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At least 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Machine learning of consistent thermodynamic models using automatic differentiation

In this study, we propose a data-driven method to describe consistent equations of state (EOS) for arbitrary systems. Complex EOS are traditionally obtained by fitting suitable analytical expressions to thermophysical data. A key aspect of EOS is that the relationships between state variables are given by derivatives of the system free energy. In this work, we model the free energy with an artificial neural network and utilize automatic differentiation to directly learn the derivatives of the free energy. We demonstrate this approach on two different systems, the analytic van der Waals EOS and published data for the Lennard-Jones fluid, and we show that it is advantageous over direct learning of thermodynamic properties (i.e., not as derivatives of the free energy but as independent properties), in terms of both accuracy and the exact preservation of the Maxwell relations. Furthermore, the method implicitly provides the free energy of a system without explicit integration.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Differentiable vertex fitting for jet flavor tagging

This work explores the use of differentiable programming to integrate domain knowledge, in the form of domain specific software, into neural networks to develop scientific machine learning systems. We propose a differentiable vertex fitting algorithm that estimates the crossing point of multiple curves. In the high energy physics setting, these curves are defined by particle equations of motion and the crossing point represents the origin of particle production. This differentiable vertex fitting algorithm can be seamlessly integrated into neural networks, and we show its utility and efficacy in the high energy physics application of the classification of jets, i.e., collimated streams of particles in particle detectors whose originating parent particle we aim to classify. We demonstrate how differentiable vertex fitting can be integrated into larger transformer-based models for jet flavor tagging and show improvements in heavy flavor jet classification when compared to baseline models. Published by the American Physical Society 2024

Smith, Rachel E. C. (ORCID:0000000335851262)↗
DOE OSTI2023

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
DOE OSTI2021

A Sparse-Grid Probabilistic Scheme for Approximation of the Runaway Probability of Electrons in Fusion Tokamak Simulation

Runaway electrons (RE) generated during magnetic disruptions present a major threat to the safe operation of plasma nuclear fusion reactors. A critical aspect of understanding RE dynamics is to calculate the runaway probability, i.e., the probability that an electron in the phase space will runaway on, or before, a prescribed time. Such probability can be obtained by solving the adjoint equation of the underlying Fokker-Planck equation that controls the electron dynamics. In this effort, we present a sparse-grid probabilistic scheme for computing the runaway probability. The key ingredient of our approach is to represent the solution of the adjoint equation as a conditional expectation, such that discretizing the differential operator reduces to the approximation of a set of integrals. Adaptive sparse grid interpolation is utilized to approximate the map from the phase space to the runaway probability. The main novelties of this effort are the integration of the sparse-grid method into the probabilistic numerical scheme for computing escape probability, and the application of the proposed method in computing RE probabilities. Two numerical examples are given to illustrate that the proposed method can achieve O(Δt) convergence, and that the local anisotropic adaptive refinement strategy (M. Stoyanov, Adaptive sparse grid construction in a context of local anisotropy and multiple hierarchical parents. In: Sparse Grids and Applications-Miami 2016, Springer, Berlin, 2018, pp. 175–199) can effectively handle the sharp transition layer between the runaway and non-runaway regions.

Yang, Minglei↗
DOE OSTI2020

Method of Green’s Potentials for Elliptic PDEs in Domains with Random Apertures

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. Here, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green’s kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal ϵ -2 asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
DOE OSTI2025

Leveraging differentiable programming in the inverse problem of neutron stars

Neutron stars (NSs) probe the high-density regime of the nuclear equation of state (EOS). However, inferring the EOS from observations of NSs is a computationally challenging task. Here, in this work, we efficiently solve this inverse problem by leveraging differential programming in two ways. First, we enable full Bayesian inference in under one hour of wall time on a GPU by using gradient-based samplers, without requiring pretrained machine learning emulators. Moreover, we demonstrate efficient scaling to high-dimensional parameter spaces. Second, we introduce a novel gradient-based optimization scheme that recovers the EOS of a given NS mass-radius curve. We demonstrate how our framework can reveal consistencies or tensions between nuclear physics and astrophysics. First, we show how the breakdown density of a metamodel description of the EOS can be determined from NS observations. Second, we demonstrate how degeneracies in EOS modeling using nuclear empirical parameters can influence the inverse problem during gradient-based optimization. Looking ahead, our approach opens up new theoretical studies of the relation between NS properties and the EOS, while effectively tackling the data analysis challenges brought by future detectors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

coh3

CoH3 (CoH ver.3) is an optical model, exciton pre-equilibrium, and Hauser-Feshbach statistical model code, which calculates nuclear reaction cross sections for medium to heavy targets in the keV to MeV energy region. This program is written in standard C++, divided into approximately 200 source and header files. CoH solves the Schroedinger equation for optical potentials defined in the code, and calculates differential elastic scattering, reaction, and total cross sections, for neutron, proton, deuteron, triton, 3He, and alpha-particle. Deformed optical potentials are solved with the coupled-channels method, in which the ground state rotational band members, or vibrational phonon states are coupled. The optical model gives particle transmission coefficients that are fed into the statistical model calculations. CoH includes the pre-equilibrium model (exciton model), the direct/semidirect capture model, and the multi-stage Hauser-Feshbach statistical decay with width fluctuation correction based on the Gaussian orthogonal ensemble. For weakly coupled levels, the DWBA (distorted wave Born approximation) method is used to calculate the direct inelastic scattering process to the excited states.

Kawano, Toshihiko↗
DOE OSTI2025

Weak Form Scientific Machine Learning: Test Function Construction for System Identification

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

FOS: Computer and information sciences↗
DOE OSTI2023

DPFEHM: a differentiable subsurface physics simulator

The Earth’s subsurface is a key resource that provides energy via fossil fuels and geothermal sources, stores drinking water, and is used in the fight against climate change via carbon sequestration. Simulating the physical processes that occur in the Earth’s subsurface with computers enables better use of this resource. DPFEHM is a Julia package that includes computer models with a focus on the Earth’s subsurface, especially fluid flow, which is critical for the aforementioned applications. DPFEHM is able to solve the groundwater flow equations (single phase flow), Richards equation (air/water), the advection-dispersion equation, and the 2d wave equation. One of the key features of DPFEHM is that it supports automatic differentiation, so it can be integrated into machine learning workflows using frameworks such as Flux or PyTorch. The automatic differentiation capabilities give it the same performance as adjoint methods.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A small heterocyclic molecule as a multistate transistor: a quantum many-body approach

Weakly coupled molecular junctions are an active and important field of research due to their non-linear charge carrier transport. In this study, we investigate transport properties in a weakly coupled molecule, B 2 C 2 N 2 H 6 , using a combined quantum many-body approach and kinetic (master) equations. Various non-linear current–voltage characteristics such as negative differential conductance (NDC), rectifications, and Coulomb staircase, which are the hallmarks of multistate transport devices, have been obtained. We further explore the effect of different perturbations such as gate voltage and perpendicular magnetic field on molecular transport. Depending on the strength of the applied perturbing field, several phenomena such as current switching, and suppression of NDC, have been realized in the device. This study demonstrates small molecules as promising components in next-generation nano-devices.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Highly accurate and constrained density functional obtained with differentiable programming

Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain a highly accurate neural network–based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. Here we evaluate our model against different families of XC approximations and show that at the meta-GGA level our functional exhibits unprecedented accuracy for both energy and density predictions. For nonempirical functionals, there is a strong linear correlation between energy and density errors. We use this correlation to define an XC functional quality metric that includes both energy and density errors, leading to an improved way to rank different approximations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Voltage Probability Density Function Shaping Control Strategy Considering Grid Operational Uncertainties

It is well-known that power systems operation always affected by various uncertainties which make the bus voltage a random process that can be characterized by its probability density function (PDF) at any time instant. In this context, this paper presents a novel PDF-based voltage control framework for power systems. By modeling voltage as a stochastic process, we formulate a stochastic differential equationthat captures grid uncertainties. The associated Fokker-Planck-Kolmogorov equation is derived to describe the evolution of the voltage PDF, which enables the formulation of a PDF-shaping control strategy. To simplify the PDF control formulation, a B-spline neural network is introduced for real-time estimation and regulation of the voltage distribution. The proposed PDF control law updates voltage references for energy storage systems and synchronous generators using real-time PDF measurements and feedback signals. The proposed method is validated on a modified Kundur’s two-area system. Simulation results demonstrate that the controller can significantly improve the voltage stability under stochastic conditions, highlighting its effectiveness in modern inverter-rich grids.

Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗
DOE OSTI2020

Using Differential Forms to Find Symmetries in the Noh Problem for an Ideal Gas in a Spherical System

The Euler equations describe inviscid, compressible gas flow and are derived using the laws of conservation of mass, momentum, and energy. From these equations a common test problem, the Noh problem, can be solved for invariant solutions in planar, cylindrical, and spherical geometries. Using Lie group analysis methods, we will solve the Noh Problem for an ideal gas in a spherical system.

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

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Imposing equilibrium on experimental 3-D stress fields using Hodge decomposition and FFT-based optimization

Here, we present a methodology to impose micromechanical constraints, i.e. stress equilibrium at grain and sub-grain scale, to an arbitrary (non-equilibrated) voxelized stress field obtained, for example, by means of synchrotron X-ray diffraction techniques. The method consists in finding the equilibrated stress field closest (in L 2 -norm sense) to the measured non-equilibrated stress field, via the solution of an optimization problem. The extraction of the divergence-free (equilibrated) part of a general (non-equilibrated) field is performed using the Hodge decomposition of a symmetric matrix field, which is the generalization of the Helmholtz decomposition of a vector field into the sum of an irrotational field and a solenoidal field. The combination of: a) the Euler–Lagrange equations that solve the optimization problem, and b) the Hodge decomposition, gives a differential expression that contains the bi-harmonic operator and two times the curl operator acting on the experimental stress field. These high-order derivatives can be efficiently performed in Fourier space. The method is applied to filter the non-equilibrated parts of a synthetic piecewise constant stress fields with a known ground truth, and stress fields in Gum Metal, a beta-Ti-based alloy measured in-situ using Diffraction Contrast Tomography (DCT). In both cases, the largest corrections were obtained near grain boundaries.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Spin Diagnostics Using Mott Polarimeter for the EIC Pre-Injector

Polarization measurement and front-end commissioning are critical steps in the EIC preinjector program. We designed a spin-diagnostics beamline at around 4 MeV for front-end commissioning. This paper describes a high-energy Mott polarimeter, including Mott scattering, the Sherman function, and extrapolation toward single elastic scattering in finite-thickness foils. We summarize the key equations used to calculate essential design parameters, including detection time, effective Sherman function, differential cross section, and Mott polarimeter figure of merit. We also present the diagnostics beamline lattice design and kicker design for continuous spin-polarization monitoring. These notes provide concepts, formulas, and methods for diagnostic-beamline design and commissioning measurements.

43 PARTICLE ACCELERATORS↗