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DOE OSTI2025

Stability-preserving Lossy Compression for Large-scale Partial Differential Equations

Checkpoint/Restart (C/R) strategies are vital for fault tolerance in PDE-based scientific simulations, yet traditional checkpointing incurs significant I/O overhead. Lossy compression offers a scalable solution by reducing checkpoint data size, but conventional methods often lack control over physical invariants (e.g., energy), leading to instability such as oscillations or divergence in Partial Differential Equations (PDE) systems. This paper introduces a stability-preserving compression approach tailored for PDE simulations by explicitly controlling kinetic and potential energy perturbations to ensure stable restarts. Extensive experiments conducted across diverse PDE configurations demonstrate that our method maintains numerical stability with minimal error magnification—even across multiple checkpoint-restart cycles—outperforming state-of-the-art lossy compressors. Parallel evaluations on the Frontier supercomputer show up to 8.4× improvement in checkpoint write performance and 6.3× in read performance, while maintaining relative L2 errors ∼ 2e-6 throughout continued simulation. These results provide practical guidance for balancing compression accuracy, stability, and computational efficiency in large-scale PDE applications.

Gong, Qian [ORNL] (ORCID:0000000235704142)↗

DOE OSTI2021

Galvanostatic Intermittent Titration Technique Reinvented: Part I. A Critical Review

The galvanostatic intermittent titration technique (GITT), introduced in 1977 by Weppner and Huggins, provided a readily accessible means to measuring the chemical diffusion coefficient of electrochemical electrode materials. The method continues to be widely used today, but the reported diffusivity values are highly inconsistent, ranging as much as four orders of magnitude for some Li layered oxide compositions. Even qualitative trends of diffusivity are inconsistent, suggesting significant flaws in the implementation of the method. Other variants of the GITT method also suffer from similar inconsistency problems. Here we identify numerous sources of significant error including composition-dependent reaction overpotentials, mathematical flaws in the relaxation analysis methods, finite-size and non-planar geometry effects, inter-particle inhomogeneity issues, early transient effects, and surface area uncertainties. We propose a simple relaxation analysis scheme using the time variable t relax + τ - t relax , where t relax is relaxation time and τ is the galvanostatic pulse duration. We also propose to use dense diffusion-limited samples to isolate the bulk-diffusion process in the time domain. Chemical diffusivity can be extracted much more reliably with this improved implementation of the GITT method.

25 ENERGY STORAGE↗

DOE OSTI2025

Partnership Center for High-Fidelity Boundary Plasma Simulation (Final Report)

Within the Partnership Center for High-Fidelity Boundary Plasma Simulation (HBPS), work at UT-Austin was aimed at improved verification, validation, and uncertainty quantification (VVUQ) for edge plasma simulations and on performing gyrokinetics simulations of pedestal instabilities and turbulence in order to expand foundational understanding of pedestal transport. Regarding VVUQ, the accomplishments can be summarized as follows. First, it was shown that the Moment Preserving Constrained Resampling technique, when applied periodically in particle-in-cell simulations in the XGC code, can dramatically improve the accuracy of the simulation at essentially equivalent computational cost. Second, a technique for estimating model correlations, which are required to solve the model selection and sample allocation problem in multifidelity UQ techniques, without sampling the highest fidelity, most computationally expensive model, was developed and demonstrated. Third, previously developed methods for estimating statistical and discretization errors were applied to numerical methods relevant to edge plasma simulations, namely in particle-in-cell-based approaches, and shown to work. Finally, benchmark studies for comparing gyrokinetic codes were developed and performed, leading to reasonable agreement between four commonly used codes. Regarding physics studies, gyrokinetic simulations to investigate microtearing modes in the DIII-D pedestal were performed using the GENE code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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 OSTI2022

An Online Dynamic Amplitude-Correcting Gradient Estimation Technique to Align X-ray Focusing Optics

High-brightness X-ray pulses, as generated at synchrotrons and X-ray free electron lasers (XFELs), are used in a variety of scientific experiments. At these facilities, measurements often require optical equipment, e.g Compound Refractive Lenses (CRLs) to be precisely aligned and focused. The lateral alignment of CRLs to a beamline requires precise positioning along four axes: two translational, and the two rotational. At a synchrotron, alignment is often accomplished manually. However, XFEL beamlines present a beam brightness that fluctuates stochastically, making manual alignment a time-consuming endeavor. Automation using simplex or classic stochastic descent often fails, given the errant gradient estimates. Herein we present a dynamic-amplitude correction to the usual gradient based on the combination of a generalized finite difference stencil and a time-dependent sampling pattern. Intensity is recorded periodically, then used to normalize numerical derivatives against fluctuations. Error expectation is analyzed, and efficacy is demonstrated on classic benchmarks. We provide a proof of concept by laterally aligning optics on a simulated XFEL beamline using data recorded at both synchrotron and XFEL facilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

P{sub N} source expansion nodal method in MPACT for boiling water reactors

This paper describes the one-node P{sub N}-Source Expansion Nodal Method (SENM) axial solver for the 2D/1D method recently implemented in MPACT to support Boiling Water Reactors (BWR) analysis. Since the BWR has a more complicated design and strong burnable absorber, the existing PN-Nodal Expansion Method (NEM) axial solver in MPACT may not be sufficient to accurately represent the intranodal flux and source profiles for BWRs. The one-node P{sub N}-SENM has been implemented in this work to reduce the axial spatial discretization error for BWRs. From numerical results, we verify that the P{sub N}-SENM can improve the accuracy of the pin power prediction, and confirm that P{sub N}-SENM can use more than a 1.5 times larger axial mesh size than P{sub N}-NEM to have similar accuracy for the BWR GE14 3D assembly problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Toward Predictive RANS and SRS Computations of Turbulent External Flows of Practical Interest

In this work, we investigate the main challenges to prediction of turbulent external flows of practical interest with Reynolds-Averaged Navier–Stokes equations (RANS) and Scale-Resolving Simulation (SRS) models. This represents a crucial step toward further developing and establishing these formulations so they can be confidently utilized in engineering problems without reference data. The study initiates by identifying the major challenges to prediction. A literature review is performed to illustrate their effects in RANS and SRS computations. Afterward, we evaluate the impact of the challenges to prediction by analyzing representative statistically steady and unsteady flows with prominent RANS and SRS methods. These include multiple turbulent viscosity and second-moment RANS closures, and hybrid and bridging SRS models. The results demonstrate the potential of the selected SRS models to predict engineering flows. Yet, they also show the importance of considering the challenges to prediction during the setup and conduction of numerical experiments. These can suppress the advantages of using SRS formulations. The data also indicate that only SRS models can confidently predict statistically unsteady flows. In contrast, the results demonstrate that mean-flow quantities of statistically steady flows can be efficiently calculated with RANS closures, especially second-moment closures. Among the selected SRS methods, bridging models reveal better suited for prediction due to their ability to prevent commutation errors and enable the robust evaluation of numerical and modeling errors. This last property allows the use of a new validation technique that does not require reference data.

42 ENGINEERING↗

DOE OSTI2023

Adaptive Time Step Control for Multirate Infinitesimal Methods

Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased computational efficiency. Generally, such methods select these different step sizes based on experimentation or stability considerations. For problems that evolve on a single time scale, adaptivity approaches that strive to control local temporal error are widely used to achieve numerical results of a desired accuracy with minimal computational effort, while alleviating the need for manual experimentation with different time step sizes. However, there is a notable gap in the publication record on the development of adaptive time step controllers for multirate methods. In this paper, we extend the single-rate controller work of Gustafsson [ACM Trans. Math. Software, 20 (1994), pp. 496-517] to the multirate method setting. Specifically, we develop controllers based on polynomial approximations to the principal error functions for both the "fast" and "slow" time scales within multirate infinitesimal (MRI) methods. We additionally investigate a variety of approaches for estimating the errors arising from each time scale within MRI methods. We then numerically evaluate the proposed multirate controllers and error estimation strategies on a range of multirate test problems, comparing their performance against an estimated optimal performance. Through this work, we combine the most performant of these approaches to arrive at a set of multirate adaptive time step controllers that robustly achieve desired solution accuracy with minimal computational effort.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Success of digital adiabatic simulation with large Trotter step

The simulation of adiabatic evolution has deep connections with adiabatic quantum computation, the quantum approximate optimization algorithm, and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. Here we show that with additional conditions, the circuit depth can be linear in simulation time T. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: (1) The fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. (2) Because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. (3) As the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Fault-tolerant connection of error-corrected qubits with noisy links

Abstract One of the most promising routes toward scalable quantum computing is a modular approach. We show that distinct surface code patches can be connected in a fault-tolerant manner even in the presence of substantial noise along their connecting interface. We quantify analytically and numerically the combined effect of errors across the interface and bulk. We show that the system can tolerate 14 times higher noise at the interface compared to the bulk, with only a small effect on the code’s threshold and subthreshold behavior, reaching threshold with ~1% bulk errors and ~10% interface errors. This implies that fault-tolerant scaling of error-corrected modular devices is within reach using existing technology.

Physics↗

DOE OSTI2023

Assessing the Optical Performance Impact of Tracking Error in an Operational Concentrated Solar Power Plant Using Monte Carlo Ray-Tracing Simulation

Concentrating Solar Power (CSP) provides firm and dispatchable electricity due to its thermal storage and hybridization capabilities, which supports the decarbonization of our energy supply. Of the various CSP technologies, parabolic trough collectors are the most mature, with over 500 MW operating worldwide. The optical performance of parabolic trough systems is sensitive to tracking error, which is defined as the angular offset of a collector away from the sun position in the transversal plane. Tracking error commonly occurs due to non-continuous adjustment of the trough angle to point toward the sun, but other factors such as gravity, heating, and wind loading can also contribute to tracking error. Researchers have explored the impact of tracking error on optical performance both numerically and experimentally, but existing studies do not include measurements from operational utility-scale power plants. Tilt angle measurements of parabolic troughs at operational utility-scale power plants illustrate spatial variations in optical performance and include various sources of tracking error such as gravity, heating, and wind loading. To fully characterize wind driven loads on parabolic troughs, we are conducting a long-term field measurement campaign at the Nevada Solar One CSP plant located in Boulder City, NV, which has a nominal capacity of 72 MW and 0.5 hours of full-load storage. We record load measurements on four outer trough rows, collecting support structure bending moments, drive torque moments, dynamic accelerations of the spaceframe, mirror displacement, and tilt angles. Using the tilt measurements acquired at 20 Hz frequency, we calculate the deviation between the nominal sun position and the tracker angle. Using a Monte-Carlo ray-tracing simulation software, we assess the impact of the tracker angle deviation on optical performance throughout the diurnal cycle at various spatial locations within the CSP plant. In our view, this first-of-a-kind study will provide important guidance for future trough designs that reduce the impact of various sources of tracking error on performance.

concentrating solar power↗

DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

A simple numerical method for evaluating heat dissipation from curved wires with periodic applied heating

In many situations, the dual-purpose heater/thermometer wires used in the three-omega method – one of the most precise and sensitive techniques for measuring the thermal conductivity of thin films and interfaces – must include bends and curves to avoid obstructions on the surface of a sample. Although the three-omega analysis assumes that the heating wire is infinitely long and straight, recent experimental work has demonstrated that in some cases curved-wire geometries can be used without introducing detectable systematic error. We describe a general numerical method that can be used to calculate the temperature of three-omega heating wires with arbitrary wire geometries. Furthermore, this method provides experimentalists with a simple quantitative procedure for calculating how large the systematic error caused by a particular wire asymmetry will be. We show calculations of two useful cases: a straight wire with a single bend of arbitrary angle and a wire that forms a circle. We find that the amplitude of the in-phase temperature oscillations near a wire that forms a circle differs from the prediction using the analytic straight-line source solution by <12%, provided that the thermal penetration depth is less than ten times the radius of curvature of the wire path. The in-phase temperature amplitude 1.5 wire widths away from a 90° bend in a wire is within 11% of the straight-line source prediction for all penetration depths greater than the wire width. Our calculations indicate that the straight-line source solution breaks down significantly when the wire bend angle is less than 45°.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2020

Local Truncation Error-Informed Code Verification

The method of manufactured solutions (MMS) has become increasingly popular in conducting code verification studies on predictive codes, such as nuclear power system codes and computational fluid dynamic codes. The reason for the popularity of this approach is that it can be used when an analytical solution is not available. Using MMS, code developers are able to verify that their code is free of coding errors that impact the observed order of accuracy. While MMS is still an excellent tool for code verification, it does not identify coding errors that are of the same order as the numerical method. This paper presents a method that combines MMS with modified equation analysis (MEA), which calculates the local truncation error (LTE) to identify coding error up to and including the order of the numerical method. This method is referred to as modified equation analysis methd of manufactured solutions (MEAMMS). MEAMMS is then applied to a custom-built code, which solves the shallow water equations, to test the performance of the code verification method. MEAMMS is able to detect all coding errors that impact the implementation of the numerical scheme. To show how MEAMMS is different than MMS, they are both applied to the same first-order numerical method test problem with a first-order coding error. When there are first-order coding errors, only MEAMMS is able to identify them. Finally, this shows that MEAMMS is able to identify a larger set of coding errors while still being able to identify the coding errors MMS is able to identify.

42 ENGINEERING↗

DOE OSTI2024

Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning

This repository contains python scripts and numerical data accompanying the paper: "Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning," Tyler Chang, Andrew Gillette, Romit Maulik, 2024. The following subdirectories are included: - "interpolants" contains our interpolation scripts used for all studies - "experiments" contains scripts demonstrating our experiments with synthetic data - "airfoil" contains scripts demonstrating our experiments with the publicly available UIUC airfoil dataset. Further instructions are provided in READMEs within the sub-directories.

Gillette, Andrew↗

DOE OSTI2026

A fast and robust computational modeling approach for density and shape predictions in powder metallurgy hot isostatic pressing

Powder metallurgy hot isostatic pressing (PM-HIP) is an advanced manufacturing process that produces near-net-shape parts with high material utilization and uniform microstructures. PM-HIP is frequently used for producing small-scale parts with complicated geometries and is potentially economical for producing large-scale parts. However, excessive post-HIP shape distortions can reduce its effectiveness and economic advantage, especially for larger parts. A PM-HIP computational model can predict and help mitigate these distortions. However, due to complex deformation mechanisms and thermo-mechanical coupling present in PM-HIP processes, these non-linear computational models sometimes become numerically unstable. The numerical instabilities in these models can lead to very slow convergence or no convergence at all, which often translates to slow and unreliable models. These limitations are more pronounced in large models with complicated geometries. Hence, in this work, an alternative modeling approach is presented that improves numerical stability and computational performance. The presented approach achieves these improvements through approximating the fully coupled thermo-mechanical PM-HIP model as a decoupled model and adding inertial damping to the model’s mechanical part. In conclusion, a comparison with the fully coupled model indicated a slight dip in prediction accuracy (<5% error) but significant improvements in numerical stability (>20 times larger time step size) and computational performance (5-10 times speed-up with less computational resource usage) when using the presented approach.

Hot isostatic pressing↗

DOE OSTI2022

One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons

In this work, we derive analytic formulas that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze and derive expressions for the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows that our formulas are sufficient for determining error budgets for high-fidelity gates, obviating numerical simulations in future projects. All of the derivations are general to any internal qubit state, and any mixed state of the ion crystal's motion that is diagonal in the Fock state basis. Our treatment of static motional frequency shifts, trap anharmonicities, heating, and motional dephasing apply to both laser-based and laser-free gates, while our treatment of field inhomogeneities applies to laser-free systems.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

Reconfigurable Intelligent Surfaces Empowered THz Communication in LEO Satellite Networks

Massive swarms of low Earth orbit (LEO) satellites are poising to serve for high-speed and low-latency ubiquitous connectivity with almost global coverage. Broadband inter-satellite communication is one of the key elements of satellite communication systems that orchestrate massive satellite swarms in cooperation. Thanks to technological advancements in microelectronics and micro-systems, the terahertz (THz) band has emerged as a strong candidate for inter-satellite links (ISLs) due to its promise of wideband communication. Especially, multi-antenna systems can improve the system performance along with the wideband supported by the THz band. However, multi-antenna systems should be reconsidered due to their size, weight, and price/power (SWaP) constraints. On the other hand, as a state-of-art multi-antenna technology, reconfigurable intelligent surface (RIS) is able to relax SWaP constraints because of its passive component-based structures. However, as similar reflection characteristic throughout wideband is difficult to meet, it is possible to observe beam misalignment. In this work, we first provide an assessment of the use of the THz band for ISLs and quantify the impact of misalignment fading on error performance. Then, in order to compensate for the high path loss associated with high carrier frequencies, and to further improve the signal-to-noise ratio (SNR), we propose the use of RISs mounted on neighboring satellites to enable signal propagation. Based on a mathematical analysis of the problem, we present the error rate expressions for RIS-assisted ISLs with misalignment fading. Also, numerical results show that RIS can leverage the error rate performance and achievable capacity of THz ISLs.

reconfigurable intelligent surfaces (RISs)↗