 and toll and Imd signaling pathway. The previous identified platelet-derived immune mediators such as P2Y1, P2Y12, PF4, GPIbα, CD40L, ICAM2, CCL5 (RANTES), TGF-β (TGF-β1 and TGF-β2) and PDGF (PDGFB and PDGFA) are also included in these over expressed mRNAs, implying these factors may trigger inflammatory cascades and promote the development of AS. Additionally, we found two down-regulated circRNA (circPTPN22 and circFCHSD2) from the intersection analyses of platelets and spinal ligament tissues of AS patients. The circRNA-miRNA-mRNA regulatory network of these two circRNAs was constructed, and the target mRNAs were enriched in Th17 cell differentiation, inflammatory bowel disease, cell adhesion molecules, cytokine-cytokine receptor interaction, Jak-STAT and Wnt signaling pathway, all these pathways participate in the bone remodeling and pro/anti-inflammatory immune regulation in AS. Then, qRT-PCR was performed to validate the expression of selected key mRNAs and circRNAs and the results demonstrated that the expression levels of P2Y12, GPIbα, circPTPN22 and circFCHSD2 were consistent with the sequencing analysis. In addition, the high expression of five predicted miRNAs interacting with circPTPN22 and circFCHSD2 were also detected in AS by qRT-PCR. Taken together, our study presents a comprehensive overview of mRNAs and circRNAs in platelets in AS patients and offers new insight into the mechanisms of platelet involving in the pathogenesis of AS. The mRNAs and circRNAs identified in this study may serve as candidates for diagnosis and targeted treatment of AS.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Evaluation of Differential Peptide Loading on Tandem Mass Tag-Based Proteomic and Phosphoproteomic Data Quality

Global and phosphoproteome profiling has demonstrated great utility for the analysis of clinical specimens. One major barrier to the broad clinical application of proteomic profiling is the large amount of biological material required, particularly for phosphoproteomics—currently on the order of 25 mg wet tissue weight, depending on tissue type. For hematopoietic cancers such as acute myeloid leukemia (AML), the sample requirement is in excess of 10 million (1E7) peripheral blood mononuclear cells (PBMCs). Throughout the course of a prospective study, this requirement will certainly exceed what is obtainable from many of the individual patients/timepoints. For this reason, we were interested in examining the impact of differential peptide loading across multiplex channels on proteomic data quality. Methods: To achieve this, we tested a range of channel loading amounts (20, 40, 100, 200, and 400 µg of tryptic peptides, or approximately the material obtainable from 5E5, 1E6, 2.5E6, 5E6, and 1E7 AML patient cells) to assess proteome coverage, quantification reproducibility and accuracy in experiments utilizing isobaric tandem mass tag (TMT) labeling. As expected, we found that fewer missing values are observed in TMT channels with higher peptide loading amounts compared to those with lower loading. Moreover, channels with lower loading amounts have greater quantitative variability than channels with higher loading amounts. Statistical analysis of the differences in means among the five loading groups showed that the 20 µg loading group was significantly different from the 400 µg loading group. However, no significant differences were detected among the 40, 100, 200 and 400 µg loading groups. Conclusions: These assessment data demonstrate the practical limits of loading differential quantities of peptides across channels in TMT multiplexes, and provide a basis for designing the optimal clinical proteomics study when specimen quantities are limited.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Differentiable modeling and optimization of non-aqueous Li-based battery electrolyte solutions using geometric deep learning

Electrolytes play a critical role in designing next-generation battery systems, by allowing efficient ion transfer, preventing charge transfer, and stabilizing electrode-electrolyte interfaces. In this work, we develop a differentiable geometric deep learning (GDL) model for chemical mixtures, DiffMix, which is applied in guiding robotic experimentation and optimization towards fast charging battery electrolytes. In particular, we extend mixture thermodynamic and transport laws by creating GDL-learnable physical coefficients. We evaluate our model with mixture thermodynamics and ion transport properties, where we show improved prediction accuracy and model robustness of Diff-Mix than its purely data-driven variants. Furthermore, with a robotic experimentation setup, Clio, we improve ionic conductivity of electrolytes by over 18.8% within 10 experimental steps, via differentiable optimization built on DiffMix gradients. By combining GDL, mixture physics laws, and robotic experimentation, DiffMix expands the predictive modeling methods for chemical mixtures and enables efficient optimization in large chemical spaces.

25 - ENERGY STORAGE↗
DOE OSTI2023

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Differentiable physics-enabled closure modeling for Burgers’ turbulence

Abstract Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers’ turbulence. We consider the one-dimensional Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models across a range of system parameters, including viscosity, time, and grid resolution. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models, outperforming state-of-the-art baselines. Addition of structure in the form of physics information also brings a level of interpretability to the models, potentially offering a stepping stone to the future of closure modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

MapsTorch : automatic differentiation for X-ray fluorescence data analysis

X-ray fluorescence (XRF) is a popular spectroscopy technique for elemental analysis. Spectrum fitting and parameter tuning are at the core of XRF analysis and are conventionally manually intensive, especially for synchrotron experiments involving large amounts of diverse samples. This work introduces the automatic differentiation (AD) technique to XRF and an open-source package called MapsTorch. By transforming an analytical model of the XRF spectrum into a differentiable computation graph with AD, MapsTorch enables robust optimization of parameters and elemental intensities. We evaluate MapsTorch by conducting computational experiments on a large number of historical synchrotron XRF datasets and compare its performance with the currently practiced fitting tool NLopt. The results show that MapsTorch consistently achieves high-quality fits and often leads to better fitting quality than NLopt, particularly in tasks such as initial spectrum fitting and elemental intensity refinement. The robust performance of MapsTorch paves the way for developing automated and high-throughput XRF data analysis workflows to handle the increasing data volumes expected from next-generation synchrotron facilities.

X-ray fluorescence↗