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DOE OSTI2024

Benchmarking machine learning strategies for phase-field problems

Abstract We present a comprehensive benchmarking framework for evaluating machine-learning approaches applied to phase-field problems. This framework focuses on four key analysis areas crucial for assessing the performance of such approaches in a systematic and structured way. Firstly, interpolation tasks are examined to identify trends in prediction accuracy and accumulation of error over simulation time. Secondly, extrapolation tasks are also evaluated according to the same metrics. Thirdly, the relationship between model performance and data requirements is investigated to understand the impact on predictions and robustness of these approaches. Finally, systematic errors are analyzed to identify specific events or inadvertent rare events triggering high errors. Quantitative metrics evaluating the local and global description of the microstructure evolution, along with other scalar metrics representative of phase-field problems, are used across these four analysis areas. This benchmarking framework provides a path to evaluate the effectiveness and limitations of machine-learning strategies applied to phase-field problems, ultimately facilitating their practical application.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Modeling plasma toroidal flow profile control via NTV torque with n = 2 3D fields in MAST-U

Toroidal modeling utilizing the MARS-Q code shows that large (compared to electromagnetic torque) neoclassical toroidal viscous (NTV) torque can be achieved in the plasma core region in reference MAST(-U) L-mode plasmas, by applying the n=2 (n is the toroidal mode number) 3-D fields generated by the magnetic coils used for controlling the edge localized mode and/or by the error field correction coils. Large NTV torque, occurring at relatively slow plasma flow, in combination with strong variation of the torque amplitude versus the coil phasing of the 3-D coils, offers a tool to control the plasma toroidal rotation profile in spherical tokamaks. To effectively employ the toroidal NTV torque, the potentially fast initial flow needs to first be damped by 3-D fields. In conclusion, MARS-Q quasi-linear initial value simulations demonstrate that this is achievable in MAST-U, within the designed 3-D coil current capability for the device.

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

Provably accurate simulation of gauge theories and bosonic systems

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ − 1 , an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on Λ that achieves accuracy ϵ , obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ = polylog ( ϵ − 1 ) .

Tong, Yu↗

DOE OSTI2025

Unified architecture for quantum lookup tables

Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications depends crucially on gate-efficient implementations of these oracles, which are commonly some reversible versions of the Boolean circuit for a classical lookup table. Here, we present a general parametrized architecture for quantum circuits implementing a lookup table that encompasses all prior work in realizing a continuum of optimal trade-offs between qubits, non-Clifford gates, and error resilience, up to logarithmic factors. Our architecture assumes only local 2D connectivity, yet recovers results, with the appropriate parameters, polylogarithmic error scaling. We also identify regimes, such as simultaneous sublinear scaling, in all parameters. These results enable tailoring implementations of the commonly used lookup table primitive to any given quantum device with constrained resources.

quantum circuits↗

DOE OSTI2024

Stochastic Error Cancellation in Analog Quantum Simulation

Analog quantum simulation is a promising path towards solving classically intractable problems in many-body physics on near-term quantum devices. However, the presence of noise limits the size of the system and the length of time that can be simulated. In our work, we consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian we want to simulate by small local perturbations, which are assumed to be random and unbiased. We analyze the error accumulated in observables in this setting and show that, due to stochastic error cancellation, with high probability the error scales as the square root of the number of qubits instead of linearly. We explore the concentration phenomenon of this error as well as its implications for local observables in the thermodynamic limit. Moreover, we show that stochastic error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise. This indicates that, to reach a certain fidelity, more noise can be tolerated than implied by the worst-case bound if the noise comes from many statistically independent sources.

Analog quantum simulation↗

DOE OSTI2020

An error-controlled adaptive time-stepping method for particle advancement in coupled CFD-DEM simulations

Coupled Computational-Fluid-Dynamics (CFD) and Discrete-Element-Method (DEM) models provide an accurate description of multiphase physical systems where a solid granular particle phase exists in an underlying gaseous continuous medium. The time integration of the granular phase in these simulations is typically handled using an explicit scheme with a constant time-step among all particles that is invariant in time to resolve inter-particle collisions. A locally third-order accurate adaptive time integration technique for particles that employs an embedded locally second-order scheme for error determination is presented in this work. The particle time-step size is dynamically adapted based on solution error, thus leading to significant savings in computational time. The efficacy of our scheme is quantified using four test cases of varying complexity (binary collision, homogeneous cooling system, fluidized bed and hopper discharge). The adaptive time-stepping method exhibits improved performance (~ 2–3 times in most of the cases studied) compared to three commonly used non-adaptive time-step methods (first-order Euler-explicit, second-order Adams-Bashforth and third-order Runge-Kutta schemes), while maintaining the same level of accuracy and parallel scalability.

42 ENGINEERING↗

DOE OSTI2021

Local prediction of Laser Powder Bed Fusion porosity by short-wave infrared imaging thermal feature porosity probability maps

We report that local thermal history can significantly vary in parts during metal Additive Manufacturing (AM), leading to local defects. However, the sequential layer-by-layer nature of AM facilitates in-situ part voxelmetric observations that can be used to detect and correct these defects for part qualification and quality control. The challenge is to relate this local radiometric data with local defect information to estimate process error likelihood in future builds. This paper uses a Short-Wave Infrared (SWIR) camera to record the temperature history for parts manufactured with Laser Powder Bed Fusion (LPBF) processes. The porosity from a cylindrical specimen is measured by ex-situ micro-computed tomography (μCT). Specimen data from the SWIR camera, combined with the μCT data, are used to generate thermal feature-based porosity probability maps. The porosity predictions made by various SWIR thermal feature-porosity probability maps of a specimen with a complex geometry are scored against the true porosity obtained via μCT. The receiver operating characteristic curves constructed from the predictions for the complex sample demonstrate the porosity probability mapping methodology’s potential for in-situ based porosity detection.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware

Teleporting physical quantities to remote locations remains a key challenge for quantum information science and technology. Quantum teleportation has enabled the transfer of quantum information, but teleportation of quantum physical quantities has not yet been realized. Here we report the realization and observation of quantum energy teleportation on real superconducting quantum hardware. We achieve this by using several IBM superconducting quantum computers. The results are consistent with the exact solution of the theory and are improved by the mitigation of measurement error. Quantum energy teleportation requires only local operations and classical communication. Furthermore, our results provide a realistic benchmark that is fully achievable with current quantum computing and communication technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Machine Learning-Based Prediction of Distribution Network Voltage and Sensor Allocation

Increasing penetration levels of fast-varying energy resources might negatively affect power system operation. At the same time, sensor deployment throughout distribution networks improves system awareness and enables the development of new and advanced voltage control solutions. Such control techniques rely on accurate prediction in anticipation of voltage violation scenarios. This paper analyzes various approaches to voltage prediction in a distribution system, and it is shown that combining multiple techniques into a single regressor improves its predictive power. Moreover, a two-step regressor is proposed in which initial predictions based on a global regressor are refined by local regressors; in this case, prediction errors decrease significantly. Additionally, a clustering approach is employed to perform sensor allocation so that only the most influential buses are selected for monitoring without diminishing prediction accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Machine Learning-Based Prediction of Distribution Network Voltage and Sensors Allocation: Preprint

Increasing penetration of fast-varying energy resources may negatively affect power systems' operation. At the same time, sensor deployment throughout distribution networks improves system awareness and enables the development of new and advanced voltage control solutions. Such control techniques rely on accurate prediction in anticipation to voltage violation scenarios. This paper analyzes various approaches for voltage prediction in a distribution system; it is shown that combining multiple techniques into a single regressor improves its predictive power. Moreover, a two-step regressor is proposed, where initial predictions based on a global regressor are refined by local regressors; in this case, prediction errors decrease significantly. Additionally, a clustering approach is employed for performing sensor allocation, so that only the most influential buses are selected for monitoring without diminishing prediction accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Machine Learning-Based Prediction of Distribution Network Voltage and Sensor Allocation

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2023

Time-Energy Uncertainty Relation for Noisy Quantum Metrology

Detection of very weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. To sense an unknown physical parameter, one prepares an initial state of a probe system, allows the probe to evolve as governed by a Hamiltonian 𝐻 for some time 𝑡, and then measures the probe. If 𝐻 is known, we can estimate 𝑡 by this method; if 𝑡 is known, we can estimate classical parameters on which 𝐻 depends. The accuracy of a quantum sensor can be limited by either intrinsic quantum noise or by noise arising from the interactions of the probe with its environment. In this work, we introduce and study a fundamental trade-off, which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which a party Alice prepares an initial pure state of the clock, allows the clock to evolve for a time that is not precisely known, and then transmits the clock through a noisy channel to a party Bob. Meanwhile, the environment (Eve) receives any information about the clock that is lost during transmission. We prove that Bob’s loss of quantum Fisher information about the elapsed time is equal to Eve’s gain of quantum Fisher information about a complementary energy parameter. We also prove a similar, but more general, trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two noncommuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise, which form a subset of the Knill-Laflamme error-correction conditions. A state and its local time-evolution direction, if they satisfy these conditions, are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as a quantum error-correcting code with similar distance in which the Hamiltonian acts as a logical operator, potentially offering new schemes for constructing states that do not lose any sensitivity upon application of a noisy channel. We discuss applications of the trade-off relation to sensing using a quantum many-body probe subject to erasure or amplitude-damping noise.

metrology↗

DOE OSTI2024

Estimation and Visualization of Isosurface Uncertainty from Linear and High-Order Interpolation Methods

Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is easy to implement, it has limitations when the underlying data is complex and high-order, which is the case for most real-world data. Linear interpolation can output vertices at the wrong location. Its inability to deal with sharp features and features smaller than grid cells can lead to an incorrect isosurface with holes and broken pieces. Despite these limitations, isosurface visualizations typically do not include insight into the spatial location and the magnitude of these errors. We utilize high-order interpolation methods with MC algorithms and interactive visualization to highlight these uncertainties. Our visualization tool helps identify the regions of high interpolation errors. It also allows users to query local areas for details and compare the differences between isosurfaces from different interpolation methods. In addition, we employ high-order methods to identify and reconstruct possible features that linear methods cannot detect. We showcase how our visualization tool helps explore and understand the extracted isosurface errors through synthetic and real-world data.

Ouermi, Timbwaoga↗

DOE OSTI2025

On infinite tensor networks, complementary recovery and type II factors

We initiate a study of local operator algebras at the boundary of infinite tensor networks, using the mathematical theory of inductive limits. In particular, we consider tensor networks in which each layer acts as a quantum code with complementary recovery, a property that features prominently in the bulk-to-boundary maps intrinsic to holographic quantum error-correcting codes. In this case, we decompose the limiting Hilbert space and the algebras of observables in a way that keeps track of the entanglement in the network. As a specific example, we describe this inductive limit for the holographic Harlow-Pastawski-Preskill-Yoshida code model and relate its algebraic and error-correction features. We find that the local algebras in this model are given by the hyperfinite type II$_\infty$ factor. Next, we discuss other networks that build upon this framework and comment on a connection between type II factors and stabilizer circuits. We conclude with a discussion of multiscale entanglement renormalization ansatz networks in which complementary recovery is broken. We argue that this breaking possibly permits a limiting type III von Neumann algebra, making them more suitable ansätze for approximating subregions of quantum field theories.

holographic dualities↗

DOE OSTI2026

Introduction to and comparison of deep learning and optimization approaches to analytical wake modeling of a tilted wind turbine

This paper introduces innovative optimization and deep learning techniques to enhance the prediction of complex wake dynamics in the downstream wind velocity of tilted wind turbines. Traditional methods for calibrating the Bastankhah wake model often lead to increased errors in wind velocity distribution due to overfitting of the local wake characteristics. To address this issue, we propose an additional global optimization step to reduce errors in wind velocity predictions with respect to various wake parameters. Despite this improvement, the Bastankhah model's axisymmetric Gaussian wake shape limits its accuracy for complex wake structures. Therefore, we also propose a deep learning approach, which demonstrates promising results by accurately modeling complex wake shapes across a broader range of tilt angles with minimal computational cost. The deep learning approach achieves near-identical predictions to high-fidelity large-eddy simulations, representing a promising advancement in wake modeling.

17 WIND ENERGY↗

DOE OSTI2025

Impact of dynamics, entanglement and Markovian noise on the fidelity of few-qubit digital quantum simulation

Quantum algorithms have been proposed to accelerate the simulation of the chaotic dynamical systems that are ubiquitous in the physics of plasmas. Quantum computers without error correction might even use noise to their advantage to calculate the Lyapunov exponent by measuring the Loschmidt echo fidelity decay rate. For the first time, digital Hamiltonian simulations of the quantum sawtooth map, performed on the IBM-Q quantum hardware platform, show that the fidelity decay rate of a digital quantum simulation increases during the transition from dynamical localization to chaotic diffusion in the map. The observed error per CNOT gate increases by $1.5{\times }$ as the dynamics varies from localized to diffusive, while only changing the phases of virtual RZ gates and keeping the overall gate count constant. A gate-based Lindblad noise model that captures the effective change in relaxation and dephasing errors during gate operation qualitatively explains the effect of dynamics on fidelity as being due to the localization and entanglement of the states created. Specifically, highly delocalized states that are entangled with random phases show an increased sensitivity to dephasing and, on average, a similar sensitivity to relaxation as localized states. In contrast, delocalized unentangled states show an increased sensitivity to dephasing but a lower sensitivity to relaxation. This gate-based Lindblad model is shown to be a useful benchmarking tool by estimating the effective Lindblad coherence times during CNOT gates and finding a consistent $2\unicode{x2013}3{\times }$ shorter $T_2$ time than reported for idle qubits. Thus, the interplay of the dynamics of a simulation with the noise processes that are active can strongly influence the overall fidelity decay rate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.

42 ENGINEERING↗