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At least 271 records · Page 15

A tensor train-based isogeometric solver for large-scale 3D poisson problems

We introduce a three-dimensional (3D), fully tensor train (TT) assembled isogeometric analysis (IGA) framework, TT-IGA, for solving partial differential equations (PDEs). Our method reformulates IGA discrete operators into TT format, enabling efficient compression and computation. Geometry evaluations use the original NURBS description at sampling points and TT approximation is applied to geometry-derived coefficient fields and discrete operators. We demonstrate the effectiveness of the proposed TT-IGA framework on the three-dimensional Poisson equation, achieving substantial reductions in memory and computational cost without compromising solution quality.

97 MATHEMATICS AND COMPUTING↗

A comprehensive and fair comparison of two neural operators (with practical extensions) based on $\mathrm{FAIR}$ data

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet, was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO, was published in 2020, and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. Here we consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions.

42 ENGINEERING↗

Hydropower Cyber-Physical Configurations

The U.S. Department of Energy’s Water Power Technologies Office funded Pacific Northwest National Laboratory, Argonne National Laboratory, and the National Renewable Energy Laboratory to develop a typology to characterize the variety and pervasiveness of cyber-physical configurations across the nation’s hydropower fleet. Outreach to owners and operators returned configurations for 275 hydropower plants or approximately 12% of the fleet. Components (OT and IT), systems, and connections among systems differed among plants according to function, age, position in the river cascade, and many other factors. Seven cyber-physical configuration types labeled A through I, included from 2 to dozens of plants. They were differentiated by how pervasive data and control connections were among cyber-physical components and how frequently control signals paired with data signals in a feedback loop. The flow of data and control within each type implies what cybersecurity vulnerabilities may exist, and what mitigation actions may be most effective. A self-assessment approach allows plant operators to identify the configuration type similar to their plant and link to the lessons learned and best practices information. The cyber-physical typology reinforces the idea that hydropower facilities vary widely, but it also identifies groups that highlight similarities in how their cyber-physical components interact. This helps address fleetwide cybersecurity needs by identifying a reasonable number of configuration types that share risks, vulnerabilities, and potential mitigations.

13 HYDRO ENERGY↗

Design of an epithermal neutron velocity selection system for the Penn State Breazeale Reactor

A series of mechanical neutron choppers to operate as a velocity selection system have been developed for the Pennsylvania State Breazeal Reactor (PSBR). This chopper system will provide pulsed epithermal neutrons in the energy range of 0.5–40 eV with 2% or better energy resolution, and with a transmission of 1E-6 or better. Four different chopper geometries have been evaluated for their utility as mechanical neutron choppers. Specifically, Fermi, ring, piston, and disc choppers have been evaluated to assess their potential neutronics performance and mechanical constructability. A series of high-speed disc choppers were selected for the final design, and optimization work was performed to maximize the neutron pulse intensity. It is estimated that the optimized system will produce an epithermal neutron intensity of approximately 96 n/s. This system can also be operated in a time of flight (TOF) configuration such that the neutrons arriving at the source have a white spectrum. This operation can be accomplished by leaving the second stage of choppers in the open position, or by removing it from the beam completely. Such unique source of epithermal neutrons produced by this chopper system will have applications in both prompt and delayed epithermal neutron activation analysis (ENAA), as well as in neutron resonance transmission analysis (NRTA).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NLML: A Deep Neural Network Emulator for the Exact Nonlinear Interactions in a Wind Wave Model

Nonlinear wave interactions describe the resonant energy transfer between wave components, playing a fundamental role in the evolution of ocean wave spectra. Nonlinear wave interactions significantly influence wave growth and development, making them essential for accurate wave modeling. However, resolving the full six-dimensional Boltzmann integral of the exact nonlinear wave interactions (Webb-Resio-Tracy method, WRT) is computationally expensive, limiting its application in real-time operational wave forecasting and for research purposes. Current approximations, such as the Discrete Interaction Approximation (DIA), prioritize computational speed over accuracy, resulting in significant errors in wave mean parameters. Here, we introduce NLML, a machine learning (ML) emulator designed to approximate the exact nonlinear wave interactions within WAVEWATCH III (WW3), with the goal of achieving the accuracy of WRT while maintaining the stability and computational speed of DIA. By leveraging GPU capabilities such as half precision inference, we achieved substantial speedups, up to 136x mathematical equation faster than the WRT and only a modest 1.04x mathematical equation slowdown relative to DIA, while achieving 2x mathematical equation the accuracy of DIA in global wave spectral energy and mean wave parameters, with up to 7x mathematical equation higher accuracy in some regions. Unlike previous ML approaches, NLML maintained inherent stability throughout model integration in a standalone, year-long WW3 simulation, without requiring additional constraints. Our new ML parameterization bridges the gap between accuracy and efficiency, offering a promising alternative for improving wave modeling in operational settings and research purposes.

16 TIDAL AND WAVE POWER↗

A computationally-efficient method for flamelet calculations

A new open-source code for the simulation of the diffusion flamelet equations is proposed. Emphasis is placed on using an approximate Jacobian to reduce the computational cost of the matrix operations. Performance of the proposed solvers is tested by performing flamelet calculations with kinetic mechanisms of varying sizes. For the unity Lewis number equations, the present iterative Newton solver using an approximate Jacobian greatly outperforms direct Newton solvers using exact Jacobians. The computation cost scales linearly with the number of species, leading to a reduction in solution times by two orders of magnitude for mechanisms containing thousands of species. The applicability of the Jacobian approximations to the solution of the non-unity Lewis number flamelet equations is assessed. The approximations are generally inadequate to solve the full non-unity Lewis number equations but can be used in some applications depending on the balance of terms in the flamelet equations. As an example, the flamelet solver is applied to the study of sooting tendencies in laminar co-flow diffusion flames where modified non-unity Lewis number flamelet equations, previously shown to accurately reproduce experimentally-measured Yield Sooting Indices (YSI), are solved. Here, the accelerated flamelet solver is well suited for sensitivity analysis and uncertainty quantification with large detailed kinetic mechanisms, tasks for which the computational cost was previously prohibitive.

42 ENGINEERING↗

Extending Parsimonious Bayesian Inference

Parsimonious Bayesian inference is a theoretical framework for efficient data assimilation that seeks to balance increased consistency between predictions and training data against corresponding increases in model complexity. Within this framework, over-training is understood as optimization that encodes excessive information within model parameters while only achieving small improvements between predictions and training data. This project aims to develop practical methods of limiting excess model information during optimization. One key observation is that practical heuristics for parsimonious learning in high-dimensions must balance expressivity, i.e. the ability of the model to capture diverse predictions with only a few non-zero parameters, against discoverability, i.e. the ability to train the model with gradient-based optimization and drive parameters to low information states. As such, we developed logical activation functions that are able to adaptively approximate arbitrary truth tables that define Boolean logic operations within a probabilistic framework. These functions have demonstrated the ability to learn exclusive disjunction (XOR) and conditioned disjunction (if [condition] then [result_if_true] else [result_if_false]) within a single layer of a neural network. To efficiently exploit these activation functions to drive parsimonious learning required several other advances within the domain of variational inference. The most efficient form of complexity suppression is structured sparsification, driving most model parameters to zero while achieving the structural coherence among nonzeros needed for bandwidth reduction. Such models are not only far more efficient at suppressing information-theoretic complexity, they also reduce the other forms of complexity (computations, communication, storage, and the number of dependencies needed to evaluate predictions). Aiming to support enhanced sparsification, this project examined new approaches to high-dimensional variational inference that allow us to calibrate and control parameter uncertainty during optimization. By identifying which parameters can sustain sparsifying perturbations with little impact on prediction quality, we can develop better pruning strategies by framing them as approximate Bayesian inference. These advances also open paths to mitigate concerns with deploying advanced learning methods in resource-constrained environments, such as running models on power-limited or communication-limited devices.

97 MATHEMATICS AND COMPUTING↗

A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

97 MATHEMATICS AND COMPUTING↗

Snow ALbedo eVOlution (SALVO) Campaign Broadband Albedo from April - June, 2024 in Utqiagivk, AK level a1

A field-portable broadband (285 – 2800 nm) albedometer was used to make spatially distributed albedo measurements on tundra and sea ice surfaces. The albedometer consists of paired upward-looking and downward-looking pyranometers, which were both connected to a data logger. The instrument was mounted approximately 1 m above the surface using a tripod and was placed on a 1.4 m-long boom to minimize the impacts of shading from the operator and to observe surfaces undisturbed by footprints (see Appendix for photos of measurement setup and uncertainty assessment). Albedo measurements were taken parallel to the 200-m albedo lines at 5-m increments (41 measurements) ~1.2 m south of the line. On the operator’s end of the boom, there was a bubble level that was aligned with the bubble level on the upward-looking pyranometer. To take a measurement, the operator first relocated the tripod to the measurement location, then leveled the instrument and held it level for at least twice the pyranometers’ response time (5 or 15 seconds, see below), and finally depressed a trigger on the data logger. The data logger recorded the instantaneous voltage on both pyranometers, the measurement number, and the time. The data logger also converted the voltages to irradiances, and from these computed the ratio (outgoing/incoming) for albedo, which could be checked in the field. The operator recorded in a field notebook the measurement number that corresponded with the locations on the line and any pertinent notes (e.g., invalid measurements). With this setup, a trained operator could measure a 200-m albedo line (41 measurements) in approximately 30 minutes. Measurements were made within 3 hours of solar noon. The data logger had sufficient storage capacity to record all measurements from the campaign, but data were downloaded to a computer after each measurement day.

54 ENVIRONMENTAL SCIENCES↗

Thermodynamics and collisionality in firehose-susceptible high- β plasmas

We study the evolution of collisionless plasmas that, due to their macroscopic evolution, are susceptible to the firehose instability, using both analytic theory and hybrid-kinetic particle-in-cell simulations. We establish that, depending on the relative magnitude of the plasma β, the characteristic time scale of macroscopic evolution and the ion-Larmor frequency, the saturation of the firehose instability in high-β plasmas can result in three qualitatively distinct thermodynamic (and electromagnetic) states. By contrast with the previously identified ‘ultra-high-beta’ and ‘Alfvén-inhibiting’ states, the newly identified ‘Alfvén-enabling’ state, which is realised when the macroscopic evolution time τ exceeds the ion-Larmor frequency by a β-dependent critical parameter, can support linear Alfvén waves and Alfvénic turbulence because the magnetic tension associated with the plasma’s macroscopic magnetic field is never completely negated by anisotropic pressure forces. We characterise these states in detail, including their saturated magnetic-energy spectra. The effective collision operator associated with the firehose fluctuations is also described; we find it to be well approximated in the Alfvén-enabling state by a simple quasi-linear pitch-angle scattering operator. The box-averaged collision frequency is ν eff ∼ β/τ, in agreement with previous results, but certain subpopulations of particles scatter at a much larger (or smaller) rate depending on their velocity in the direction parallel to the magnetic field. Our findings are essential for understanding low-collisionality astrophysical plasmas including the solar wind, the intracluster medium of galaxy clusters and black hole accretion flows. We show that all three of these plasmas are in the Alfvén-enabling regime of firehose saturation and discuss the implications of this result.

astrophysical plasmas↗

Estimating Higher-Order Moments Using Symmetric Tensor Decomposition

In this paper, we consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in machine learning. The dth-order empirical moment tensor of a set of p observations of n variables is a symmetric d-way tensor. Our goal is to nd a low-rank tensor approximation comprising r $\ll$ p symmetric outer products. The challenge is that forming the empirical moment tensor costs O(pn d ) operations and O(n d ) storage, which may be prohibitively expensive; additionally, the algorithm to compute the low-rank approximation costs O(n d ) per iteration. Our contribution is avoiding formation of the moment tensor, computing the low-rank tensor approximation of the moment tensor implicitly using O(pnr) operations per iteration and no extra memory. This advance opens the door to more applications of higher-order moments since they can now be efficiently computed. We present numerical evidence of the computational savings and show an example of estimating the means for higher-order moments.

97 MATHEMATICS AND COMPUTING↗

Scale up production of carbon fibers from petroleum mesophase pitch

This work investigates the scale-up of pitch precursors for the carbon fiber market using mesophase pitch formulated and produced by Advanced Carbon Products Technologies’ (ACPT’s) patented mesophase pitch processing technology. Through use of its patented process, ACPT developed strategic materials by converting petroleum-based pitch into a high-value, low-cost, carbon-rich feedstock for carbon fiber and other materials critical to our national security. The team successfully developed processing criteria for the tailored mesophase pitch material that can be processed further into precursor and carbon fiber. Processability of the mesophase pitch into precursor and carbon fiber was demonstrated at scale. The resulting materials sequester the carbon that would otherwise be burned and released into the atmosphere, making this an environmentally friendly way to produce these materials in the United States.Pitch-based carbon fibers offer a promising pathway toward cost-effective, high-performance materials for structural and high-modulus composite applications; however, adoption has been limited by challenges in precursor processability and scale-up. In this work, tailored isotropic and mesophase petroleum-derived pitch materials were developed and evaluated for precursor and carbon fiber production through a collaborative effort between Oak Ridge National Laboratory (ORNL) and ACPT. Processing conditions were established at ORNL’s Carbon Fiber Technology Facility to enable stable melt-blowing of pitch-based precursors under continuous operation. Mesophase pitch precursor fibers were produced following oxidation and carbonization, corresponding to a diameter shrinkage of approximately 12%–13% and an estimated mass yield of about 75%–80%. Continuous melt-blowing steady-state operation was demonstrated over time, indicating robust process stability. Melt-blowing was achieved at throughput rates of approximately 20 lb/h⁻¹, validating the commercial viability of petroleum-derived pitch feedstocks for fiber production. Further studies are required to tailor carbon fiber microstructure and properties for specific composite applications.

99 GENERAL AND MISCELLANEOUS↗

Physics-constrained deep neural network method for estimating parameters in a redox flow battery

Here, in this paper, we present a physics-constrained deep neural network (PCDNN) method for parameter estimation in the zero-dimensional (0D) model of the vanadium redox flow battery (VRFB). In this approach, we use deep neural networks to approximate the model parameters as functions of the operating conditions. This method allows the integration of VRFB computational models as the physical constraints in the parameter learning process, leading to enhanced accuracy of parameter estimation and cell voltage prediction. Using an experimental dataset, we demonstrate that the PCDNN method can estimate model parameters for a range of operating conditions and improve the 0D model prediction of voltage compared to the 0D model prediction with constant operation-condition-independent parameters estimated with traditional inverse methods. We also demonstrate that the PCDNN approach has an improved generalization ability for estimating parameter values for operating conditions not used in the training process.

25 ENERGY STORAGE↗

Electrically Conductive Amine Functionalized Reduced Graphite Oxide Foam for CO 2 Removal from the Air

Rapid regeneration of CO 2 adsorbents is critical to improving the productivity of direct air capture (DAC) systems. In this study, we codesigned a material to have appropriate electrical conductivity and CO 2 adsorption properties to enable efficient CO 2 capture from air. Specifically, we present a poly(ethylenimine) (PEI)-impregnated thermally annealed graphite oxide (TAGO900) foam adsorbent tailored for vacuum-assisted electrically driven thermal swing adsorption (V-ETSA). This structured adsorbent leverages the high electrical conductivity of the reduced graphite oxide framework to enable fast and direct heating of the adsorbent material by electrical resistance heating (Joule heating). An optimal sample, 40 wt % PEI (molecular weight 25k) impregnated TAGO900, shows the best balance between adsorption capacity (1.54 mmol g –1 ) and adsorption rates (0.016 mmol g –1 min –1 ) using fixed bed breakthrough experiments at 25 °C and 70% RH using 50 sccm 400 ppm of CO 2 /N 2 flow. Compared to conventional temperature vacuum swing adsorption (TVSA), the V-ETSA approach achieves substantially faster CO 2 desorption, achieving average desorption rates (including cooling time) of 0.09 mmol g –1 min –1 ─approximately 2.5 times faster than TVSA under similar operating conditions. The maximum desorption rate reaches 0.23 mmol/g/min during the desorption stage. These results underscore the importance of the direct heating strategy, such as Joule heating, for fast and highly productive vacuum swing adsorption in DAC systems.

amines↗

Constrained nuclear–electronic orbital method for periodic density functional theory: Application to H 2 chemisorption on Si(001) surfaces

The nuclear–electronic orbital (NEO) method provides a powerful computational framework for incorporating nuclear quantum effects (NQE) in electronic structure calculations beyond the Born–Oppenheimer approximation. By incorporating additional constraints to the position operator on quantum particles like protons, the NEO method enables calculation of effective potential that accounts for NQE. Here, in this work, we present a new constrained NEO (cNEO) formulation for density functional theory (cNEO-DFT) calculations in the context of extended periodic systems. Using the nudged elastic band method, we discuss an application of the cNEO-DFT approach to studying the adsorption of a hydrogen molecule on the Si(001) surfaces. The calculation shows how NQE impacts the reaction energetics. The proton density changes are computed along the reaction pathways. This work demonstrates the capability of the new cNEO-DFT method to study a wide range of chemical processes, such as surface reactions where the quantum nature of light atoms like protons is non-negligible.

Chemical processes↗

Improving the nonlinear control performance of the supply fan at air handling units using a gain scheduling control strategy

Due to its nonlinear nature, the supply fan at air handling units with the controller tuned at the design condition tends to be aggressive and oscillate under partial load conditions. Here, the objective of this paper is to develop and validate a gain scheduling control strategy to improve its nonlinear control performance. First, a control-oriented model, which does not require numerous physical parameters and extensive test data, is developed to study the nonlinearity of the fan system. Based on the theoretical model and experimental verifications, the issue of an aggressive response with a conventional fixed-gain controller is caused by the fact that the system gain is proportional to the ratio of the duct static pressure to the fan speed. To address the issue, a scheduling function of the measurable duct static pressure and fan speed is proposed to be included in the conventional fixed-gain controller to compensate for the fan system gain variation. The gain scheduling control strategy is found to approximately maintain the identical control performance under all operation conditions. Most importantly, the gain scheduling control strategy can be readily implemented without intensive computation and additional measurements, showing a promising potential in industrial applications.

42 ENGINEERING↗

Impact of ionization peak location on measured opaqueness in DIII-D H-mode plasmas

This study investigates the relationship between electron pedestal density and the location of the ionization peak on neutral penetration in DIII-D H-mode plasmas, utilizing a database of Lyman-α emission measurements. The high electron density leads to neutrals being ‘screened’ and the ionization front being pushed out into the Scrape-Off Layer (SOL). This is also referred to as the neutral opaqueness, which is heuristically expected to scale with edge plasma density and machine size. However, at lower electron pedestal density, the penetration depth of the neutrals varies, and measured opaqueness deviates from the heuristic scaling. The database reveals that at low density, when the ionization peak is located in SOL region, the linear relationship between the electron density and neutral penetration holds. However, when the peak is located inside the separatrix, the penetration of the neutrals (λ n 0 ) is much wider ~3.0–3.5 cm, breaking the heuristic opaqueness approximation. These findings provide valuable insights into fueling efficiency and plasma behavior, with implications for Fusion Pilot Plants where high pedestal densities are anticipated and where the neutral opaqueness behaves like its heuristic approximation. This analysis offers a framework to refine neutral opaqueness approximations, enhancing the predictive capability for advanced tokamak operations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quantum algorithms for open lattice field theory

Certain aspects of some unitary quantum systems are well described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be accommodated in a corresponding unitary system + environment model via a generalization of Wigner-Weisskopf theory. This demonstrates the physical relevance of novel features such as exceptional points in quantum dynamics, and opens up avenues for studying many-body systems in the complex plane of coupling constants. In the case of lattice field theory, sparsity lends these channels the promise of efficient simulation on standardized quantum hardware. We thus consider quantum operations that correspond to Suzuki-Lie-Trotter approximation of lattice field theories undergoing nonunitary time evolution, with potential applicability to studies of spin or gauge models at finite chemical potential, with topological terms, to quantum phase transitions—a range of models with sign problems. We develop non-Hermitian quantum circuits and explore their promise on a benchmark, the quantum one-dimensional Ising model with complex longitudinal magnetic field, showing that observables can probe the Lee-Yang edge singularity. The development of attractors past critical points in the space of complex couplings indicates a potential for study on near-term noisy hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗