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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Compact finite difference schemes for the time fractional diffusion equation with nonlocal boundary conditions

Fourth-order compact finite difference schemes for solving the time fractional diffusion equation with nonlocal boundary conditions are considered in this paper. The second-order derivative in one space variable is approximated by a fourth-order compact finite difference. Two different time derivatives, the Caputo derivative and Riemann–Liouville derivative are considered in the equations that we discuss. The Caputo time derivative is discretized by the L1-approximation and a second-order approximation is used for the Riemann–Liouville derivative. Stability analysis using the discrete energy method for Scheme I is given, and error estimation of this scheme is derived by conducting the local truncation error analysis, using the stability result. Numerical results are provided to show that both two fully discrete schemes have fourth-order accuracy in space, and 2−γ order of accuracy in time for Scheme I with γ being the order of the fractional derivative, while Scheme II has second-order accuracy in time when the theoretical solutions are smooth with zero initial values.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quantifying local and global mass balance errors in physics-informed neural networks

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Study of self-interaction-errors in barrier heights using locally scaled and Perdew-Zunger self-interaction methods

We study the effect of self-interaction errors on the barrier heights of chemical reactions. For this purpose we use the well-known Perdew-Zunger [J. P. Perdew and A. Zunger, Phys. Rev. B,23, 5048 (1981)] self-interaction-correction(PZSIC), as well two variations of the recently developed, locally scaled self-interaction correction (LSIC) [Zope et al.,J. Chem. Phys.151, 214108 (2019)] to study the barrier heights of the BH76 benchmark dataset. Our results show that both PZSIC and especially the LSIC methods improve the barrier heights relative to the local density approximation(LDA). The version of LSIC that uses the iso-orbital indicator z as a scaling factor gives a more consistent improvement than an alternative version that uses an orbital-dependent factor based on the ratio of orbital densities to the total electron density. We show that LDA energies evaluated using the self-consistent and self-interaction-free PZSIC densities can be used to assess density-driven errors. Furthermore, the LDA reaction barrier errors for the BH76 set are found to contain significant density-driven errors for all types of reactions contained in the set, but the corrections due to adding SIC to the functional are much larger than those stemming from the density for the hydrogen transfer reactions and of roughy equal size for the non-hydrogen transfer reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗
DOE OSTI2020

Hybridizing pseudo-Hamiltonians and non-local pseudopotentials in diffusion Monte Carlo

An accurate treatment of effective core potentials (ECPs) requires care in continuum quantum Monte Carlo (QMC) methods. While most QMC studies have settled on the use of familiar non-local (NL) pseudopotentials with additional localization approximations, these approaches have been shown to result in moderate residual errors for some classes of molecular and solid state applications. Here, we revisit an idea proposed early in the history of QMC ECPs that does not require localization approximations, namely, a differential class of potentials referred to as pseudo-Hamiltonians. We propose to hybridize NL potentials and pseudo-Hamiltonians to reduce residual non-locality of existing potentials. We derive an approach to recast pseudopotentials for 3d elements as hybrid pseudo-Hamiltonians with optimally reduced NL energy. We demonstrate the fidelity of the hybrid potentials by studying atomic ionization potentials of Ti and Fe and the binding properties of TiO and FeO molecules with diffusion Monte Carlo (DMC). We show that localization errors have been reduced relative to potentials with the same NL channels for Sc–Zn by considering the DMC energy change with respect to the choice of approximate localization. While localization error decreases proportionate to the reduced NL energy without a Jastrow, with a Jastrow, the degree of reduction decreases at higher filling of the d-shell. Our results suggest that a subset of existing ECPs may be recast in this hybrid form to reduce the DMC localization error. They also point to the prospect of further reducing this error by generating ECPs within this hybrid form from the start.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Charge transfer excitation energies from ground state density functional theory calculations

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an N-electron system from a ground state KS or generalized KS calculations of an (N-1)-electron system via its orbital energies. In the present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependent DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as ΔSCF, G 0 W 0 with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction methods like CC2. Our analysis shows that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with the minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Fault-tolerant optical interconnects for neutral-atom arrays

We analyze the use of photonic links to enable large-scale fault-tolerant connectivity of locally error-corrected modules based on neutral atom arrays. Our approach makes use of recent theoretical results showing the robustness of surface codes to boundary noise and combines recent experimental advances in atom-array quantum computing with logical qubits with optical quantum networking techniques. We find the conditions for fault tolerance can be achieved with local two-qubit Rydberg gate and nonlocal Bell-pair errors below 1% and 10%, respectively, without requiring distillation or space-time overheads. Realizing the interconnects with a lens, a single optical cavity, or an array of cavities enables—with sufficient multiplexing—a Bell-pair generation rate in the 1–50 MHz range. When directly interfacing logical qubits, this rate translates to error-correction cycles in the 25–2000 kHz range, satisfying all requirements for fault tolerance and in the upper range fast enough for 100 kHz logical clock cycles. Published by the American Physical Society 2025

Sinclair, Josiah (ORCID:0000000215238295)↗
DOE OSTI2025

Noisy Approach to Intrinsically Mixed-State Topological Order

We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed state can display (imTO)—topological order that is not expected to occur in the ground state of 2D local gapped Hamiltonians. Specifically, we show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, is more naturally phrased as, and provides a physical mechanism for, “gauging out” anyons in the original Hilbert space. We find that gauging out anyons generically results in imTO, with the decohered mixed state strongly symmetric under certain anomalous 1-form symmetries. This framework lays bare a striking connection between the decohered density matrix and , which can appear as anomalous surface states of three-dimensional topological orders. Through a series of examples, we show that the decohered state can display a classical memory, encode logical qubits (i.e., exhibit a quantum memory), and even host chiral or nonmodular topological order. We argue that a partial classification of imTO is given in terms of nonmodular braided-fusion categories. Published by the American Physical Society 2025

Sohal, Ramanjit (ORCID:0000000292975715)↗
DOE OSTI2020

Improved performance of stellarator coil design optimization

Following up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a Wendelstein 7-X test case. This is done by increasing the sample size and applying fully three-dimensional perturbations, but most importantly, by changing the design sequence in which the optimization targets are applied: optimization for field error is conducted first, with coil shape penalties only added to the objective function at a later step in the design process. A robust, feasible coil configuration with a local maximum field error of 3.66 % and an average field error of 0.95 % is achieved here, as compared to a maximum local field error of 6.08 % and average field error of 1.56 % found in our earlier work. These new results are compared to those found without stochastic optimization using the FOCUS and ONSET suites. The relationship between local minima in the optimization space and coil shape penalties is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 2: A semi-discrete error analysis framework for assessing coupling schemes

Abstract. Part 1 (Wan et al., 2024) of this study discusses the motivation and empirical evaluation of a revision to the aerosol-related numerical process coupling in the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) to address the previously reported issue of strong sensitivity of the simulated dust aerosol lifetime and dry removal rate to the model's vertical resolution. This paper complements that empirical justification of the revised scheme with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods. The framework distinguishes the error due to numerical splitting from the error due to the time integration method(s) used for each individual process. Such a distinction results in a framework that provides an intuitive understanding of the causes of the splitting error. The application of this framework to the dust life cycle in EAMv1 confirms (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes and (ii) that the revised splitting reduces that artificial strengthening. While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes and (ii) the choices of input state and time step size for the isolated integration of processes. Such a perspective has the potential for the rapid development of alternative coupling approaches that utilize knowledge both about the desired accuracy and about the computational costs of individual processes.

58 GEOSCIENCES↗
DOE OSTI2019

Error detection and correction utilizing locally stored parity information

A processing system includes a memory coupled to a processor. The memory stores data blocks, with each data block having a separate associated checksum value stored along with the data block in the memory. The processor has a storage location that stores parity information for the data blocks, with the parity information having a plurality of parity blocks. Each parity block represents a parity of a corresponding set of data blocks. The parity blocks can be accessed for use in error detection and correction schemes used by the processing system.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2024

Local modeling for FRF estimation with noisy input measurements

The frequency response function (FRF) is an essential means by which dynamic systems are qualified. In recent years, local modeling approaches have been extensively researched and shown to significantly outperform traditional FRF estimators. However, the standard local modeling approach assumes a perfectly-known system input, which results in biased FRF estimates in the presence of input noise. This paper derives a simple adjustment that can be used to improve FRF estimation for systems subjected to random excitation with noisy input data. This improvement can be implemented with little modification to standard local modeling algorithms and with little additional computational burden. The adjustment is coupled with a model selection procedure to avoid underfitting and overfitting. In conclusion, the methods presented in this paper are validated on a simulation, and they are shown to reduce bias due to input noise.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Statistical learning for predicting density–matrix-based electron dynamics

In this study, we consider the problem of learning density-dependent molecular Hamiltonian matrices from time series of electron density matrices, all in the context of Hartree–Fock theory. Prior work developed a solution to this problem for small molecular systems with density and Hamiltonian matrices of size at most 6 × 6. Here, using a battery of techniques, we scale prior methods to larger molecular systems with, for example, 29 × 29 matrices. This includes systems that either have more electrons or are expressed in large basis sets such as 6-311++G**. Scaling the method to larger systems enhances its relevance for realistic applications in chemistry and physics. To achieve this scaling, we apply dimensionality reduction, ridge regression and analytic computation of Hessians. Through the combination of these techniques, we are able to learn Hamiltonians by minimizing an objective function that encodes local propagation error. Importantly, these learned Hamiltonians can then be used to predict electron dynamics for thousands of steps: When we use our learned Hamiltonians to numerically solve the time-dependent Hartree–Fock equation, we obtain predicted dynamics that are in close quantitative agreement with ground truth dynamics. This includes field-off trajectories similar to the training data and field-on trajectories outside of the training data.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

U-net architected deep material network training with microstructure local field information

The Deep Material Network (DMN) has recently emerged as a powerful reduced-order modeling framework for simulating the mechanical response of heterogeneous materials such as composites. Unlike most data-driven approaches that directly learn a material’s response under prescribed loading, the DMN acts as a homogenization operator, learning the kinematic constraints and mechanical interactions of the underlying microstructure. However, traditional DMN training relies exclusively on homogenized effective properties derived from Direct Numerical Simulations (DNS), discarding the rich local field data that govern microstructural interactions. In this work, we extend the DMN framework to incorporate such local field information into the offline training process. Utilizing a U-Net architecture, we augment the DMN training objective to include the first and second statistical moments of the local stress fields obtained from linear DNS. This ensures that the learned network topology not only fits the effective stiffness but also accurately reflects the internal local stress and strain partitioning of the microstructure. The results confirm that supervising the localization process during training yields a superior surrogate model, reducing local prediction errors by an order of magnitude and significantly improving generalization to unseen nonlinear constitutive behaviors compared to traditional DMNs.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Evaluating a Simple Fracturing Criterion for a Hydraulic Fracture Crossing Stress and Stiffness Contrasts

Hydraulic fracture height containment is a critical issue in the development of unconventional reservoirs. The extent of fracture height growth depends on a variety of factors, particularly stress and stiffness contrasts between adjacent layers. Accurate simulation of fracture growth and containment requires a reliable fracturing criterion. The virtual crack closure technique (VCCT) is a widely used method for computing energy release rate. However, it is based on the assumption that a small crack extension does not significantly alter the state of the crack tip, which is generally not the case when a fracture crosses strong stress and/or stiffness contrasts. In this work, we assess the applicability and accuracy of a modified virtual crack closure technique (MVCCT) for a fluid-driven fracture in breaking through interfaces with significant stress and/or stiffness contrasts, through comparisons with analytical and reference numerical solutions. Here, the results show that significant error could occur when the fracture tip is very near or at stress/stiffness interfaces. However, this error is localized to the interface and proves to be inconsequential to the predicted penetration depth into the rock layer beyond the interface. Finally, this study validates the applicability of MVCCT in 3D hydraulic fracturing simulation in strongly heterogeneous rock formations.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes

In this paper, numerical solution of the FitzHugh–Nagumo (FN) equation is presented based on the nonstandard finite-difference (NSFD) scheme. At first, two exact finite-difference schemes for FN equation are obtained. Moreover, two NSFD schemes are presented for this equation. The positivity, boundedness, and local truncation error of the schemes are discussed. The numerical results obtained by the NSFD schemes are compared with the exact solution and some available methods, to verify the accuracy and efficiency of the NSFD schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Generalized trigonometric Fourier-series method with automatic time step control for non-linear point kinetics equations

The trigonometric Fourier-series method (TFS) is generalized to provide approximate solutions for non-linear point kinetics equations with feedback using varying step sizes. This method can provide a very stable solution against the size of the discrete time step allowing much larger step sizes to be used. Systems of the point kinetics equations are solved using Fourier-series expansion over a partition of the total time interval. The approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high-order derivatives of the solution vector at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. This system is similar to the Vandermonde system. Two successive orders of the partial sums are used to estimate the local truncation error. This error and some other constrains are used to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The process of calculating suitable step sizes should be automatic and inexpensive. Convergence and stability of the proposed method are discussed and a new formula is introduced to maintain stability. The proposed method solves the general linear and non-linear kinetics problems. The method has been applied to five different types of reactivities including step/ramp insertions with temperature feedback. The method is seemed to be valid for larger time intervals than those used in the conventional numerical integration, and is thus useful in reducing computing time. Computational results are found to be consistent with the analysis, they demonstrate that the convergence of the iteration scheme can be accelerated and the resulting computing times can be greatly reduced while maintain computational accuracy.

97 MATHEMATICS AND COMPUTING↗