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DOE OSTI2021

The statistical mechanics of near-BPS black holes

Due to the failure of thermodynamics for low temperature near-extremal black holes, it has long been conjectured that a 'thermodynamic mass gap' exists between an extremal black hole and the lightest near-extremal state. For non-supersymmetric near-extremal black holes in Einstein gravity with an AdS2 throat, no such gap was found. Rather, at that energy scale, the spectrum exhibits a continuum of states, up to non-perturbative corrections. In this paper, we compute the partition function of near-BPS black holes in supergravity where the emergent, broken, symmetry is PSU(1, 1|2). To reliably compute this partition function, we show that the gravitational path integral can be reduced to that of a $\mathcal{N}=4$ supersymmetric extension of the Schwarzian theory, which we define and exactly quantize. In contrast to the non-supersymmetric case, we find that black holes in supergravity have a mass gap and a large extremal black hole degeneracy consistent with the Bekenstein–Hawking area. Furthermore, our results verify a plethora of string theory conjectures, concerning the scale of the mass gap and the counting of extremal micro-states.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Nuclear cusps and singularities in the nonadditive kinetic potential bifunctional from analytical inversion

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $\rho_{\rm B}$ and $\rho_{\rm tot} = \rho_{\rm A} + \rho_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of $\rho_{\rm B}$ and $\rho_{\rm tot}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi$^+$, and H$_2$, using analytical inversion to obtain a numerically exact $v^{\rm NAD}$ for the local density approximation. We examine features of $v^{\rm NAD}$ which can be used for development and testing of approximations to $v^{\rm NAD}[\rho_{\rm B},\rho_{\rm tot}]$ and kinetic-energy functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

QCD Constraints on Isospin-Dense Matter and the Nuclear Equation of State

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential μ I bounds the partition function for a baryon chemical potential μ B = 3 μ I / 2 , these calculations also provide rigorous nonperturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Structural and electronic properties of the first iridium containing mixed B-site spinel oxide: Cu [ Ir 1.5 Cu 0.5 ] O 4

Geometrically frustrated systems populated with large spin-orbit coupled ions are an ideal setting for the exploration of novel exotic states of matter. In this study we present an example of iridium on a mixed B-site spinel oxide structure: Cu [ Ir 1.498 ( 2 ) Cu 0.502 ( 2 ) ] O 4 . Synchrotron XRD refinements reveal a face-centered-cubic structure with space group F d 3 ¯ m and mixed Cu-Ir site disorder within the B 2 O 4 rocksalt substructure. Electrical properties reveal a metallic state within the 50–600-K range with a Kondo effect at T < 50 K . X-ray absorption spectroscopy (XAS) measurements show a mixed Cu 1 + / 2 + and Ir 3 + / 4 + charge partitioned picture, which suggests a metallic/band description with reduced on-site Coulomb interactions. Spin-glass-like freezing is seen at T g = 49 K , and the hysteresis behavior for T > T g resembles that of a strongly frustrated magnet. DFT calculations show sizable hybridization between the Cu 3 d and Ir 5 d states with an effective mixed Ir 3 + / 4 + charge partitioned picture, supporting the electronic and XAS results.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Composite Qdrift-product formulas for quantum and classical simulations in real and imaginary time

Recent study has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian H for a given simulation problem into subsets A and B such that H = A + B , where the terms in A are simulated with a Trotter-Suzuki channel and the B terms are randomly sampled via the Qdrift algorithm. Here we extend Qdrift and composite product formulas to imaginary time, formulating candidate classical algorithms for quantum Monte Carlo calculations. We upper bound the induced Schatten- 1 → 1 norm on both imaginary-time Qdrift and composite channels. Another recent result demonstrated that simulations of lattice Hamiltonians containing geometrically local interactions can be improved using a Lieb-Robinson argument to decompose H into subsets that contain only terms supported on that subset of the lattice. Here, we provide a quantum algorithm by unifying this result with the composite approach into “local composite channels” and we upper bound the diamond distance. We provide exact numerical simulations of algorithmic cost by counting the number of gates of the form e − i H j t and e − H j β to meet a certain error tolerance ε . In doing so, we optimize the partitioning into sets A and B using gradient boosted tree models from machine learning. These numerical studies are important given that product formulas have been historically known to outperform analytic upper bounds. We show constant factor advantages for a variety of interesting Hamiltonians, the maximum of which is a ≈ 20 -fold speedup that occurs in the simulation of Jellium. Published by the American Physical Society 2024

Pocrnic, Matthew (ORCID:0000000203089376)↗

DOE OSTI2020

Ion versus Electron Heating in Compressively Driven Astrophysical Gyrokinetic Turbulence

The partition of irreversible heating between ions and electrons in compressively driven (but subsonic) collisionless turbulence is investigated by means of nonlinear hybrid gyrokinetic simulations. We derive a prescription for the ion-to-electron heating ratio Q i /Q e as a function of the compressive-to-Alfvénic driving power ratio P compr /P AW , of the ratio of ion thermal pressure to magnetic pressure β i , and of the ratio of ion-to-electron background temperatures T i /T e . It is shown that Q i /Q e is an increasing function of P compr /P AW . When the compressive driving is sufficiently large, Q i /Q e approaches ≃P compr /P AW . This indicates that, in turbulence with large compressive fluctuations, the partition of heating is decided at the injection scales, rather than at kinetic scales. Analysis of phase-space spectra shows that the energy transfer from inertial-range compressive fluctuations to sub-Larmor-scale kinetic Alfvén waves is absent for both low and high β i , meaning that the compressive driving is directly connected to the ion-entropy fluctuations, which are converted into ion thermal energy. This result suggests that preferential electron heating is a very special case requiring low βi and no, or weak, compressive driving. Our heating prescription has wide-ranging applications, including to the solar wind and to hot accretion disks such as M87 and Sgr A*.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

DRIPS: Dynamic Rebalancing of Pipelined Streaming Applications on CGRAs

Coarse-grained reconfigurable arrays (CGRAs) provide higher flexibility than application-specific integrated circuits (ASICs) and higher efficiency than fine-grained reconfigurable devices such as Field Programmable Gate Arrays (FPGAs). However, CGRAs are generally designed to support offloading of a single kernel. While their design, based on communicating functional units, appears to naturally suit data streaming applications composed of multiple cooperating kernels, current approaches only statically partition the resources across application kernels. However, emerging streaming applications at the edge (scientific instruments, sensor networks, network processing) perform much more than digital signal processing and often are data and input dependent. This leads to extremely variable kernel execution times, severely impacting the throughput of the entire pipeline if resources are only statically allocated. Therefore, in this paper, we propose DRIPS — a coarse-grained, dynamically, and partially reconfigurable array for data-dependent streaming applications. We present a unified compiler framework to facilitate the mapping of a given streaming application onto the DRIPS CGRA architecture. The experimental results show that DRIPS achieves an average throughput improvement of 1.46$\times$ across a set of representative applications over a statically partitioned solution. The additional area overhead to enable dynamic rebalancing consumes 16.34% of the entire area for a 5x5 CGRA prototype.

Tan, Cheng↗

DOE OSTI2021

DynPaC: Coarse-Grained, Dynamic, and Partially Reconfigurable Array for Streaming Applications

Coarse-grained reconfigurable arrays (CGRAs) provide higher flexibility than application-specific integrated circuits (ASICs) and higher efficiency than fine-grained reconfigurable devices such as Field Programmable Gate Arrays (FPGAs). However, CGRAs are generally designed to support offloading of a single kernel. While their design, based on communicating functional units, appears to naturally suit streaming applications composed of multiple cooperating kernels, current approaches only statically partition the resources across kernels. However, streaming applications often are data-dependent, leading to variable kernel execution times depending on the input data and impacting the throughput of the entire pipeline if resources are statically allocated. Therefore, in this paper, we discuss the design of DynPaC — a coarse-grained, dynamically, and partially reconfigurable array for data-dependent streaming applications. We discuss the required software and hardware components to manage partial dynamic reconfiguration. We demonstrate that by supporting partial dynamic reconfiguration, we can obtain an average speedup of 1.44X for a representative set of applications w.r.t. static partitioning, with a limited area overhead (6.4% of the entire chip).

Tan, Cheng↗

DOE OSTI2021

Reoptimization of Quantum Circuits via Hierarchical Synthesis

The current phase of quantum computing is in the Noisy Intermediate-Scale Quantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much noisier than single-qubit gates, so it is essential to minimize their count. Quantum circuit synthesis is a process of decomposing an arbitrary unitary into a sequence of quantum gates, and can be used as an optimization tool to produce shorter circuits to improve overall circuit fidelity. However, the time-to-solution of synthesis grows exponentially with the number of qubits. As a result, synthesis is intractable for circuits on a large qubit scale. In this paper, we propose a hierarchical, block-by-block opti-mization framework, QGo, for quantum circuit optimization. Our approach allows an exponential cost optimization to scale to large circuits. QGo uses a combination of partitioning and synthesis: 1) partition the circuit into a sequence of independent circuit blocks; 2) re-generate and optimize each block using quantum synthesis; and 3) re-compose the final circuit by stitching all the blocks together. We perform our analysis and show the fidelity improvements in three different regimes: small-size circuits on real devices, medium-size circuits on noisy simulations, and large-size circuits on analytical models. Our technique can be applied after existing optimizations to achieve higher circuit fidelity. Further, using a set of NISQ benchmarks, we show that QGo can reduce the number of CNOT gates by 29.9% on average and up to 50% when compared with industrial compiler optimizations such as t|ket). When executed on the IBM Athens system, shorter depth leads to higher circuit fidelity. We also demonstrate the scalability of our QGo technique to optimize circuits of 60+ qubits, Our technique is the first demonstration of successfully employing and scaling synthesis in the compilation tool chain for large circuits. Overall, our approach is robust for direct incorporation in production compiler toolchains to further improve the circuit fidelity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Distributed Macroscopic Traffic Simulation with Open Traffic Models

This paper presents OTM-MPI, an extension of the Open Traffic Models platform (OTM) for running macroscopic traffic simulations in high-performance computing environments. OTM-MPI represents the first open-source, distributed-memory, macroscopic simulation model developed for modern high performance parallel machines and large networks. Macroscopic simulations are appropriate for studying regional traffic scenarios when aggregate trends are of interest, rather than individual vehicle traces. They are also appropriate for studying the routing behavior of classes of vehicles, such as app-informed vehicles. The network partitioning was performed with METIS. Inter-process communication was done with MPI (message-passing interface). Results are provided for two networks: one realistic network which was obtained from Open Street Maps for Chattanooga, TN, and another larger synthetic grid network. The software recorded a speedups of 198x using 256 cores for Chattanooga, and 475x with 1,024 cores for the synthetic network.

macro-scopic traffic simulation↗

DOE OSTI2020

Learning-Accelerated ADMM for Distributed DC Optimal Power Flow

We suggest a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions. Using previous observations of ADMM trajectories for a given system under varying load, the method trains a recurrent neural network (RNN) to predict the converged values of dual and consensus variables. Given a new realization of system load, a small number of initial ADMM iterations is taken as input to infer the converged values and directly inject them into the iteration. We empirically demonstrate that the online injection of these values into the ADMM iteration accelerates convergence by a significant factor for partitioned 14-, 118-and 2848-bus test systems under differing load scenarios. The proposed method has several advantages: it maintains the security of private decision variables inherent in consensus ADMM; inference is fast and so may be used in online settings; RNN-generated predictions can dramatically improve time to convergence but, by construction, can never result in infeasible ADMM subproblems; it can be easily integrated into existing software implementations. While we focus on the ADMM formulation of distributed DC-OPF in this paper, the ideas presented are naturally extended to other distributed optimization problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Impact of Reordering on the LU Factorization Performance of Bordered Block-Diagonal Sparse Matrix

Power engineers rely on computer-based simulation tools to assess grid performance and ensure security. At the core of these tools are solvers for sparse linear equations. When transformed into a bordered block-diagonal (BBD) structure, part of the sparse linear equation solving can be parallelized. This work focuses on using the Schur-complement-based method for LU factorization on BBD matrices, specifically, Jacobian matrices from large-scale systems. Our findings show that the natural ordering method outperforms the default ordering method in computational performance for each block of the BBD matrix. This observation is validated using synthetic 25k-bus and 70k-bus cases, showing a speedup of up to 38% when using natural ordering without permutation. Additionally, the impact of the number of partitions is studied, and the result shows that computational performance improves with more, smaller partitions in the BBD matrices.

BBD matrix↗

DOE OSTI2020

FPDeep: Scalable Acceleration of CNN Training on Deeply-Pipelined FPGA Clusters

In this paper, we propose a framework called FPDeep, which uses a hybrid of model and layer paral- lelism to configure distributed reconfigurable clusters to train DNNs. This approach has numerous benefits. First, the design does not suffer from batch size growth. Second, novel workload and weight partitioning leads to balanced loads of both among nodes. And third, the entire system is fine-grained pipeline. This leads to high parallelism and utilization and also minimizes the time features need to be cached while waiting for back-propagation.

Wang, Tianqi↗

DOE OSTI2022

A Block-Based Triangle Counting Algorithm on Heterogeneous Environments

Triangle counting is a fundamental building block in graph algorithms. In this article, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Fast and Invertible Simplicial Approximation of Magnetic‐Following Interpolation for Visualizing Fusion Plasma Simulation Data

We introduce a fast and invertible approximation for fusion plasma simulation data represented as 2D planar meshes with connectivities approximating magnetic field lines along the toroidal dimension in deformed 3D toroidal spaces. Scientific variables (e.g., density and temperature) in these fusion data are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in the 3D space poses challenges for root-finding and interpolation. To this end, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deformed 3D space. Our algorithm generates a tetrahedral mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. Specifically, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then, we independently search for a feasible tetrahedralization of each partition, considering nonconvexity. We demonstrate our method with two X-Point Gyrokinetic Code (XGC) simulation datasets on the International Thermonuclear Experimental Reactor (ITER) and Wendelstein 7-X (W7-X), and use an ocean simulation dataset to substantiate broader applicability of our method. An open source implementation of our algorithm is available at https://github.com/rcrcarissa/DeformedSpaceTet.

Ren, Congrong [The Ohio State Univ., Columbus, OH ↗

DOE OSTI2020

A proximity‐based image‐processing algorithm for colloid assignment in segmented multiphase flow datasets

Summary Colloidal transport and deposition are of both environmental and engineering importance. Easier access to x‐ray microtomography (XMT) coupled with improved imaging resolution has made XMT a unique and viable tool for visualizing and quantifying these processes. Currently, there is scant information in the literature addressing colloid segmentation and analysis in saturated and unsaturated porous media, in particular related to spatial partitioning of colloids. To support this need, an approach to assign segmented colloidal particles and aggregates to different partitioning classes based on their proximity to different phases is presented here. The method uses different markers for each attachment site (e.g. wetting‐nonwetting phase interfaces). An example XMT dataset from a drainage experiment is used to demonstrate the efficacy of the image processing algorithms. Flow conditions, and fluid and colloid properties, can thus be compared to the behaviour of colloids within the porous medium. This algorithm can help elucidate colloidal deposition mechanisms and the importance of different attachment sites, explore the importance of fluid properties, as well as the arrangement and shape of the colloids.

BRUECK, C. L.↗

DOE OSTI2026

Modelling belowground plant acclimation to low soil nitrogen – a heuristic optimality-based approach

Increased root growth to access greater soil mineral nitrogen resources and increased root exudation to stimulate microbial mineralization of soil organic nitrogen are widely observed plant acclimations to nitrogen limitation. However, their quantitative contribution to plant growth and ecosystem productivity remains largely elusive. Here, we present a novel optimality-based eco-evolutionary model in which plants dynamically regulate carbon partitioning between root growth and exudation to maximize their aboveground growth. Our simulations indicated that the availability of soil mineral and organic nitrogen as well as plant nitrogen demand and nitrogen uptake capacity shape optimal carbon partitioning between root growth and exudation. The simulated carbon allocation patterns aligned with empirical studies on belowground plant responses to varying soil nitrogen resources. Our eco-evolutionary approach represents a paradigmatic change in modelling plant nitrogen foraging, which is essential to generate hypotheses on optimal plant acclimation in future soil environments characterized by more erratic nitrogen availability.

Chakrawal, Arjun (ORCID:0000000345724347)↗

DOE OSTI2020

Retrospective analysis of biochemical limitations to photosynthesis in 49 species: C 4 crops appear still adapted to pre‐industrial atmospheric [ CO 2 ]

Abstract Leaf CO 2 uptake ( A ) in C 4 photosynthesis is limited by the maximum apparent rate of PEPc carboxylation ( V pmax ) at low intercellular [CO 2 ] ( c i ) with a sharp transition to a c i ‐saturated rate ( V max ) due to co‐limitation by ribulose‐1:5‐bisphosphate carboxylase/oxygenase (Rubisco) and regeneration of PEP. The response of A to c i has been widely used to determine these two parameters. V max and V pmax depend on different enzymes but draw on a shared pool of leaf resources, such that resource distribution is optimized, and A maximized, when V max and V pmax are co‐limiting. We collected published A / c i curves in 49 C 4 species and assessed variation in photosynthetic traits between phylogenetic groups, and as a function of atmospheric [CO 2 ]. The balance of V max ‐ V pmax varied among evolutionary lineages and C 4 subtypes. Operating A was strongly V max ‐limited, such that re‐allocation of resources from V pmax towards V max was predicted to improve A by 12% in C 4 crops. This would not require additional inputs but rather altered partitioning of existing leaf nutrients, resulting in increased water and nutrient‐use efficiency. Optimal partitioning was achieved only in plants grown at pre‐industrial atmospheric [CO 2 ], suggesting C 4 crops have not adjusted to the rapid increase in atmospheric [CO 2 ] of the past few decades.

Pignon, Charles P.↗