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All sources NASA NTRS DOE OSTI

DOE OSTI2017

Vertex operator algebras of Argyres-Douglas theories from M5-branes

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N = ( 2 ,   0 ) theory of type J on a punctured sphere. We denote the AD theories as (J b [k], Y), where J b [k] and Y represent an irregular and a regular singularity respectively. We restrict to the ‘minimal’ case where J b [k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra W k 2 d ( J ,   Y   ) , where k 2 d = − h + b b + k with h being the dual Coxeter number of J. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b = h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Theory of overparametrization in quantum neural networks

The prospect of achieving quantum advantage with quantum neural networks (QNNs) is exciting. Understanding how QNN properties (for example, the number of parameters $M$) affect the loss landscape is crucial to designing scalable QNN architectures. Here we rigorously analyze the overparametrization phenomenon in QNNs, defining overparametrization as the regime where the QNN has more than a critical number of parameters $M_c$ allowing it to explore all relevant directions in state space. In this study, our main results show that the dimension of the Lie algebra obtained from the generators of the QNN is an upper bound for $M_c$, and for the maximal rank that the quantum Fisher information and Hessian matrices can reach. Underparametrized QNNs have spurious local minima in the loss landscape that start disappearing when $M$ ≥ $M_c$. Thus, the overparametrization onset corresponds to a computational phase transition where the QNN trainability is greatly improved. We then connect the notion of overparametrization to the QNN capacity, so that when a QNN is overparametrized, its capacity achieves its maximum possible value.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

ChatMPI: LLM-Driven MPI Code Generation for HPC Workloads

The Message Passing Interface (MPI) standard plays a crucial role in enabling scientific applications for parallel computing and is an essential component in high-performance computing (HPC). However, implementing MPI code manually—especially applying a proper domain decomposition and communication pattern—is a challenging and error-prone task. We present ChatMPI, an AI assistant for MPI parallelization of sequential C codes. In our analysis, we focus on testing six essential HPC workloads, which are based on Basic Linear Algebra Subprograms levels 1, 2, and 3 as well as sparse, stencil, and iterative operations. We analyze the process of creating ChatMPI by using the ChatHPC library. This lightweight large language model (LLM)–based infrastructure enables HPC experts to efficiently create and supervise trustworthy AI capabilities for critical HPC software tasks. We study the data required for training (fine-tuning) ChatMPI to generate parallel codes that not only use MPI syntax correctly but also apply HPC techniques to reduce memory communication and maximize performance by using proper work decomposition. With a relatively small training dataset composed of a few dozen prompts and fewer than 15 minutes of fine-tuning on one node equipped with two NVIDIA H100 GPUs, ChatMPI elevates trustworthiness for MPI code generation of current LLMs (e.g., Code Llama, ChatGPT-4o and ChatGPT 5). Additionally, we evaluate the performance of the MPI codes generated by ChatMPI in comparison with the ones generated by ChatGPT-4o and ChatGPT-5. The codes generated by ChatMPI provide up to a 4 × boost in performance by using better problem decomposition, communication patterns, and HPC techniques (e.g., communication avoiding).

Valero Lara, Pedro [ORNL] (ORCID:0000000214794310)↗

DOE OSTI2023

Tools for analysis of optimization models

The software is code for analyzing, debugging, and solving optimization models. The code implements several algorithms and provides convenient APIs to apply these algorithms to optimization models. The algorithms are primarily based on graph theory. They compute well-known partitions of graphs, and use these partitions to provide the user information about their optimization model, including diagnosing certain types of structural modeling errors. Some algorithms may be used as a subroutine to solve an optimization problem, and may call an optimization solver to facilitate this. Well-known linear algebra routines are called to provide further diagnostics. The software contains no data and no models other than toy models used for testing.

Parker, Robert↗

DOE OSTI2017

Diffeomorphism Group Representations in Relativistic Quantum Field Theory

We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

A robust and efficient generalized real cascade model

This paper describes a new separation cascade model that allows for arbitrary cascade connectivity and includes the effects of mixing, material losses and generalized separation element performance. The model also accommodates mixtures with an arbitrary number of component species. The mathematical and numerical framework of this model includes both time-dependent and steady state cascade simulation. Robust numerical approximations of the continuous mathematical model are accomplished using the Sundials suite of nonlinear algebraic and differential-algebraic equation solvers. Verification of the model is accomplished using manufactured solutions while validation is demonstrated by comparison to published experimental results and benchmarks.

36 MATERIALS SCIENCE↗

NASA NTRS1986

Time scale analysis of a closed-loop discrete optimal control system

A two-time scale discrete control system is considered. The closed-loop optimal linear quadratic (LQ) regulator for the system requires the solution of a full-order algebraic matrix Riccati equation. Alternatively, the original system is decomposed into reduced-order slow and fast subsystems. The closed-loop optimal control of the subsystems requires the solution of two algebraic matrix Riccati equations of order lower than that required for the full-order system. A composite, closed-loop suboptimal control is created from the sum of the slow and fast feedback optimal controls. Numerical results obtained for an aircraft model show a very close agreement between the exact (optimal) solutions and computationally simpler composite (suboptimal) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the closed-loop optimal control of digital flight systems.

Naidu, D. S.↗

NASA NTRS1998

Study of Boundary Layer Development in a Two-Stage Low-Pressure Turbine

Experimental data from jet-engine tests have indicated that unsteady blade row (wake) interactions and separation can have a significant impact on the efficiency of turbine stages. The effects of these interactions can be intensified in low-pressure turbine stages because of the low Reynolds number operating environment. Measured turbine efficiencies at takeoff can be as much as two points higher than those at cruise conditions. Thus, during the last decade a significant amount of effort has been put into determining the effects of transition and turbulence on the performance of low pressure turbine stages. Experimental investigations have been performed, for example, by Hodson et al. and Halstead et al. These investigations have helped identify/clarify the roles that factors such as the Reynolds number, free stream turbulence intensity, pressure gradient and curvature have in the generation of losses. In parallel to the experimental investigations, there have been significant analytical efforts to improve the modeling of transition. Examples of such efforts include the works of Mayle and Gostelow et al. These newer models show promise of providing accurate transition predictions over a wide range of flow conditions, although they have yet to be implemented into the numerical flow analyses used by the turbine design community. Some recent computational investigations of interest include the works of Chernobrovkin and Lakshminarayana and Eulitz and Engel. The focus of the current effort has been to -use a viscous, unsteady quasi-three-dimensional Navier-Stokes analysis to study boundary layer development in a two-stage low-pressure turbine. A two-layer algebraic turbulence model, along with a natural transition model and a bubble transition model, have been used, The geometry used in the simulations has been the subject of extensive experiments. The predicted results have been compared with experimental data, including airfoil loadings and time-averaged/unsteady integral boundary layer quantities.

Dorney, Daniel J.↗

DOE OSTI2017

Parallel Asynchronous Distributed-Memory Maximal Independent Set Algorithm with Work Ordering

The maximal independent set (MIS) graph problem arises in many applications such as computer vision, information theory, molecular biology, and process scheduling. The growing scale of graph data suggests the use of distributed memory hardware as a cost-effective approach to providing necessary compute and memory resources. Existing distributed memory parallel MIS algorithms rely on synchronous communication and use techniques such as subgraph computations. In this paper, we present an asynchronous distributed-memory parallel graph algorithm that relies on a virtual directed acyclic graph (DAG) that is created during the algorithm execution. We introduce two additional algorithms that save computations by ordering generated work. The first algorithm applies ordering globally to reduce computations, and the second algorithm applies ordering locally at the level of threads to minimize the synchronization overhead. We use two different implementations of Luby’s algorithm variants as baseline to compare the performance of the presented algorithms: (1) vertex-centric Luby A and Luby B implementations, and (2) the CombBLAS linear-algebra Luby A implementation. Results show that proposed algorithms outperform both implementations of Luby algorithms, especially in distributed execution. Furthermore, we show that for low-diameter graphs the algorithm that applies global ordering scales better than other algorithms and for high diameter graphs the original asynchronous algorithm and thread-level ordering algorithm show better performance.

maximal independent set (MIS), distributed memory ↗

DOE OSTI2015

On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors

The manycore paradigm shift, and the resulting change in modern computer architectures, has made the development of optimal numerical routines extremely challenging. In this work, we target the development of numerical algorithms and implementations for Xeon Phi coprocessor architecture designs. In particular, we examine and optimize the general and symmetric matrix-vector multiplication routines (gemv/symv), which are some of the most heavily used linear algebra kernels in many important engineering and physics applications. We describe a successful approach on how to address the challenges for this problem, starting with our algorithm design, performance analysis and programing model and moving to kernel optimization. Our goal, by targeting low-level and easy to understand fundamental kernels, is to develop new optimization strategies that can be effective elsewhere for use on manycore coprocessors, and to show significant performance improvements compared to existing state-of-the-art implementations. Therefore, in addition to the new optimization strategies, analysis, and optimal performance results, we finally present the significance of using these routines/strategies to accelerate higher-level numerical algorithms for the eigenvalue problem (EVP) and the singular value decomposition (SVD) that by themselves are foundational for many important applications.

Kabir, Khairul↗

NASA NTRS1973

Development of guidelines for the definition of the relavant information content in data classes

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

Schmitt, E.↗

NASA NTRS1987

Algebraic grid generation about wing-fuselage bodies

An algebraic procedure for generating boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration consists of two aircraft components specified by cross sections and mathematically represented by Coons' patches. Several grid blocks are constructed to cover the entire region surrounding the configuration, and each grid block maps into a computational cube. Grid points are first determined on the six boundary surfaces of a block and then in the interior. Grid points on the surface of the configuration are derived from the intersection of planes with the Coons' patch definition. Approximate arc length distributions along the resulting grid curves concentrate and disperse grid points. The two-boundary technique and transfinite interpolation are used to determine grid points on the remaining boundary surfaces and block interiors.

Smith, R.E.↗

NASA NTRS1991

A second-order modeling study of confined swirling flow

A numerical study of a confined strong swirling flow is presented. Computations are performed using a differential second-moment closure. The effect of inlet dissipation rate on calculated mean and turbulence fields is investigated. Two pressure-strain models with various model constants are examined to demonstrate their influences on the predicted results. Finally, comparison of the differential second-moment calculation is made with algebraic second-moment results to determine a better suited model for complex swirling flows.

Nikjooy, M.↗

DOE OSTI2023

Mixed Precision Numerical Linear Algebra (Final Report)

The objective of this subcontract was to identify opportunities for the use of mixed precision within iterative solvers and to explore these opportunities both theoretically and experimentally. All quarterly milestones were achieved. Quarterly achievements are summarized in sections.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Diffusion Synthetic Acceleration for High Order S{sub N} Transport on Meshes with Curved Surfaces

Thermal radiation transport is integral to multiphysics applications such as inertial confinement fusion and astrophysics. Materials in these problems can be exceptionally optically thick and diffusive. A transport solver must be capable of accurate and efficient solutions to such problems. Previously, Woods et al. established a proof-of-concept for high order (HO) discontinuous Galerkin finite element (DGFEM) transport on meshes with curved surfaces. They numerically demonstrated the spatial convergence is order p + 1. Remarkably, these convergence rates are relatively invariant to the amount of curvature of the spatial mesh. We present here an extension of this work that demonstrates a rapidly-convergent iterative solver for the FEM transport equations on meshes with curved sides. We use the modified interior penalty (MIP) diffusion synthetic acceleration (DSA) established by Wang and Ragusa. The partially consistent MIP equations stem from the symmetric interior penalty (IP) derivation of the diffusion equation. The IP method is not stable for optically thick cells so it was combined with the diffusion conforming form (DCF), a discretized diffusion equation derived from the discretized S N equations that is not stable for intermediate optical thicknesses. The MIP equations adapt a 'switch' to the IP method in optically thinner regions and the DCF method in optically thicker regions. The literature does not reveal any Fourier analyses performed for iterative transport on meshes with curved surfaces. Wang and Ragusa performed a Fourier analysis for orthogonal meshes and our results appear to be as expected. Previous literature has reported on some of the sensitivities that affect the spectral radius of DSA schemes: polynomial order, and scattering ratios. Presently, we focus on the sensitivity of the spectral radius to polynomial order, scattering ratio, the constant C, and mesh curvature for varying cell thicknesses. We also numerically study the behavior of the spectral radius to verify our DSA implementation. A sequence of problems is designed to exercise the acceleration. As the problems become more optically thick and diffusive, the accelerated solution continues to converge toward the analytic solution. We employ the Modular Finite Element Methods (MFEM) package, developed at Lawrence Livermore National Laboratory, to generate the linear algebraic system of equations for each angle in the discrete ordinates quadrature set, and use UMFPack to solve this system of equations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1982

Algebraic grid generation

The numerical solution of partial differential equations about irregular geometries and with varying characteristic scales has created the need for coordinate systems and associated transformations which reflect both geometric and physical requirements. The process of finding coordinate transformations in discrete representations is called 'grid generation'. The present investigation is concerned with three algebraic grid generation methods. The methods include transfinite interpolation, the multisurface method, and the two-boundary technique. Interpolation formulas, in terms of homotopic mappings and constraints in terms of point positions and/or derivatives are the essential elements of the techniques. The methods are relatively simple to understand, they are explicit and do not require extensive computational effort, and they have a high degree of generality.

Smith, R. E.↗

NASA NTRS1984

Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

Lawrence, J. L.↗

NASA NTRS1986

Transonic airfoil calculations including wind tunnel wall-interference effects

The results of Reynolds-averaged time-dependent inviscid and turbulent compressible Navier-Stokes computations using the implicit finite-difference approach of Steger (1978), modified by incorporating a pressure boundary condition, (PBC) to account for wall interference are compared with experimental data on a NACA 64A010 airfoil (Johnson and Bachalo, 1980) in graphs and briefly characterized. The computational approach is the same as that used by King and Johnson (1980), but a 137 x 50 mesh is used instead of a 97 x 35 mesh, and special care is taken in resolving the nose, shock, and trailing-edge regions. Imposition of PBC is shown to improve significantly the accuracy of the computations for the flowfield on the upper surface of the airfoil, shifting the shock forward to its experimentally measured position in the case of turbulent flow. The failure of the method, even with PBC, to match the experimental shock location in the case of a flow with a separation bubble is attributed to inadequacies in the algebraic turbulence model employed (Baldwin and Lomax, 1978).

King, L. S.↗