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DOE OSTI2022

Challenge Problem 1: Preliminary Model Development and Assessment of Flexible Heat Transfer Modeling Approaches

This report presents the modeling progress of a university consortium studying flexible modeling for turbulent heat transfer. In the context of advanced nuclear reactor design, where challenges include non-unity Prandtl fluids, free and mixed convection, and transitional flow, computational fluid dynamics methods are underutilized due to low confidence in modeling approaches and high computational cost. This report evaluates the performance of engineering CFD models in diabatic, buoyant turbulent flow. It finds that all turbulence models including several variants of the k-ε and k-ω models struggle to predict accurate turbulent momentum and heat transfer in such flows. The Nusselt numbers have been compared between the models and the DNS data, where calculations have been performed for each case and trends have shown a good agreement between DNS estimated Nusselt numbers and available correlations as well as experimental data. A novel DNS correlation for high Pr cases as they are transitioning from mixed convection to natural convection has been proposed. While Nusselt number errors relative to DNS range from 20% to 50%, the models capture similar trends to DNS with respect to Nusselt suppression and amplification under varying levels of buoyancy effect. This report also highlights model form error as a significant contributor to CFD predictions and proposes a framework for quantifying model error and improving confidence in CFD calculations. To improve the predictive capability of engineering CFD models, data-driven approaches for turbulence models are investigated. Theoretical frameworks based on the invariant tensor / vector basis neural networks for prediction of Reynolds stresses and turbulent heat fluxes are employed. The models are developed using direct numerical simulations data for forced convection flows of different fluids in vertical planar channel domain. The framework is implemented in spectral element solvers Nek5000 / nekRS and has shown a potential for future development and consideration of mixed convection flows.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Robustness of Kardar-Parisi-Zhang-like transport in long-range interacting quantum spin chains

Isotropic integrable spin chains such as the Heisenberg model feature superdiffusive spin transport belonging to an as-yet-unidentified dynamical universality class closely related to that of Kardar, Parisi, and Zhang (KPZ). To determine whether these results extend to more generic one-dimensional models, particularly those realizable in quantum simulators, we investigate spin and energy transport in non-integrable, long-range Heisenberg models using state-of-the-art tensor network methods. Despite the lack of integrability and the asymptotic expectation of diffusion, for power-law models (with exponent 2<α<∞) we observe long-lived z=3/2 superdiffusive spin transport and two-point correlators consistent with KPZ scaling functions, up to times t∼103/J. We conjecture that this KPZ-like transport is due to the proximity of such power-law-interacting models to the integrable family of Inozemtsev models, which we show to also exhibit KPZ-like spin transport across all interaction ranges. Finally, we consider anisotropic spin models naturally realized in Rydberg atom arrays and ultracold polar molecules, demonstrating that a wide range of long-lived, non-diffusive transport can be observed in experimental settings.

Anand↗

DOE OSTI2023

Learning local equivariant representations for large-scale atomistic dynamics

Abstract A simultaneously accurate and computationally efficient parametrization of the potential energy surface of molecules and materials is a long-standing goal in the natural sciences. While atom-centered message passing neural networks (MPNNs) have shown remarkable accuracy, their information propagation has limited the accessible length-scales. Local methods, conversely, scale to large simulations but have suffered from inferior accuracy. This work introduces Allegro, a strictly local equivariant deep neural network interatomic potential architecture that simultaneously exhibits excellent accuracy and scalability. Allegro represents a many-body potential using iterated tensor products of learned equivariant representations without atom-centered message passing. Allegro obtains improvements over state-of-the-art methods on QM9 and revMD17. A single tensor product layer outperforms existing deep MPNNs and transformers on QM9. Furthermore, Allegro displays remarkable generalization to out-of-distribution data. Molecular simulations using Allegro recover structural and kinetic properties of an amorphous electrolyte in excellent agreement with ab-initio simulations. Finally, we demonstrate parallelization with a simulation of 100 million atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Learning to classify quantum phases of matter with a few measurements

We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region. By using a combination of classical and quantum techniques, such as tensor networks, kernel methods, generalization bounds, quantum algorithms, and shadow estimators, we show that, in some cases, the certification of new ground states can be obtained with a polynomial number of measurements. An important application of our findings is the classification of the phases of matter obtained in quantum simulators, e.g. cold atom experiments, capable of efficiently preparing ground states of complex many-particle systems and applying simple measurements, e.g. single qubit measurements, but unable to perform a universal set of gates.

quantum machine learning↗

DOE OSTI2026

Locally purified maximally mixed states at scale: Entanglement pruning and symmetries

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. Here, in this work we perform a comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue, we analyze two numerical tools, one analytic method, and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Further, away from the maximally mixed state, our simulations highlight how the truncation threshold smoothly interpolate, as a function of depolarization, between established matrix product results and our new results. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network’s fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that are accessible on near-term quantum devices.

Gangapuram, Amit Jamadagni [Oak Ridge National Lab↗

DOE OSTI2022

Multiarea Distribution System State Estimation via Distributed Tensor Completion

Here, this paper proposes a model-free distribution system state estimation method based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A three-way tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A distributed closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. The convergence properties of the distributed algorithm and the sufficient conditions on the number of samples for each smaller network that guarantee the identifiability of the factors of the state tensor are presented. To demonstrate the efficacy of the proposed algorithm and to check the identifiability conditions, numerical simulations are carried out using the IEEE 123-bus system and a large-scale real utility feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Symmetry reduction of tensor networks in many-body theory: I. Automated symbolic evaluation of SU(2) algebra

Abstract The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU (2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

Tichai, A.↗

DOE OSTI2024

QuTree: A tree tensor network package

Here we present QuTree, a C++ library for tree tensor network approaches. QuTree provides class structures for tensors, tensor trees, and related linear algebra functions that facilitate the fast development of tree tensor network approaches such as the multilayer multiconfigurational time-dependent Hartree approach or the density matrix renormalization group approach and its various extensions. We investigate the efficiency of relevant tensor and tensor network operations and show that the overhead for managing the network structure is negligible, even in cases with a million leaves and small tensors. QuTree focuses on providing simple, high-level routines while retaining easy access to the backend to facilitate novel developments. We demonstrate the capabilities of the package by computing the eigenstates of coupled harmonic oscillator Hamiltonians and performing random circuit simulations on a virtual quantum computer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

The influence of packing structure and interparticle forces on ultrasound transmission in granular media

Ultrasound propagation through externally stressed, disordered granular materials was experimentally and numerically investigated. Experiments employed piezoelectric transducers to excite and detect longitudinal ultrasound waves of various frequencies traveling through randomly packed sapphire spheres subjected to uniaxial compression. The experiments featured in situ X-ray tomography and diffraction measurements of contact fabric, particle kinematics, average per-particle stress tensors, and interparticle forces. The experimentally measured packing configuration and inferred interparticle forces at different sample stresses were used to construct spring networks characterized by Hessian and damping matrices. The ultrasound responses of these network were simulated to investigate the origins of wave velocity, acoustic paths, dispersion, and attenuation. Results revealed that both packing structure and interparticle force heterogeneity played an important role in controlling wave velocity and dispersion, while packing structure alone quantitatively explained most of the observed wave attenuation. This research provides insight into time- and frequency-domain features of wave propagation in randomly packed granular materials, shedding light on the fundamental mechanisms controlling wave velocities, dispersion, and attenuation in such systems.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Breaking the curse of dimensionality: Solving configurational integrals for crystalline solids by tensor networks

Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a tensor network approach that reformulates the high-dimensional configurational integral for identical-particle crystals into a sequence of computationally efficient summations. We represent the integrand as a high-dimensional tensor and apply tensor-train (TT) decomposition together with a custom TT-cross interpolation. This approach circumvents the need to explicitly construct the full tensor. We introduce tailored rank-1 and rank-2 schemes optimized for sharply peaked Boltzmann probability densities, typical for identical-particle crystals. When applied to the calculation of internal energy and pressure-temperature curves for crystalline Cu and Ar at high (GPa) pressures, as well as the alpha-to-beta phase transition diagram of Sn, our method accurately reproduces molecular dynamics simulation results using tight-binding, machine learning, hierarchical interacting particle–neural network, and modified embedded atom method potentials,all within seconds of computation time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

The structure and migration of twin boundaries in tetragonal β -Sn: An application of machine learning based interatomic potentials

Although atomistic simulations have contributed significantly to our understanding of twin boundary structure and migration in metals and alloys with hexagonal close packed (HCP) crystal structures, few direct atomistic studies of twinning have been conducted for other types of low symmetry materials, in large part due to a lack of reliable interatomic potentials. In this work, we examine twin boundary structure and migration in a tetragonal material, β-Sn, comparing high resolution Transmission Electron Microscopy (TEM) images of deformation twins in β-Sn to the results of direct atomistic simulations using multiple interatomic potentials. ML-based potentials developed in this work are found to give results consistent with our experimental data, revealing faceted twin boundary structures formed by the nucleation and motion of twinning disconnections. We use bicrystallographic methods in combination with atomistic simulations to analyze the structure, energy and shear coupled migration of observed twin facets in β-Sn. In analogy to Prismatic-Basal (PB/BP) interfaces in HCP metals, we discover low energy asymmetric Prismatic-A-plane (PA/AP) interfaces important to twin growth in β-Sn. Finally, a Moment Tensor Potential (MTP) and Rapid Artificial Neural Network (RANN) interatomic potential suitable for studying twinning and phase transformations in Sn are made publicly available as part of this work.

36 MATERIALS SCIENCE↗

DOE OSTI2024

QFw: A Quantum Framework for Large-scale HPC Ecosystems

This work extends Quantum Framework (QFw) by integrating it with Northwest Quantum Simulator (NWQ-Sim) and by introducing a lightweight python library that allows multiple frontends (e.g., Qiskit) to interact with QFw. This extension enables QFw to flexibly decouple frontends from backends (e.g., NWQ-Sim). We demonstrate this capability by executing a Greenberger-Horne-Zeilinger (GHZ) circuit using Qiskit and Pennylane with NWQ-Sim and Tensor-Network Quantum Virtual-Machine (TN-QVM). QFw enables easy scaling to multiple nodes. We showcase this with scaling tests using GHZ with up to 32 qubits for different number of nodes on the Frontier supercomputer. And, to demonstrate the use of QFw for real world problems, we solve a metamaterial optimization problem, using a Quantum Approximate Optimization Algorithm (QAOA). We observe that QFw over NWQ-Sim marginally improves Qiskit-aer’s accuracy in reaching the lowest energy state. These additions to QFw prepare it to run hybrid applications in a hybrid resource environment since it treats actual quantum hardware and simulators alike.

Chundury, Srikar↗

DOE OSTI2022

Characterizing Tradeoffs in Memory, Accuracy, and Speed for Chemistry Tabulation Techniques

Chemistry tabulation is a common approach in practical simulations of turbulent combustion at engineering scales. Linear interpolants have traditionally been used for accessing precomputed multidimensional tables but suffer from large memory requirements and discontinuous derivatives. Higher-degree interpolants address some of these restrictions but are similarly limited to relatively low-dimensional tabulation. Artificial neural networks (ANNs) can be used to overcome these limitations but cannot guarantee the same accuracy as interpolants and introduce challenges in reproducibility and reliable training. These challenges are enhanced as the physics complexity to be represented within the tabulation increases. Here, we assess the efficiency, accuracy, and memory requirements of Lagrange polynomials, tensor product B-splines, and ANNs as tabulation strategies. We analyze results in the context of nonadiabatic flamelet modeling where higher dimension counts are necessary. While ANNs do not require structuring of data, providing benefits for complex physics representation, interpolation approaches often rely on some structuring of the table. Interpolation using structured table inputs that are not directly related to the variables transported in a simulation can incur additional query costs. This is demonstrated in the present implementation of heat losses. We show that ANNs, despite being difficult to train and reproduce, can be advantageous for high-dimensional, unstructured datasets relevant to nonadiabatic flamelet models. Furthermore we demonstrate that Lagrange polynomials show significant speedup for similar accuracy compared to B-splines.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Pairwise connected tensor network representation of path integrals

It has been recently shown how the tensorial nature of real-time path integrals (PIs) involving the Feynman-Vernon influence functional can be utilized with matrix product states, taking advantage of the finite length of the bath-induced memory. Tensor networks (TNs) promise to provide a unified language to express the structure of a PI. A generalized TN specifically incorporating the pairwise interaction structure of the influence functional and its invariance with respect to the average forward-backward position or the sojourn value in the form of the blip representation is derived and implemented. This pairwise connected TNPI (PC-TNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage and performance scalings are reported, showing the compactness of the representation and the efficiency of the contraction process. Finally, taking advantage of the compressed representation, the viability of using PC-TNPI for simulating multistate problems is demonstrated. The PC-TNPI structure can be shown to yield other TN algorithms currently in use. Consequently, it should be possible to use it as a starting point for deriving other optimized procedures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Physics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor

Reduced models describing the Lagrangian dynamics of the velocity gradient tensor (VGT) in homogeneous isotropic turbulence (HIT) are developed under the physics-informed machine learning (PIML) framework. We consider the VGT at both Kolmogorov scale and coarse-grained scale within the inertial range of HIT. Building reduced models requires resolving the pressure Hessian and subfilter contributions, which is accomplished by constructing them using the integrity bases and invariants of the VGT. The developed models can be expressed using the extended tensor basis neural network (TBNN) introduced by Ling et al. [J. Fluid Mech. 807, 155 (2016)]. Physical constraints, such as Galilean invariance, rotational invariance, and incompressibility condition, are thus embedded in the models explicitly. Our PIML models are trained on the Lagrangian data from a high-Reynolds number direct numerical simulation (DNS). To validate the results, we perform a comprehensive out-of-sample test. We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the “ground-truth” DNS data. A number of other important features describing the structure of HIT are reproduced by the model successfully. We have also identified challenges in modeling inertial range dynamics, which indicates that a richer modeling strategy is required. This helps us identify important directions for future research, in particular towards including inertial range geometry into the TBNN.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Adjoint Waveform Tomography for Crustal and Upper Mantle Structure the Middle East and Southwest Asia for Improved Waveform Simulations Using Openly Available Broadband Data

We present a new model of radially anisotropic seismic wavespeeds for the crust and upper mantle of a broad region of the Middle East and Southwest Asia (MESWA) derived from adjoint waveform tomography. We inverted waveforms from 192 Global Centroid Moment Tensor earthquakes (MW 5.5-7.0) recorded by over 1000 openly available broadband seismic stations from permanent and temporary networks in the region. Spatial coverage of the available data is highly uneven due to earthquakes clustered along plate boundaries and sparse coverage of open seismic networks in the region. We considered three possible starting models: the SPiRaL global model (Simmons et al., 2021); MEC-1 (Kaviani et al., 2020); and CSEM2.0 (Noe et al., 2023). Because the SPiRaL model provides good fits to the observed waveforms measured by the time-bandwidth product of selected windows in several period bands, provides all the necessary parameters and covers the entire domain we used it for the starting model with the period band 50-100 seconds. Inversion iterations proceeded using time-frequency phase misfits in six stages and 54 total iterations reducing the minimum period to 30 seconds. Our final model, MESWA, provides improved waveform fits compared to the starting model for both the data used in the inversion and an independent validation data set of 66 events. Two metrics of waveform fit (the time-frequency phase misfit used in the optimization and normalized L2 misfit) were both reduced by nearly 60% for both data sets and MESWA provides significantly larger misfit reductions relative to the SPiRaL model than the MEC-1 or CSEM models. We also find that MESWA provides a larger time-bandwidth product of selected windows indicating that more information content of the observed waveforms is explained by MESWA than the other models. Our new model reveals tectonic features imaged by other studies and methods but in a new holistic model of shear and compressional wavespeeds (v S and v P , respectively) with anisotropy covering the crust and uppermost mantle of a larger domain. MESWA has smaller scale-length features and tends to sharpen some features relative to the SPiRaL starting model. Examples include: low crustal v S in the TurkishIranian Plateau, Zagros Mountains, Afghan Central Blocks and Sulaiman Fold Belt; low mantle vSfollowing divergent (Gulf of Aden, Red Sea) and transform (Dead Sea Fault) margins of the Arabian Plate; low and high v S in the mantle beneath the Arabian Shield and Platform, respectively. Low vS is imaged below Cenozoic volcanic centers of the Arabian Peninsula, the so-called Mecca-Madina-Nafud (MMN) Line. Positive anisotropy (v SH > v SV ) is inferred for asthenospheric depths across the region except where up/downwelling may influence fabric alignment (e.g. Afar, Red Sea, Arabian Shield). Elevated vS tracks Makran subduction under southeast Iran. MESWA resembles the SPiRaL model in its long-wavelength structure, but enhances shorter wavelengths features on the order of 200 km and smaller. The resulting model could be used for as a starting model for further improvements, say using waveforms from in-country seismic networks that are not openly available or smaller-scale studies targeting shorter period waveforms. The model also could be used for source characterization and moment tensor inversion to improve earthquake hazard studies and nuclear explosion monitoring.

58 GEOSCIENCES↗

DOE OSTI2023

A Physics-Based Data-Driven Approach for Modeling of Environmental Degradation in Elastomers

Abstract Elastomers are now commonly used in a number of industries, including aerospace, structure, transportation, shipbuilding, and automotive, due to their excellent workability, formability, and flexibility. During their activity, elastomers are subjected to harsh environmental conditions, which decreases their resilience. False predictions made early in their lives can have major financial and environmental implications. Elastomers’ performance and properties, such as strength, durability, and density, are influenced by chemical changes in these materials, known as degradation, which occurs over time. This process can alter the morphology of a polymer matrix as well as cause chain scission and cross-linking, resulting in different behaviors than that of the unaged material. To demonstrate the effect of thermaloxidative aging on the mechanical behavior of elastomers, several experimental and theoretical models have been proposed. In view of the large volume of experimental data available on micro-structural evolution in the course of aging, we propose a physics-based data-driven approach to overcome the shortcomings of both phenomenological and micro-mechanical models. This work presents a novel thermodynamically consistent, multiagent machine-learned model for predicting the constitutive behavior of cross-linked elastomers during environmental aging, such as thermo-oxidative and hydrolytic aging for various states of deformation. Single mechanism degradation changes the polymer matrix over time where it is causing chain scission, reduction of cross-links, and morphology change. To capture the idealized Mullins effect and permanent set due to the effect of single aging mechanisms on nonlinear mechanical responses of elastomers, we propose a data-driven model for simulating inelastic elements in a polymer matrix. By using a sequential order reduction, we were able to reduce the 3D stress-strain tensor mapping problem to a small number of super-constrained 1D mapping problems. To systematically classify such mapping problems into a few categories, an assembly of multiple replicated conditional neural network learning agents (L-agents) is used based on our recent work. Each category is represented by a different type of agent. The effect of deformation history, aging time, and aging temperature is captured by this model. The model is validated using a broad collection of data, ranging from our experimental results to data from the literature. In addition, thermodynamic consistency and frame independence are investigated. The most significant achievements of this model are its precision, simplicity, and prediction of inelasticity under various states of deformation. The model’s accuracy and simplicity make it a good option for commercial and industrial applications. Conveniently, due to the model modular nature, it can be expanded in the future to include viscoelasticity and non-isotropic formation for better precision.

Ghaderi, Aref↗