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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2021

Optimal design of acoustic metamaterial cloaks under uncertainty

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. Additionally, we demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method’s Hessian computation is viable for large, complex problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Local convergence analysis of an inexact trust-region method for nonsmooth optimization

In Baraldi, we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. Furthermore, this algorithm has demonstrated excellent performance and scalability with problem size. In this paper, we enrich the convergence analysis for this algorithm, proving strong convergence of the iterates with guaranteed rates. In particular, we demonstrate that the trust-region algorithm recovers superlinear, even quadratic, convergence rates when using a second-order Taylor approximation of the smooth objective function term.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
DOE OSTI2020

Heat of Mixing During Fast Charge/Discharge of a Li-Ion Cell: A Study on NMC523 Cathode

Predicting temperature rise accurately during fast charge/discharge of a Li-ion cell is essential to avoid thermal runaway and extend battery life. While modeling the temperature rise, it is necessary to model the heat generation correctly. Heat of mixing, one of the four main sources of heat generation in a Li-ion battery, has often been considered insignificant and therefore excluded from modeling. When included, it is modeled using the expression from a Taylor expansion approximation. In this work, we have shown the conditions when including the heat of mixing becomes important and quantified the error associated with using the Taylor expansion, especially under high charge/discharge conditions. Consequently, we carry out the calculation of the rate of enthalpy change and the heat generation rate from the most fundamental equation for the rate of the total enthalpy change without simplifying assumptions or approximations. The heat generation rate calculated doing so naturally includes irreversible, reversible and mixing heat. We then exclusively separate out the heat of mixing by subtracting the rate of enthalpy change by reaction from the rate of the total enthalpy change. Results show that the contribution of heat of mixing in the total heat generated increases with the charge/discharge rate and is as large as 23% for a 6 C discharge. This result suggests that while modeling heat generation for fast charge/discharge, it is necessary to include the heat of mixing and avoid calculating it using the Taylor expansion approximation.

25 ENERGY STORAGE↗
DOE OSTI2021

Simulation of dynamic crystal plasticity with a Lagrangian discontinuous Galerkin hydrodynamic method

Here we present a new Lagrangian modal discontinuous Galerkin (DG) hydrodynamic method that supports a dynamic dislocation based crystal plasticity model for simulating the mechanical behavior of crystallographic materials, both single crystal and polycrystalline, under dynamic conditions. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. These polynomials describe macro-scale hydrodynamic behavior while their evolution is determined by evaluating the dynamic crystal plasticity model at material points within the element. The dynamic crystal plasticity model is sensitive to the time increment size, with too large of time increments leading to instability in the model. To mitigate this, the temporal evolution of the dynamic crystal plasticity model is achieved with the combination of a sub-incrementing scheme with Heun’s third-order time integration scheme, which is also used to temporally evolve the governing equations. The implementation of the dynamic crystal plasticity model within the DG framework is tested using a 2D approximation of the Taylor impact test with a single crystal material, using quadratic elements that have faces that can bend. In addition to the standard continuous material modeling, we propose a new simulation method that would represent the heterogeneous behavior of polycrystalline microstructures within an element by varying the position and material properties of the material points within the element. This method is demonstrated using random orientation distributions on materials points that are arranged in both structured and random configurations.

42 ENGINEERING↗
DOE OSTI2022

Exponential time differencing scheme for mass transport and depletion in molten salt reactors

This work extends the capability previously shown for addressing the problem of computing depletion and mass transport calculations in molten salt reactors (MSRs) by calculating matrix exponentials. Additional algorithms are implemented to compute the matrix exponential and the action of the matrix exponential on a matrix. These algorithms include two methods based on the Pade approximation, a Taylor series method, and three methods based on Cauchy's integral formula. In addition to the added matrix exponential solvers, a variable-order total variation diminishing scheme is applied to the convective flux approximation to provide enhanced accuracy. Finally, a simplified MSR problem is shown for each of the exponential time differencing solvers along with classical backwards differencing integrators. The results show excellent convergence for exponential time differencing methods. Computation time is a key element for selecting the optimal solver in these problems, and this work shows that Pade and Cauchy-based solvers may provided the fastest and most accurate solutions. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Trajectory prediction dimensionality reduction for low-cost connected automated vehicle systems

Here, to facilitate low-cost connected automated vehicle (CAV) system development, this study proposes two interpretable dimensionality reduction techniques in vehicle trajectory prediction, i.e., the piecewise Taylor series approximation (PTA) and the piecewise Fourier series approximation (PFA), to lower computation complexity, reduce device investment, and decrease computation energy consumption. Two benchmarks are developed, the long short-term memory (LSTM)-based model without dimensionality reduction and the LSTM-based model with encoder-decoder (a widely used dimensionality reduction technique). Results show that the four predictions have similar accuracy, and the training time (proportional to computation energy consumption) of models with dimensionality reduction techniques is greatly reduced. The reduction is even more significant when PTA/PFA is used. Sensitivity analysis advises PFA/PTA parameter selections to reduce computation complexity without significant loss of prediction accuracy. Further, the robustness of the LSTM PTA/PFA is proven by the investigation of data noises.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

High order explicit local time stepping methods for hyperbolic conservation laws

In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta discontinuous Galerkin (RK-DG) methods and design LTS algorithms based on the strong stability preserving Runge-Kutta (SSP-RK) schemes, that allow spatially variable time step sizes to be used for time integration in different regions of the computational domain. The proposed algorithms are of predictor-corrector type, in which the interface information along the time direction is first predicted based on the SSP-RK approximations and Taylor expansions, and then the fluxes over the region of the interface are corrected to conserve mass exactly at each time step. Following the proposed framework, we detail the corresponding LTS schemes with accuracy up to the fourth order, and prove their conservation property and nonlinear stability for the scalar conservation laws. Numerical experiments are also presented to demonstrate excellent performance of the proposed LTS algorithms.

58 GEOSCIENCES↗
DOE OSTI2023

A Voltage Inference Framework for Real-Time Observability in Active Distribution Grids

Active distribution grids are gaining traction to meet the growing environmental, socio-economic, and sustainability targets. Various advanced smart grid technologies facilitate the integration of Distributed Energy Resources (DERs) by supporting the bi-directional power flow. The limited observability of distribution grids, primarily related to their location at the very edge of power system infrastructure, brings challenges to optimal grid management. Moreover, only a limited number of measurements at regular intervals are usually available. This paper presents a novel inference framework, referred to as “Voltage Inference”, to overcome the observability issues. The proposed framework employs a prediction step based on the Multivariate Taylor series approximation, followed by a corrector step that minimizes the estimation error to infer the otherwise unknown voltages from the available measurements. Furthermore, numerical results on the IEEE 13-bus test feeder validate the accuracy and computational performance of the proposed framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Improved Prediction of Cold-Air Pools in the Weather Research and Forecasting Model Using a Truly Horizontal Diffusion Scheme for Potential Temperature

The terrain-following vertical coordinate system used by many atmospheric models, including the Weather Research and Forecasting (WRF) Model, is prone to errors in regions of complex terrain. These errors stem, in part, from the calculation of horizontal gradients within the diffusion term of the momentum or scalar evolution equations. In WRF, such gradients can be calculated along coordinate surfaces, or using metric terms that help account for grid skewness. However, neither of these options ensures a truly horizontal gradient calculation, especially if a grid cell is skewed enough that the heights of the neighboring grid points used in the calculation fall outside the vertical range of the cell. In this work, an improved scheme that uses Taylor series approximations to vertically interpolate variables to the level necessary for a truly horizontal gradient calculation is implemented in WRF for the diffusion of potential temperature. The scheme is validated using an atmosphere-at-rest configuration, in which spurious flows develop only as a result of numerical errors and can thus be used as a proxy for model performance. Following validation, the method is applied to the simulation of cold-air pools (CAPs), which occur in regions of complex terrain and are characterized by strong near-surface temperature gradients. Using the truly horizontal scheme, idealized simulations demonstrate reduced numerical mixing in a quiescent CAP, and a realistic case study in the Columbia River basin shows a reduction in positive wind speed bias by up to roughly 20% compared to observations from the Second Wind Forecast Improvement Project.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Spatially Accelerated Winding Numbers for Curved Geometry

The generalized winding number (GWN) is a scalar field that supports robust containment queries on curved geometry, including non-watertight, overlapping, and nested boundary representations. While queries can be easily parallelized over samples, direct evaluation on parametric curves and surfaces remains costly for large and complex models. Fast, state-of-the-art GWN approaches leverage a spatial index to approximate the GWN, typically coupled with a Taylor expansion which approximates the GWN contribution for far clusters of geometric primitives. However, such methods operate only on discrete inputs such as triangle meshes and point clouds, and would introduce containment errors near boundaries if applied to curved input. We extend support for fast GWN evaluation over arbitrary collections of NURBS curves in 2D and trimmed NURBS patches in 3D via a Bounding Volume Hierarchy that stores efficiently precomputed moment data in the hierarchy nodes. When querying the hierarchy, approximations for far clusters are used alongside direct evaluation for nearby NURBS primitives, achieving sub-linear complexity while preserving the geometric features in the vicinity of the query point. Central to our performance improvements is an adaptive subdivision strategy for NURBS primitives during a preprocessing phase, creating better spatial partitions while retaining the same accuracy for containment decisions as a direct evaluation. We demonstrate the performance and accuracy of our approach across a large collection of 2D and 3D datasets.

Computer science↗
DOE OSTI2023

Simple and Sophisticated Models of Taylor's Cylinder Impact

We present a study based on the simplest possible models for Taylor’s cylinder impact problem, in addition to examination of using convolutional neural networks (CNNs) to map cylinder profiles to strength calibrations. We find that the approximate treatments of Taylor and Hawkyard compare well with hydrodynamic simulations using an equivalent assumption of constant flow stress. The CNN models prove to be well suited to successfully infer parameterizations of the Preston-Tonks-Wallace model of plastic deformation based on the deformed profile of an impacted cylinder

36 MATERIALS SCIENCE↗
DOE OSTI2023

Simple and sophisticated models of Taylor’s cylinder impact

We present a study based on the simplest possible models for Taylor’s cylinder impact problem, in addition to examina-tion of using convolutional neural networks (CNNs) to map cylinder profiles to strength calibrations. We find that the approximate treatments of Taylor and Hawkyard compare well with hydrodynamic simulations using an equivalent assumption of constant flow stress. The CNN models prove to be well suited to successfully infer parameterizations of the Preston-Tonks-Wallace model of plastic deformation based on the deformed profile of an impacted cylinder.

36 MATERIALS SCIENCE↗
DOE OSTI2021

All-Order Full-Coulomb Quantum Spectral Line-Shape Calculations

Understanding how atoms interact with hot dense matter is essential for astrophysical and laboratory plasmas. Interactions in high-density plasmas broaden spectral lines, providing a rare window into interactions that govern, for example, radiation transport in stars. However, up to now, spectral line-shape theories employed at least one of three common approximations: second-order Taylor treatment of broadening operator, dipole-only interactions between atom and plasma, and classical treatment of perturbing electrons. In this Letter, we remove all three approximations simultaneously for the first time and test the importance for two applications: neutral hydrogen and highly ionized magnesium and oxygen. Finally, we found 15%–50% change in the spectral line widths, which are sufficient to impact applications including white-dwarf mass determination, stellar-opacity research, and laboratory plasma diagnostics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Self-similar Reynolds-averaged mechanical–scalar turbulence models for reshocked Richtmyer–Meshkov instability-induced mixing in the small Atwood number limit

Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged mechanical–scalar turbulence models describing incompressible turbulent Richtmyer–Meshkov instability-induced mixing in planar geometry derived in the small Atwood number limit are extended to construct models for reshocked Richtmyer–Meshkov mixing. In this study, the models are based on the turbulent kinetic energy K and its dissipation rate ε, together with the scalar variance S and its dissipation rate χ modeled either differentially or algebraically. The three- and four-equation models allow for a simultaneous description of mechanical and scalar mixing, i.e., mixing layer growth and molecular mixing. Mixing layer growth parameters and other physical observables were obtained explicitly as functions of the model coefficients and were used to calibrate the model coefficients. Here, the solutions for the singly shocked Richtmyer–Meshkov case for the mixing layer width and the turbulent fields are used to construct piecewise-continuous generalizations of these quantities for times after reshock. For generality, the post-reshock mixing layer width is not assumed to grow with the same power-law as the pre-reshock width, and an impulsive approximation applied to Rayleigh–Taylor instability growth is used to establish the expression for the post-reshock width. A four-equation model is then used to illustrate the spatiotemporal behavior of the mean and turbulent fields and late-time turbulent equation budgets across the mixing layer. The reference solutions derived here can provide systematic calibrations and better understanding of mechanical–scalar turbulence models and their predictions for reshocked Richtmyer–Meshkov instability-induced turbulent mixing in the very large Reynolds number limit.

42 ENGINEERING↗
DOE OSTI2025

Integration of multiple coinflip devices for high-quality random sampling

Artificial intelligence, scientific computing, and probabilistic computing use random sampling to approximate solutions to various problems, with larger models requiring a substantial quantity of random numbers. To generate the required vast quantity of random numbers at high rates, we explore so-called “coinflip” devices, which are stochastic microelectronic devices ideally capable of independently generating random bits with a tunable weight at a high rate. However, coinflip devices are inherently analog and demonstrate nonidealities, like temperature dependence and drift, that can introduce determinism into the outputs. We present important considerations for building systems of multiple coinflip devices to produce high-quality bitstreams with low error and little dependency on previous bits. Using tunnel diodes as coinflip devices, we implement a control loop to adapt to temperature dependence and generate fair bitstreams with each device. While this can lead to dependencies between bits in a single bitstream, we demonstrate that combining results generated in parallel with individual tunnel diodes can produce fair and unpredictable bitstreams. The suitability of these bitstreams for use in probabilistic computing is then demonstrated through a Monte Carlo approximation of π.

Taylor, Brady Garland [Sandia National Laboratorie↗