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All sourcesNASA NTRSDOE OSTI
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 OSTI2018

54 Fe neutron elastic and inelastic scattering differential cross sections from 2–6 MeV

Measurements of neutron elastic and inelastic scattering cross sections from 54 Fe were performed for nine incident neutron energies between 2 and 6 MeV. Measured differential scattering cross sections are compared to those from previous measurements and the ENDF, JENDL, and JEFF data evaluations. TALYS calculations were performed and modifications of the default parameters are found to better describe the experimental cross sections. A spherical optical model treatment is generally adequate to describe the cross sections in this energy region; however, in 54 Fe the direct coupling is found to increase suddenly above 4 MeV and requires an increase in the DWBA deformation parameter by approximately 25%. Furthermore, this has little effect on the elastic scattering differential cross sections but makes a significant improvement in both the strength and shape of the inelastic scattering angular distribution, which are found to be very sensitive to the size and extent of the surface absorption region.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
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 OSTI2017

Symmetries of the Gas Dynamics Equations using the Differential Form Method

Here, a brief review of the theory of exterior differential systems and isovector symmetry analysis methods is presented in the context of the one-dimensional inviscid compressible flow equations. These equations are formulated as an exterior differential system with equation of state (EOS) closure provided in terms of an adiabatic bulk modulus. The scaling symmetry generators—and corresponding EOS constraints—otherwise appearing in the existing literature are recovered through the application and invariance under Lie derivative dragging operations.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2018

Parallelizable adjoint stencil computations using transposed forward-mode algorithmic differentiation

Algorithmic differentiation (AD) is a tool for generating discrete adjoint solvers, which efficiently compute gradients of functions with many inputs, for example for use in gradient-based optimization. AD is often applied to large computations such as stencil operators, which are an important part of most structured-mesh PDE solvers. Stencil computations are often parallelized, for example by using OpenMP, and optimized by using techniques such as cache-blocking and tiling to fully utilize multicore CPUs and many-core accelerators and GPUs. Differentiating these codes with conventional reverse-mode AD results in adjoint codes that cannot be expressed as stencil operations and may not be easily parallelizable. They thus leave most of the compute power of modern architectures unused. We present a method that combines forward-mode AD and loop transformation to generate adjoint solvers that use the same memory access pattern as the original computation that they are derived from and can benefit from the same optimization techniques. The effectiveness of this method is demonstrated by generating a scalable adjoint CFD solver for multicore CPUs and Xeon Phi accelerators.

algorithmic differentiation↗
DOE OSTI2017

Differential cross sections for excitation of H 2 by low-energy electron impact

Experimental and theoretical differential cross sections (DCS) for the electron-impact excitation of molecular hydrogen to the $B{}^{1}{{\rm{\Sigma }}}_{u}^{+}$, $c{}^{3}{{\rm{\Pi }}}_{u}$, $a{}^{3}{{\rm{\Sigma }}}_{g}^{+}$, $C{}^{1}{{\rm{\Pi }}}_{u}$, and the $E(F){}^{1}{{\rm{\Sigma }}}_{g}^{+}$ states are presented at incident energies near to threshold. The experimental DCSs were taken at incident energies of 14, 15, 16 and 17.5 eV and for scattering angles from 10° to 130°. In conclusion, the theoretical DCSs are from the convergent close-coupling method which has recently successfully modeled differential electron scattering from H 2 when compared with available experiment at energies of 17.5 eV and above.

74 ATOMIC AND MOLECULAR PHYSICS↗
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↗
DOE OSTI2020

Differentially Private Generation of Social Networks via Exponential Random Graph Models

Many social networks contain sensitive relational information. One approach to protect the sensitive relational information while offering flexibility for social network research and analysis is to release synthetic social networks at a pre-specified privacy risk level, given the original observed network. In this work, we propose the DP-ERGM procedure that synthesizes networks that satisfy the differential privacy (DP) via the exponential random graph model (EGRM). We apply DP-ERGM to a college student friendship network and compare its original network information preservation in the generated private networks with two other approaches: differentially private DyadWise Randomized Response (DWRR) and Sanitization of the Conditional probability of Edge given Attribute classes (SCEA). The results suggest that DP-EGRM preserves the original information significantly better than DWRR and SCEA in both network statistics and inferences from ERGMs and latent space models. In addition, DP-ERGM satisfies the node DP, a stronger notion of privacy than the edge DP that DWRR and SCEA satisfy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Efficient GPU Implementation of Automatic Differentiation for Computational Fluid Dynamics

Many scientific and engineering applications require repeated calculations of derivatives of output functions with respect to input parameters. Automatic Differentiation (AD) is a method that automates derivative calculations and can significantly speed up code development. In Computational Fluid Dynamics (CFD), derivatives of flux functions with respect to state variables (Jacobian) are needed for efficient solutions of the nonlinear governing equations. AD of flux functions on graphics processing units (GPUs) is challenging as flux computations involve many intermediate variables that create high register pressure and require significant memory traffic because of the need to store the derivatives. This paper presents a forward-mode AD method based on multivariate dual numbers that addresses these challenges and simultaneously reduces the floating-point operation count. The dimension of the multivariate dual numbers is optimized for performance. The flux computations are restructured to minimize the number of temporary variables and reduce register pressure. For effective utilization of memory bandwidth, shared memory is used to store the local flux Jacobian. This AD implementation is compared with several other Jacobian implementations on an NVIDIA V100 GPU (V100). For three-dimensional perfect-gas compressible-flow equations implemented in a practical CFD code, the AD implementation of a flux Jacobian based on multivariate dual numbers of dimension 5 outperforms all other GPU AD implementations on V100. Its performance is comparable with the optimized hand-differentiated version. Finally, the implementation achieves 75% of the peak floating-point throughput and 61 % of the peak global device memory bandwidth usage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗
DOE OSTI2018

Releasing Correlated Trajectories: Towards High Utility and Optimal Differential Privacy

A mutual correlation between trajectories of two users is very helpful to real-life applications such as product recommendation and social media. While providing tremendous benefits, the releasing of correlated trajectories may leak sensitive social relations, due to potential links between mutual correlations and social relations. To the best of our knowledge, here we take the first step to propose a mathematically rigorous n-body Laplace framework, satisfying epsilon-differential privacy, which efficiently prevents a social relation inference through the mutual correlation between n-node trajectories of two users. The problem is mathematically formulated by defining a trajectory correlation score to measure the social relation between two users. Then, under the n-body Laplace framework, we propose two Lagrange Multiplier-based Differentially Private (LMDP) approaches to optimize the privacy budgets, for the data utility measured by location distances and the data utility measured by location correlations, i.e., UD-LMDP and UC-LMDP. Also, we present detailed analyses of privacy, data utility, adversary knowledge and the constrained optimizations. Finally, we perform experimental studies with real-life data. Our experimental results show that our proposed approaches achieve better privacy and data utility than the existing approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Characterization of the First Prototype of the L1K65n Differential-Output Charge-Sensitive Preamplifier ASIC for High-Performance, Low-Background HPGe Detector Readout

Next-generation neutrinoless double-beta (0νββ) decay searches require a large detector/isotope mass and very low radioactive backgrounds. The upcoming LEGEND-1000 experiment (Large Enriched Germanium Experiment for Neutrinoless double-beta Decay) constitute a ton-scale array of several hundred high-purity germanium (HPGe) detectors enriched in 76Ge, the isotope of interest. It aims to reach a sensitivity beyond 10 28 years on the 0νββ decay half-life of 76Ge, necessitating an order of magnitude reduction in background with respect to the state of the art. This will require the implementation of a dedicated application specific integrated circuit (ASIC) preamplifier that will significantly lower background contribution compared to the conventional low-mass front end (LMFE) employed in the Majorana Demonstrator and LEGEND-200 experiments while maintaining or improving energy resolution and other performance parameters. Features include a high (9 MeV) dynamic range with noise low enough to achieve a trigger threshold of <1 keV, a single power supply to reduce background-inducing cabling, and a differential output to maintain signal integrity over several meters of transmission line. The chip would be optimized to operate in liquid argon (87 K) and be able to do so reliably for ten years. Following on from an earlier 180-nm prototype, we have developed a differential-output charge-sensitive preamplifier ASIC fabricated in a 65-nm process, 1×2 mm in size, that addresses these needs. Here, we present recent results from the successful testing and characterization of the first version of this device.

ASIC↗