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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results of our research show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Input/Output Subroutine Library Program

Efficient, easy-to-use program moved easily to different computers. Purpose of NAVIO, Input/Output Subroutine Library, provides input/output package of software for FORTRAN programs that is portable, efficient, and easy to use. Implemented as hierarchy of libraries. At bottom is very small library containing only non-portable routines called "I/O Kernel." Design makes NAVIO easy to move from one computer to another, by simply changing kernel. NAVIO appropriate for software system of almost any size wherein different programs communicate through files.

Collier, James B.↗
DOE OSTI2021

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation

Here, we study reproducing kernel (RK) collocation method for peridynamic Navier equation. In the first part, we apply a linear RK approximation to both displacement and dilatation, and then back-substitute dilatation and solve the peridynamic Navier equation in a pure displacement form. The RK collocation scheme converges to the nonlocal limit for a fixed nonlocal interaction length and also to the local limit as nonlocal interactions vanish. The stability is shown by comparing the collocation scheme with the standard Galerkin scheme using Fourier analysis. In the second part, we apply the RK collocation to the quasi-discrete peridynamic Navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed. The analysis is carried out on a special family of rectilinear Cartesian grids for the RK collocation method with a designated kernel with finite support. We assume the Lamé parameters satisfy λ ≥ μ to avoid extra assumptions on the nonlocal kernel. Finally, numerical experiments are conducted to validate the theoretical results.

42 ENGINEERING↗
NASA NTRS2019

Challenges Using Linux as a Real-Time Operating System

Human-in-the-loop (HITL) simulation groups at NASA and the Air Force Research Lab have been using Linux as a real-time operating system (RTOS) for over a decade. More recently, SpaceX has revealed that it is using Linux as an RTOS for its Falcon launch vehicles and Dragon capsules. As Linux makes its way from ground facilities to flight critical systems, it is necessary to recognize that the real-time capabilities in Linux are cobbled onto a kernel architecture designed for general purpose computing. The Linux kernel contain numerous design decisions that favor throughput over determinism and latency. These decisions often require workarounds in the application or customization of the kernel to restore a high probability that Linux will achieve deadlines.

Madden, Michael M.↗
DOE OSTI2023

Physics-constrained Gaussian process model for prediction of hydrodynamic interactions between wave energy converters in an array

To improve the efficiency of wave farms and achieve maximum power generation, the layout of wave energy converters (WECs) in an array needs to be carefully designed so that the hydrodynamic interactions can be positively exploited. For this, the hydrodynamic characteristics of the WEC array in different layouts need to be calculated. However, such calculations using numerical models usually entail significant computational cost, especially for large arrays of WECs. To address the computational challenge, a physics-constrained Gaussian process (GP) model is proposed to replace the original expensive numerical model and predict the hydrodynamic characteristics of the WECs for any array layout. By exploring the relationship between the WEC array (i.e., the input) and different hydrodynamic characteristics (i.e., the output), here we summarize a set of physical constraints/features, including invariance, symmetry, and additivity. This prior knowledge about the input-output relationship is then directly embedded in the constructed GP model through the design of physics-constrained kernels. In particular, a double-sum invariant kernel is first developed to incorporate the invariance and symmetry features, and then an additive kernel is developed to incorporate the additive feature of the problem. The invariant kernel and the additive kernel are then integrated to construct the physics-constrained GP model. Compared to the standard GP model, the proposed physics-constrained GP models require less training data to achieve the desired accuracy in predicting the hydrodynamic characteristics and are also less vulnerable to the curse of dimensionality (i.e., good scalability for large arrays) due to the use of an additive kernel. The efficiency, accuracy, and scalability of the proposed approach are demonstrated through an application to predict the hydrodynamic characteristics for WEC arrays of different sizes and layouts.

16 TIDAL AND WAVE POWER↗
NASA NTRS1990

Feasibility study, software design, layout and simulation of a two-dimensional fast Fourier transform machine for use in optical array interferometry

The NASA-Cornell Univ.-Worcester Polytechnic Institute Fast Fourier Transform (FFT) chip based on the architecture of the systolic FFT computation as presented by Boriakoff is implemented into an operating device design. The kernel of the system, a systolic inner product floating point processor, was designed to be assembled into a systolic network that would take incoming data streams in pipeline fashion and provide an FFT output at the same rate, word by word. It was thoroughly simulated for proper operation, and it has passed a comprehensive set of tests showing no operational errors. The black box specifications of the chip, which conform to the initial requirements of the design as specified by NASA, are given. The five subcells are described and their high level function description, logic diagrams, and simulation results are presented. Some modification of the Read Only Memory (ROM) design were made, since some errors were found in it. Because a four stage pipeline structure was used, simulating such a structure is more difficult than an ordinary structure. Simulation methods are discussed. Chip signal protocols and chip pinout are explained.

Boriakoff, Valentin↗
DOE OSTI2021

Toward Evaluating High-Level Synthesis Portability and Performance between Intel and Xilinx FPGAs

Offloading computation from a CPU to a hardware accelerator is becoming a more common solution for improving performance because traditional gains enabled by Moore’s law and Dennard scaling have slowed. GPUs are often used as hardware accelerators, but field-programmable gate arrays (FPGAs) are gaining traction. FPGAs are beneficial because they allow hardware specific to a particular application to be created. However, they are notoriously difficult to program. To this end, two of the main FPGA manufacturers, Intel and Xilinx, have created tools and frameworks that enable the use of higher level languages to design FPGA hardware. Although Xilinx kernels can be designed by using C/C++, both Intel and Xilinx support the use of OpenCL C to architect FPGA hardware. However, not much is known about the portability and performance between these two device families other than the fact that it is theoretically possible to synthesize a kernel meant for Intel to Xilinx and vice versa.In this work, we evaluate the portability and performance of Intel and Xilinx kernels. We use OpenCL C implementations of a subset of the Rodinia benchmarking suite that were designed for an Intel FPGA and make the necessary modifications to create synthesizable OpenCL C kernels for a Xilinx FPGA. We find that the difficulty of porting certain kernel optimizations varies, depending on the construct. Once the minimum amount of modifications is made to create synthesizable hardware for the Xilinx platform, more nontrivial work is needed to improve performance. However, we find that constructs that are known to be performant for an FPGA should improve performance regardless of the platform; the difficulty comes in deciding how to invoke certain kernel optimizations while also abiding by the constraints enforced by a given platform’s hardware compiler.

Cabrera, Anthony↗
DOE OSTI2021

Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Exact Gaussian processes for massive datasets via non-stationary sparsity-discovering kernels

Abstract A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. Its success is largely attributed to the GP’s analytical tractability, robustness, and natural inclusion of uncertainty quantification. Unfortunately, the use of exact GPs is prohibitively expensive for large datasets due to their unfavorable numerical complexity of $$O(N^3)$$ O ( N 3 ) in computation and $$O(N^2)$$ O ( N 2 ) in storage. All existing methods addressing this issue utilize some form of approximation—usually considering subsets of the full dataset or finding representative pseudo-points that render the covariance matrix well-structured and sparse. These approximate methods can lead to inaccuracies in function approximations and often limit the user’s flexibility in designing expressive kernels. Instead of inducing sparsity via data-point geometry and structure, we propose to take advantage of naturally-occurring sparsity by allowing the kernel to discover—instead of induce—sparse structure. The premise of this paper is that the data sets and physical processes modeled by GPs often exhibit natural or implicit sparsities, but commonly-used kernels do not allow us to exploit such sparsity. The core concept of exact, and at the same time sparse GPs relies on kernel definitions that provide enough flexibility to learn and encode not only non-zero but also zero covariances. This principle of ultra-flexible, compactly-supported, and non-stationary kernels, combined with HPC and constrained optimization, lets us scale exact GPs well beyond 5 million data points.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2024

Deep energy-pressure regression for a thermodynamically consistent EOS model

Abstract In this paper, we aim to explore novel machine learning (ML) techniques to facilitate and accelerate the construction of universal equation-Of-State (EOS) models with a high accuracy while ensuring important thermodynamic consistency. When applying ML to fit a universal EOS model, there are two key requirements: (1) a high prediction accuracy to ensure precise estimation of relevant physics properties and (2) physical interpretability to support important physics-related downstream applications. We first identify a set of fundamental challenges from the accuracy perspective, including an extremely wide range of input/output space and highly sparse training data. We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. Our evaluation results show an excellent fit of the EOS table and the predicted values are ready to use for important physics-related tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Mathematical nuances of Gaussian process-driven autonomous experimentation

Abstract The fields of machine learning (ML) and artificial intelligence (AI) have transformed almost every aspect of science and engineering. The excitement for AI/ML methods is in large part due to their perceived novelty, as compared to traditional methods of statistics, computation, and applied mathematics. But clearly, all methods in ML have their foundations in mathematical theories, such as function approximation, uncertainty quantification, and function optimization. Autonomous experimentation is no exception; it is often formulated as a chain of off-the-shelf tools, organized in a closed loop, without emphasis on the intricacies of each algorithm involved. The uncomfortable truth is that the success of any ML endeavor, and this includes autonomous experimentation, strongly depends on the sophistication of the underlying mathematical methods and software that have to allow for enough flexibility to consider functions that are in agreement with particular physical theories. We have observed that standard off-the-shelf tools, used by many in the applied ML community, often hide the underlying complexities and therefore perform poorly. In this paper, we want to give a perspective on the intricate connections between mathematics and ML, with a focus on Gaussian process-driven autonomous experimentation. Although the Gaussian process is a powerful mathematical concept, it has to be implemented and customized correctly for optimal performance. We present several simple toy problems to explore these nuances and highlight the importance of mathematical and statistical rigor in autonomous experimentation and ML. One key takeaway is that ML is not, as many had hoped, a set of agnostic plug-and-play solvers for everyday scientific problems, but instead needs expertise and mastery to be applied successfully. Graphical abstract

97 MATHEMATICS AND COMPUTING↗
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 OSTI2023

Adrastea: An Efficient FPGA Design Environment for Heterogeneous Scientific Computing and Machine Learning

We present Adrastea, an efficient FPGA design environment for developing scientific machine learning applications. FPGA development is challenging, from deployment, proper toolchain setup, programming methods, interfacing FPGA kernels, and more importantly, the need to explore design space choices to get the best performance and area usage from the FPGA kernel design. Adrastea provides an automated and scalable design flow to parameterize, implement, and optimize complex FPGA kernels and associated interfaces. We show how virtualization of the development environment via virtual machines is leveraged to simplify the setup of the FPGA toolchain while deploying the FPGA boards and while scaling up the automated design space exploration to leverage multiple machines concurrently. Adrastea provides an automated build and test environment of FPGA kernels. By exposing design space hyper-parameters, Adrastea can automatically search the design space in parallel to optimize the FPGA design for a given metric, usually performance or area. Adrastea simplifies the task of interfacing with the FPGA kernels with a simplified interface API. To demonstrate the capabilities of Adrastea, we implement a complex random forest machine learning kernel with 10,000 input features while achieving extremely low computing latency without loss of prediction accuracy, which is required by a scientific edge application at SNS. We also demonstrate Adrastea using an FFT kernel and show that for both applications Adrastea is able to systematically and efficiently evaluate different design options, which reduced the time and effort required to develop the kernel from months of manual work to days of automatic builds.

Young, Aaron↗
DOE OSTI2020

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗