Tensor Parametric Hamiltonian Operator Inference
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Gruber, Anthony David [Sandia National Laboratorie↗
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Extending Orbital-Optimized Density Functional Theory to L-Edge XPS and Beyond: Spin–Orbit Coupling via Nonorthogonal Quasi-Degenerate Perturbation Theory
Quantum mechanical calculations of core electron binding energies (CEBEs) are relevant to interpreting X-ray photoelectron spectroscopy (XPS). Orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge CEBEs but is challenged by the presence of significant spin–orbit coupling (SOC) at L- and higher edges involving inner-shell orbitals with nonzero angular momentum. Here, to extend OO-DFT to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted open-shell OO-DFT to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell (e.g., ionizing all six possible 2p spin orbitals). Nonorthogonal configuration interaction (NOCI) is then used to obtain the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. Using a screened 1-electron SOC operator parametrized with the Dirac-Coulomb-Breit (DCB) Hamiltonian results in doublet splitting (DS) values for third row elements that are nearly in quantitative agreement with experiment. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT CEBEs to yield CEBEs (split by SOC) corrected for dynamic correlation. Comparing calculations on gas phase molecules with experimental results establishes that NO-QDPT with the SCAN functional (NO-QDPT/SCAN), using the DCB screened 1-electron SOC operator is accurate to about 0.2 eV for L-edge CEBEs of molecules containing third row atoms. However, this NO-QDPT approach becomes less accurate for fourth-row elements starting in the middle of the 3d transition metal series, with errors increasing as atomic number increases.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Strong-Drive Limits in Josephson Circuits: From Chaos to an Unbound-Resonance Threshold
Strong microwave drives enable fast measurement and parametric control in superconducting circuits but can induce transitions out of the intended low-energy manifold. We develop a unified description of strong-drive limits in flux- and charge-driven Josephson circuits across drive frequency and dc flux bias. Using classical phase-space analysis and Floquet--Markov simulations, we identify distinct low- and high-frequency mechanisms. At low frequency, we characterize bound-state resonances and separatrix chaos and find that the flux-drive chaos threshold depends strongly on dc flux bias. At high frequency, these mechanisms are suppressed, and the dissipative steady state transfers from the central bound-state sector to outer resonances formed by above-barrier running trajectories. The resulting unbound-resonance threshold is nearly independent of drive frequency and circuit parameters over the regime studied and is controlled primarily by dc flux bias. Coherent simulations show that parametric operation persists beyond this threshold, but at a reduced rate, setting an effective upper bound on the achievable operation speed. We derive analytical criteria for both thresholds, validate them numerically, and experimentally confirm the predicted dc-bias dependence of the low-frequency threshold in a flux-driven SQUID. We also determine the timescales for transfer into the unbound-resonance regime and relaxation back to the bound-state manifold after the drive is removed. Finally, we relate the stability limits to a complementary picture based on the junction critical current and extend the framework to multitone drives and inductively shunted circuits. Together, these results identify the mechanisms limiting strong driving and suggest routes to extend the stable operating range of Josephson circuits.
You, Xinyuan [Fermilab] (ORCID:0000000291789419)↗
Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs
Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.
Latent representations↗
Dynamic Modeling of a Kaplan Hydroturbine Using Optimal Parametric Tuning and Real Plant Operational Data
To address grid variability caused by renewable energy integration and to maintain grid reliability and resilience, hydropower must quickly adjust its power generation over short time periods. This changing energy generation landscape requires advance technology integration and adaptive parameter optimization for hydropower systems via digital twin effort. However, this is difficult owing to the lack of characterization and modeling for the nonlinear nature of hydroturbines. To solve this issue, this paper first formulates a six-coefficient Kaplan hydroturbine model and then proposes a parametric optimization tuning framework based on the Nelder–Mead algorithm for adaptive dynamic learning of the six-coefficients so as to build models that describe the turbine. To assess the performance of the proposed optimal parametric tuning technique, operational data from a real-world Kaplan hydroturbine unit are collected and used to model the relationship between the gate opening and the generated power production. The findings show that the proposed technique can effectively and adaptively learn the unknown dynamics of the Kaplan hydroturbine while optimally tune the unknown coefficients to match the generated power output from the real hydroturbine unit with an inaccuracy of less than 5%. The method can be used to provides optimal tuning of parameters critical for controller design, operational optimization and daily maintenance for hydroturbines in general.
13 HYDRO ENERGY↗
Conjugate Heat Transfer Modeling of Salt-Filled Fuel Pins for Stable Salt Reactor Safety Analysis
The Stable Salt Reactor (SSR) combines the proven structural design of light water reactor fuel assemblies with the inherent safety and fuel-cycle advantages of molten salt technology. In its fast reactor configuration, the SSR utilizes recycled nuclear waste as fuel, sealed within narrow salt-filled fuel pins and cooled by a surrounding liquid salt coolant. Reliable transfer of heat from the molten fuel salt through the cladding to the external coolant is essential for both reactor safety and performance. This work investigates conjugate heat transfer (CHT) in the SSR’s salt-filled fuel pins using NekRS, a high-fidelity spectral element computational fluid dynamics (CFD) solver. The analyses capture internal natural convection within the molten fuel salt and external forced convection in the coolant, under steady-state and transient operating conditions. Parametric studies evaluate how variations in reactor power and coolant flow rate influence heat transfer distributions and system response. The high-fidelity CFD results are time-averaged and post-processed for direct comparison with moderate-fidelity Reynolds-averaged Navier–Stokes (RANS) models, and for the development of reduced-order models within the SAM system code. These validated models support fast-running safety analyses of normal and off-normal transients, improving predictive capability for key safety margins. By integrating advanced CFD with system-level safety tools, this study strengthens the modeling framework for SSR design, reduces uncertainty in molten salt CHT simulations, and accelerates the engineering and licensing of next-generation nuclear reactors.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
SBIR Phase II Final Report: Asynchronous Heterogeneous Distributed Tensor Communication
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97 MATHEMATICS AND COMPUTING↗
Spinor representations for fields with any spin: Lorentz tensor basis for operators and covariant multipole decomposition
This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin (j > 1/2) using chiral representations of the Lorentz group, i.e. the (j, 0) and (0, j) representations and their parity-invariant direct sum. Unlike traditional approaches that require imposing constraints to eliminate spurious degrees of freedom, these chiral representations contain exactly the 2j + 1 components needed to describe a spin-j particle. The central objects in the construction are the t-tensors, which are generalizations of the Pauli four-vector σ μ for higher spin. For the generalized spinors of these representations, we demonstrate how the algebra of the t-tensors allows to formulate a generalization of the Dirac matrix basis for any spin. For on-shell bilinears, we show that a set consisting exclusively of covariant multipoles of order 0 ≤ m ≤ 2j forms a complete basis. We provide explicit expressions for all bilinears of the generalized Dirac matrix basis, which are valid for any spin value. As a byproduct of our derivations we present an efficient algorithm to compute the t-tensor matrix elements. The formalism presented here paves the way to use a more unified approach to analyze the non-perturbative QCD structure of hadrons and nuclei across different spin values, with clear physical interpretation of the resulting distributions as covariant multipoles.
Angular momentum of light↗
Quantum Sensing Enhanced by Squeezing and Non-Hermitian Physics
We find extraordinary enhancement of sensitivity by integrating non-Hermitian and squeezing effects in a general framework for quantum sensing. When a bosonic-mode sensor operates at the parametric oscillation (PO) threshold and an exceptional point (EP), the sensing precision exhibits a quartic scaling with the perturbation strength, leading to ultrahigh sensitivity. The result generalizes to multimode squeezed-state sensors with higher-order EPs, with potential applicability across a wide range of quantum sensing platforms.
Wang, Changqing [Fermilab]↗
The role of moisture in MgCl 2 salt: A multiscale approach to TES performance
This study presents a comprehensive multiscale analysis to evaluate the influence of moisture on the thermal performance of thermal energy storage systems using magnesium chloride (MgCl 2 ) as the phase-changing material. The system uses graphite foam with 90% relative density to enhance thermal conductivity. The analysis includes thermal conductivity calculations and specific heat capacity for different hydrate phases of MgCl 2 : Anhydrous, Mono, Di, Tetra, and Hexa. These properties were evaluated for the first time using the phonon density of states from Density Functional Theory simulations. Results showed that thermal conductivity decreased, while specific heat capacity increased by a factor of two as the phase changed from anhydrous to hexahydrate. Meso-scale models were created to account for the anisotropy of graphite foam and property variations of the MgCl 2 hydrate phases. Asymptotic Expansion homogenization simulations determined the anisotropic thermal conductivity for all phases. This unique methodology improved simulation accuracy, which matched experimental data for anhydrous MgCl 2 . A parametric study examined various operating conditions and their effect on TES performance. It revealed that higher charging temperatures did not enhance exergy efficiency, but increased discharge mass flow rates improved it due to better heat transfer. Thermal performance evaluated by the exergy efficiency remained consistent across hydrate systems under the tested conditions. Furthermore, the study suggests that this uniformity is linked to missing key data, particularly latent heat and melting point for different hydrates. Overall, it highlights the importance of multiscale effects and accurate material properties in designing and optimizing TES systems.
Molten salt degradation↗
Optimization of Scrap Melting Using an Electric Arc in Steel Manufacturing
Steel industry is crucial to the national economy and security. Around 67% of crude steel in the U.S is produced in electric arc furnaces (EAF), which is energy intensive. Around 140 EAFs operate in the U.S., consuming about 8.6x10 7 MMBtu/year of electricity. One of major challenges for EAFs includes maximizing the efficiency of the electrical energy provided in the form of electric arcs to melt various scrap mixes. To address this issue, a computational fluid dynamics (CFD) methodology is chosen to analyze scrap melting using the electric arc. Due to complex furnace phenomena and the wide variety of potential scenarios, high performance computing (HPC) is essential to yield comprehensive and detailed CFD analyses and systematic parametric studies for optimized EAF operation. The objectives are to 1) simulate scrap melting using electric arc, 2) evaluate electrode/arc position for optimum scrap melting and 3) establish reduced order model for CFD data-base for fast model calculation.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Microchannel-based Membrane-less Extraction of Li from Unconventional Lithium Sources & the Separation of REE
This final report provides an overview of the Project's entire duration, covering July 1, 2021 to December 31, 2023. It primarily focuses on the achievements, technological developments, and unique challenges the team faced while working on separating and extracting Lithium from produced waters. The project's primary aim was to create an integrated, high-throughput, membrane-less, and modular microfluidic platform that could extract Lithium from unconventional sources. We have successfully met all goals and milestones envisioned in the SOPO document. The most critical primary milestones, including the Go-No-Go milestone (refer to the Gantt chart in the Appendices), were successfully accomplished. We demonstrated phase separation (>90%) and extraction (>85%) performance in the MPSE using synthetic, and representative produced water composition feed at 50 ml/min total flow through MPSE 36. We have also performed a parametric study of the MPSE operations, beyond the scope of SOPO, exploring operating conditions of current and broader interest. The extended investigation of operational parameters is concurrent with our efforts to seek further development of the MPSE technology beyond the scope of the Project. Along these lines of development, we have made efforts to be responsive to DOE calls for technological developments of other types of resources (beyond PW) for the recovery of Critical Materials and higher TRL development (beyond TRL 4). During the work on this Project, we developed and implemented three innovative technical approaches that emerged from our efforts to successfully meet the Project milestones. The innovative & original technical approaches developed and implemented in this Project are now the contributions to process engineering that could be clearly credited to the Project. First, Convergent Design Approach is a comprehensive feedforward & feedback loop of four design phases: i) design for functionality, ii) design for manufacturing, iii) design for sustainability, and iv) design for market. Next was Process Intensification. A major aim of this Project was to create an innovative phase separation & extraction microscale-based technology for Li separation – thus the words microchannel-based in the Project title. A microscale-based technology is intrinsically in the center of the Process Intensification domain as defined by its unique principles. Therefore, Process Intensification was implicitly envisioned in the Project’s SOPO. Lastly, Time Scale Analysis is a novel tool for discovering the needs and directions of Process Intensification implementations in any process technology. This Project is fully credited for developing and implementing the three novel technical approaches mentioned above. These are general contributions to process engineering that emerged from this Project. Beyond the original SOPO scope, the OSU-U.Pitt research group utilized a Convergent Design methodology, integrating first-principles mathematical modeling with experimental validation on the Minimum Development Vehicle. By creating these Digital Twins, the team rapidly assessed manufacturing iterations to support TEA analysis. This framework further enabled the development of advanced Surface Modification Techniques, where hydrophobic and oleophobic coating strategies were optimized via Digital Twin tools and validated through rigorous 100-hour longevity testing. TEA Analysis: The closing efforts of this Project were focused on the TEA analysis. TEA analysis had two primary functions: i) enabling critical assessments of design variations withing 10 the Concurrent Design Approach, thus enabling evolution of the MPSE design to reach faster- better-cheaper alternatives; and ii) to create a bridge between the accomplishments of this Project and future projects of higher TRL, beyond TRL 6 level. It is important to note that the TEA model created in the Project stirred the technological solutions for the recovery of critical materials toward a vision of a very profitable modular plant that has unique zero-waste water discharge signature. More importantly, thanks to our experimental performance data and conservative assumptions, the TEA model predicts minimal technological and investment risks. Low cost of a modular unit of a nominal capacity of [1000 tons of Li 2 CO 3 /year] positions the MPSE based technology within the reach of community investors, thus offering a paradigm shift in the development of critical technologies. The project successfully navigated two primary challenges: solvent selection and manufacturing adaptation. Restricted by the SOPO to existing literature for lithium recovery, the team identified a critical need for a "material excellence program" to develop next-generation solvents, eventually concluding with a preliminary investigation into promising Ionic Liquids (ILs). Simultaneously, COVID-19 supply chain disruptions forced a pivot from traditional manufacturing to advanced additive methods at ATAMI-OSU. By transitioning from stainless steel to 3D-printed polymer substrates, the team achieved a transformative three-order-of- magnitude reduction in manufacturing costs and compressed prototyping timelines from several months to just two days. The MPSE technology offers significant energy, environmental, and economic advantages by overcoming the traditional bottlenecks of phase-separation hardware and contactor size. Unlike conventional mixer-settlers or membrane-based systems, MPSE operates without moving parts or fouling-prone membranes, achieving robust performance even with challenging, viscous, or particulate-heavy feeds. Key performance metrics include an energy intensity reduction of 5–50x (3–40 kJ/m 3 ) compared to incumbent technologies and a dramatic reduction of processing time to under 60 seconds, which drastically reduces the physical plant footprint. These technical efficiencies translate into superior economic outcomes; for a 100 t/year Li 2 CO 3 facility, implementing MPSE is projected to nearly halve contactor CAPEX (from $\$$6.08M to $\$$3.01M) and significantly increase the project's Net Present Value (NPV), derisking new investment and enabling distributed critical-mineral processing configurations. The commercialization of MPSE technology is being spearheaded by Vigsur Dynamics Inc., which has adopted a structured, parallel approach to technical and business development since its formation in January 2026. Following extensive customer discovery and engagement with the Oregon State University accelerator, Vigsur Dynamics is working to establish a business model that transitions from pilot demonstrations to modular hardware sales, ultimately aiming for a "build-own-operate" service strategy. Current technical milestones—including 100 hours of continuous operation, superior energy efficiency, and successful 6-unit modular scale-up— provide a foundation for this transition. Backed by ongoing IP licensing and a growing network of industrial and venture advisors, the company is actively de-risking the platform to replace conventional mixer-settler systems in the critical minerals market.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Operator dynamics in Floquet many-body systems
We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems. We focus on Floquet quantum circuits, comparing their behavior with what has been found previously for circuits that are random in time. Floquet circuits, which have discrete time-translation symmetry, represent an intermediate case between circuits that are random in time and lack any symmetry, and systems with a time-independent Hamiltonian and continuous time-translation invariance. By making this comparison, one of our aims is to identify signatures of time-translation symmetry in Floquet operator dynamics. To characterize behavior we examine a variety of quantities in solvable models and numerically: operator autocorrelation functions; the partial spectral form factor; the out-of-time-order correlator (OTOC); and the paths in operator space that make the dominant contributions to the ensemble-averaged autocorrelation functions. Our most striking result is that ensemble-averaged autocorrelation functions show behavior that is distinctively different in Floquet systems compared to systems in which successive time-steps are independent. Specifically, while average autocorrelation functions decay on a microscopic timescale for circuits that are random in time, in Floquet systems they have a late-time tail with a duration that grows parametrically with the size of the operator support. In the simplest models this tail is separated from the initial decay by a minimum, so that the average autocorrelation function has an intermediate-time peak. The existence of these tails provides a way to understand deviations of the spectral form factor from random matrix behavior at times shorter than the Thouless time. In contrast to this feature in autocorrelation functions, we find no new aspects to the behavior of OTOCs for Floquet models compared to random-in-time circuits. We show that this difference between averaged autocorrelation functions and OTOCs can be understood in terms of the paths in operator space that contribute to the two quantities: paths for the former retain a limited support at late times, while paths for the latter are dominated by operator spreading. Published by the American Physical Society 2025
Yoshimura, Takato (ORCID:0000000309159846)↗
Operational Parameter Database for Molten Salt Thermal Energy Storage Tank Modeling
The second generation of concentrated solar power (CSP) plants is characterized by the use of a central receiver (either cavity or external), two molten nitrate salt tanks (60 wt.% NaNO 3 and 40 wt.% KNO 3 ), and a steam Rankine power-generation cycle connected through a primary heat exchanger. Molten salt thermal energy storage (TES) tanks have been widely deployed in commercial CSP plants worldwide and have been essential for increasing plant dispatchability and capacity factor, while also reducing the levelized cost of electricity (LCOE). These systems enable energy storage at the gigawatt-hour scale, typically providing 6 to 17 hours of storage duration. Despite being a commercial technology, the multiple failures observed after only a few months or years of operation in plants around the world demonstrate the technology's relative infancy and highlight the need for further research to improve its reliability. The National Laboratory of the Rockies (NLR), in collaboration with industry partners and academic and research institutions, has been leading multiple projects funded by the U.S. Department of Energy (DOE). These projects focus on addressing molten salt tank failures by improving tank design and welding fabrication practices, evaluating new alloys and weld fillers, and providing guidelines for tank commissioning and safe operation. In particular, this report presents modeling results on the effect of key tank operation parameters during 60 minutes of operation, including the mass flow rate and temperature of the salt inflow, tank salt inventory temperature, and inventory level for a representative molten salt tank design. These results form a database of tank operation behaviors that captures the effects of each specific parameter during charging, charging/discharging, and discharging processes.
14 SOLAR ENERGY↗
Search for New Physics via EFT in collisions containing a top quark and a boosted Z or Higgs boson
We present a generator-level sensitivity study of physics beyond the Standard Model within the framework of Effective Field Theory (EFT). The targeted signal processes are single top quark production in association with a Lorentz-boosted Higgs or Z boson (tHq and tZq) in proton-proton collisions at a center-of-mass energy of 13.6 TeV. Event selection requires one electron or muon, a high-transverse-momentum, large-radius (AK8) jet reconstructing hadronic H → b̄b or Z → b̄b decays, at least two distinct, non-overlapping small-radius (AK4) jets with one originating from a b quark, and a missing transverse energy greater than 30 GeV. Signal and background samples are generated via Monte Carlo simulation using MadGraph with MadJax to perform EFT matrix-element calculations. Deviations from the Standard Model are parametrized through dimension-six EFT operators that probe modified top quark interactions. This generator-level study identifies kinematic observables with enhanced sensitivity to EFT operators and motivates future reconstruction-level analyses of tHq and tZq channels.
Meshramkar, Daniel [Baylor U., Waco]↗
Search for New Physics via EFT in collisions containing a top quark and a boosted Z or Higgs boson
We present a generator-level sensitivity study of physics beyond the Standard Model within the framework of Effective Field Theory (EFT). The targeted signal processes are single top quark production in association with a Lorentz-boosted Higgs or Z boson (tHq and tZq) in proton-proton collisions at a center-of-mass energy of 13.6 TeV. Event selection requires one electron or muon, a high-transverse-momentum, large-radius (AK8) jet reconstructing hadronic H → b̄b or Z → b̄b decays, at least two distinct, non-overlapping small-radius (AK4) jets with one originating from a b quark, and a missing transverse energy greater than 30 GeV. Signal and background samples are generated via Monte Carlo simulation using MadGraph with MadJax to perform EFT matrix-element calculations. Deviations from the Standard Model are parametrized through dimension-six EFT operators that probe modified top quark interactions. This generator-level study identifies kinematic observables with enhanced sensitivity to EFT operators and motivates future reconstruction-level analyses of tHq and tZq channels.
Meshramkar, Daniel [Baylor U., Waco]↗
Modeling tritium inventory in hypothetical designs using MELCOR-TMAP
MELCOR-TMAP has been used to model tritium inventory in a hypothetical fusion device with a liquid immersion blanket. Parametric studies for steady-state operations due to material property uncertainties and extraction system limitations are shown, along with a flow-diagram of the model and a history of MELCOR-Fusion
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Reducing Operator Complexity of Galerkin Coarse-grid Operators with Machine Learning
Here, we propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in multigrid (MG) methods, addressing the well-known issue of increasing operator complexity. Guided by the MG theory on spectrally equivalent coarse-grid operators, we have developed novel machine learning algorithms that utilize neural networks combined with smooth test vectors from multigrid eigenvalue problems. The proposed method demonstrates promise in reducing the complexity of coarse-grid operators while maintaining overall MG convergence for solving parametric partial differential equation problems. Numerical experiments on anisotropic rotated Laplacian and linear elasticity problems are provided to showcase the performance and comparison with existing methods for computing non-Galerkin coarse-grid operators.
97 MATHEMATICS AND COMPUTING↗