Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical Computing”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 667 records · Page 37

Large language model evaluation for high–performance computing software development

We apply AI-assisted large language model (LLM) capabilities of GPT-3 targeting high-performance computing (HPC) kernels for (i) code generation, and (ii) auto-parallelization of serial code in C ++, Fortran, Python and Julia. Our scope includes the following fundamental numerical kernels: AXPY, GEMV, GEMM, SpMV, Jacobi Stencil, and CG, and language/programming models: (1) C++ (e.g., OpenMP [including offload], OpenACC, Kokkos, SyCL, CUDA, and HIP), (2) Fortran (e.g., OpenMP [including offload] and OpenACC), (3) Python (e.g., numpy, Numba, cuPy, and pyCUDA), and (4) Julia (e.g., Threads, CUDA.jl, AMDGPU.jl, and KernelAbstractions.jl). Kernel implementations are generated using GitHub Copilot capabilities powered by the GPT-based OpenAI Codex available in Visual Studio Code given simple + + prompt variants. To quantify and compare the generated results, we propose a proficiency metric around the initial 10 suggestions given for each prompt. For auto-parallelization, we use ChatGPT interactively giving simple prompts as in a dialogue with another human including simple “prompt engineering” follow ups. Results suggest that correct outputs for C++ correlate with the adoption and maturity of programming models. For example, OpenMP and CUDA score really high, whereas HIP is still lacking. We found that prompts from either a targeted language such as Fortran or the more general-purpose Python can benefit from adding language keywords, while Julia prompts perform acceptably well for its Threads and CUDA.jl programming models. Finally, we expect to provide an initial quantifiable point of reference for code generation in each programming model using a state-of-the-art LLM. Overall, understanding the convergence of LLMs, AI, and HPC is crucial due to its rapidly evolving nature and how it is redefining human-computer interactions.

97 MATHEMATICS AND COMPUTING↗

Uncertainty Visualization Challenges in Decision Systems with Ensemble Data & Surrogate Models

Uncertainty visualization is a key component in translating important insights from ensemble simulation data into actionable decision-making by visually conveying various aspects of uncertainty within a system. With the recent advent of fast surrogate models trained on ensemble data, we can substitute computationally expensive simulations, which allows users to interact with more aspects of data spaces than ever before. However, the use of ensemble data with surrogate models in a decision-making tool brings up new challenges for uncertainty visualization, namely how to reconcile and communicate the new and different types of uncertainties brought in by surrogates and how to utilize these new data estimates in actionable ways. In this work, we examine these issues as they relate to high-dimensional data visualization, the integration of discrete datasets and the continuous representations of those datasets, and the unique difficulties associated with systems that allow users to iterate between input and output spaces. We assess the role of uncertainty visualization in facilitating intuitive and actionable interaction with ensemble data and surrogate models, and highlight key challenges in this new frontier of computational simulation.

ensemble data↗

A multiscale model of the action of a capsid assembly modulator for the treatment of chronic hepatitis B

Chronic hepatitis B virus (HBV) infection is strongly associated with increased risk of liver cancer and cirrhosis. While existing treatments effectively inhibit the HBV life cycle, viral rebound frequently occurs following treatment interruption. Consequently, functional cure rates of chronic HBV infection remain low and there is increased interest in a novel treatment modality, capsid assembly modulators (CAMs). Here, we develop a multiscale mathematical model of CAM treatment in chronic HBV infection. By fitting the model to participant data from a phase I trial of the first-generation CAM vebicorvir, we estimate the drug’s dose-dependent effectiveness and identify the physiological mechanisms that drive the observed biphasic decline in HBV DNA and RNA, and mechanistic differences between HBeAg-positive and negative infection. Finally, we demonstrate analytically and numerically that the relative change of HBV RNA more accurately reflects the antiviral effectiveness of a CAM than the relative change in HBV DNA.

59 BASIC BIOLOGICAL SCIENCES↗

Revolutionizing Neuromorphic Computing for Science (Brochure on the 2024 ASCR Workshop on Neuromorphic Computing for Science)

The ASCR basic research needs for Neuromorphic Computing for Science workshop was held in September 2024. The workshop brochure and report aim to inform and draft a set of grand challenges for advancing the field of neuromorphic computing and developing proof of principle neuromorphic circuits applicable for High Performance Computer (HPC) acceleration for scientific discovery, and brainstorm ideas needed for a successful, robust, and world leading basic research program. The resulting priority research directions are: (1) Neuromorphic computing circuit primitives; (2) Connectivity, communication, and hardware integration; (3) Neuroscience-derived dynamics and algorithms; and (4) Ecosystem for scalable neuromorphic co-design. Breakthroughs in understanding, designing, and prototyping the circuitry and simulation capabilities for a truly neuromorphic computer are essential to enable progress in the field.

97 MATHEMATICS AND COMPUTING↗

Revolutionizing Neuromorphic Computing for Science (Report for the 2024 ASCR Workshop on Neuromorphic Computing for Science)

The ASCR basic research needs for Neuromorphic Computing for Science workshop was held in September 2024. The workshop brochure and report aim to inform and draft a set of grand challenges for advancing the field of neuromorphic computing and developing proof of principle neuromorphic circuits applicable for High Performance Computer (HPC) acceleration for scientific discovery, and brainstorm ideas needed for a successful, robust, and world leading basic research program. The resulting priority research directions are: (1) Neuromorphic computing circuit primitives; (2) Connectivity, communication, and hardware integration; (3) Neuroscience-derived dynamics and algorithms; and (4) Ecosystem for scalable neuromorphic co-design. Breakthroughs in understanding, designing, and prototyping the circuitry and simulation capabilities for a truly neuromorphic computer are essential to enable progress in the field.

97 MATHEMATICS AND COMPUTING↗

Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer

Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the Z 2 and U(1) lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the Z 2 lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.

97 MATHEMATICS AND COMPUTING↗

Vectorized Monte Carlo methods for reactor lattice analysis

Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.

Brown, F. B.↗

Accurate Prediction of pKb in Amines: Validation of the CAM-B3LYP/6-311+G(d,p)/SMD Model

Amines play several key roles in chemistry and biology and are involved in numerous industrial processes, often with significant economic impacts. Recently, amines are also garnering interest as catalysts for polymer synthesis and for CO 2 fixation, incentivizing the need to rapidly design and screen new amino compounds. Hence, developing reliable methods to predict their physicochemical properties, e.g., the base dissociation constant (pKb), is pivotal. Here, a density functional theory (DFT)-based approach was employed to compute the pKb of substituted amines, exploring the impact of several key parameters, including (i) the number of explicit water molecules at the reaction center, (ii) the van der Waals (vdW) surface, and (iii) solvent polarizability. In previous work, it was determined that including two explicit water molecules at the reaction center resulted in highly accurate pKb estimates for primary amines. Here, we find that including a third water molecule at the reaction center is essential for accurate pKb for secondary and tertiary amines. The revised methodology was then applied to a wider selection of amines, obtaining a minimum average error (MAE) < 0.4. In conclusion, this result represents an extension of our “easy-to-use method,” a simple and direct DFT approach exploiting CAM-B3LYP/SMD/6-311G+(d,p) to compute pKb without post facto modifications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Neural units with time-dependent functionality

We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed times is a nonmonotonic function of its inputs, so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, so it is multifunctional in a temporal sense, and able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and perform binary addition, the latter usually implemented in hardware using five logic gates. We show that a set of n oscillators, observed at different times, can perform an arbitrary number of analog-to-n-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations.

97 MATHEMATICS AND COMPUTING↗

Mode-multiplexed photonic integrated vector dot-product core from inverse design

Photonic computing has the potential to harness the full degrees of freedom (DOFs) of the light field, including the wavelength, spatial mode, spatial location, phase quadrature, and polarization, to achieve a higher level of computing parallelism and scalability than digital electronic processors. While multiplexing using the wavelength and other DOFs can be readily integrated on silicon photonics platforms with compact footprints, conventional mode-division multiplexed (MDM) photonic designs occupy areas exceeding tens to hundreds of microns for a few spatial modes, significantly limiting their scalability. Here, we utilize inverse design to demonstrate an ultracompact photonic computing core that calculates vector dot products based on MDM coherent mixing. Our dot-product core integrates the functionalities of two-mode multiplexers and one multimode coherent mixer within a nominal footprint of 5 μm x 3 μm . We have experimentally demonstrated computing examples on the fabricated dot-product core, including complex number multiplication and motion estimation using optical flow. The compact dot-product core design enables large-scale on-chip integration in a parallel photonic computing primitive cluster for high-throughput scientific computing and computer vision tasks.

97 MATHEMATICS AND COMPUTING↗

An Efficient Storage-Driven Machine Learning Model for Performance in the Era of Multimodal Scientific Data

Scientific workflows are increasingly relying on machine learning (ML), simulation, and hybrid techniques to predict, understand, and optimize the behavior of complex experiments. High-performance computing has greatly improved researchers’ ability to acquire diverse data modalities in these workflows. Recent studies suggest that the performance of machine learning models can be improved by integrating data from various sources. Unfortunately, these workloads pose unprecedent pressure on the network storage to meet the demands associated with accessing these multimodal data. To mitigate the impact of intensive IO, we propose a solution that utilizes a multi-tier High-Performance Computing (HPC) distributed storage and data processing framework, placing computation where the data resides for better performance. By adopting this project, the scientific community will gain new opportunities to explore multimodal storage-driven possibilities, integrating multiple scientific data sources with advanced streaming frameworks. Additionally, our framework effectively utilizes computing resources and bridges the gaps identified by HPC experts. Our proposed approach tackles scalability and persistence challenges by leveraging native persistency, which has posed difficulties in traditional approaches. Furthermore, we seek to enhance fault-tolerance and load-balance of computations by leveraging real-time streaming in diverse scientific computing environments, thereby propelling advanced scientific computing research into the next generation.

97 MATHEMATICS AND COMPUTING↗

Fusion and Fission Energy and Science Directorate and Information Technology Services Directorate HPC Cluster Reduction, Consolidation, and Savings in Data Center Space, Power, and Cooling

This report evaluates the benefits of decommissioning six legacy FFESD purchased HPC clusters and consolidating services and workloads into a new HPC cluster named HELIOS. The findings demonstrate significant reductions in the data center power and cooling requirements, data center footprint, and operational overhead, while simultaneously increasing computational capacity.

97 MATHEMATICS AND COMPUTING↗

Uncertainty Visualization Challenges in Decision Systems with Ensemble Data & Surrogate Models: Preprint

Uncertainty visualization is a key component in translating important insights from ensemble data into actionable decision-making by visually conveying various aspects of uncertainty within a system. With the recent advent of fast surrogate models for computationally expensive simulations, users can interact with more aspects of data spaces than ever before. However, the integration of ensemble data with surrogate models in a decision-making tool brings up new challenges for uncertainty visualization, namely how to reconcile and communicate the new and different types of uncertainties brought in by surrogates and how to utilize these new data estimates in actionable ways. In this work, we examine these issues as they relate to high-dimensional data visualization, the integration of discrete datasets and the continuous representations of those datasets, and the unique difficulties associated with systems that allow users to iterate between input and output spaces. We assess the role of uncertainty visualization in facilitating intuitive and actionable interaction with ensemble data and surrogate models, and highlight key challenges in this new frontier of computational simulation.

ensemble visualization↗

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ $\ggg$ 1 (with $\mathcal{X}$∥, $ \mathcal{X}$⟂ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. Further, the implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ~ (NΔt) 1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ = 10 10 ) .

97 MATHEMATICS AND COMPUTING↗

Semi-analytic solutions to the Noh problem with a black box EoS

The objective of this paper is to derive a method of constructing semi-analytic solutions to the Noh problem when the equation of state is a black box. Such solutions can be used for verification tests of hydrodynamics codes. We present the underlying theory, the method for finding solutions, and several examples of derived semi-analytic solutions. We end by performing a classic verification convergence test comparing numerical results from a hydrodynamics code against a non-trivial semi-analytic solution.

97 MATHEMATICS AND COMPUTING↗