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DOE OSTI2022

Hypothesis testing via AI: Generating physically interpretable models of scientific data with machine learning (Full Technical Report)

Deep learning has demonstrated an exceptional ability to solve complex tasks (an engineering success); however, it has done so at the expense of the ability to generate new knowledge (a scientific failure). We propose an alternative framework—entitled Deep Symbolic Regression (DSR)—in which artificial neural networks (NNs) rapidly generate hypotheses about physical relationships among inputs. This framework bypasses the need to interpret an NN altogether, while still leveraging the representational power of deep learning. The resulting models are tractable mathematical expressions, which are inherently and readily human interpretable and can provide insights into underlying physical phenomena. Further, we fold this methodology into the scientific process by allowing the scientist to directly integrate a priori knowledge and beliefs to accelerate learning. We demonstrate this methodology on symbolic regression—the problem of rediscovering underlying expressions describing a dataset—and achieve state-of-the-art performance across a wide variety of symbolic regression problems. Further, we generalize our DSR framework to apply to the more general class of symbolic optimization problems, in which one seeks to optimize a sequence of symbols or “tokens” under a black-box reward function. Examples of other symbolic optimization problems include neural architecture search and computational antibody design. Our generalized tool, Deep Symbolic Optimization (DSO), has been demonstrated on the task of learning symbolic control policies for reinforcement learning environments, and has been adopted as an enabling capability for computational antibody design.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

An Array of Optical Receivers for Deep-Space Communications

An array of small optical receivers is proposed as an alternative to a single large optical receiver for high-data-rate communications in NASA s Deep Space Network (DSN). Because the telescope for a single receiver capable of satisfying DSN requirements must be greater than 10 m in diameter, the design, building, and testing of the telescope would be very difficult and expensive. The proposed array would utilize commercially available telescopes of 1-m or smaller diameter and, therefore, could be developed and verified with considerably less difficulty and expense. The essential difference between a single-aperture optical-communications receiver and an optical-array receiver is that a single-aperture receiver focuses all of the light energy it collects onto the surface of an optical detector, whereas an array receiver focuses portions of the total collected energy onto separate detectors, optically detects each fractional energy component, then combines the electrical signal from the array of detector outputs to form the observable, or "decision statistic," used to decode the transmitted data. A conceptual block diagram identifying the key components of the optical-array receiver suitable for deep-space telemetry reception is shown in the figure. The most conspicuous feature of the receiver is the large number of small- to medium-size telescopes, with individual apertures and number of telescopes selected to make up the desired total collecting area. This array of telescopes is envisioned to be fully computer- controlled via the user interface and prediction-driven to achieve rough pointing and tracking of the desired spacecraft. Fine-pointing and tracking functions then take over to keep each telescope pointed toward the source, despite imperfect pointing predictions, telescope-drive errors, and vibration caused by wind.

Vilnrotter, Chi-Wung↗

DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2012

On Shaft Data Acquisition System (OSDAS)

On Shaft Data Acquisition System (OSDAS) is a rugged, compact, multiple-channel data acquisition computer system that is designed to record data from instrumentation while operating under extreme rotational centrifugal or gravitational acceleration forces. This system, which was developed for the Heritage Fuel Air Turbine Test (HFATT) program, addresses the problem of recording multiple channels of high-sample-rate data on most any rotating test article by mounting the entire acquisition computer onboard with the turbine test article. With the limited availability of slip ring wires for power and communication, OSDAS utilizes its own resources to provide independent power and amplification for each instrument. Since OSDAS utilizes standard PC technology as well as shared code interfaces with the next-generation, real-time health monitoring system (SPARTAA Scalable Parallel Architecture for Real Time Analysis and Acquisition), this system could be expanded beyond its current capabilities, such as providing advanced health monitoring capabilities for the test article. High-conductor-count slip rings are expensive to purchase and maintain, yet only provide a limited number of conductors for routing instrumentation off the article and to a stationary data acquisition system. In addition to being limited to a small number of instruments, slip rings are prone to wear quickly, and introduce noise and other undesirable characteristics to the signal data. This led to the development of a system capable of recording high-density instrumentation, at high sample rates, on the test article itself, all while under extreme rotational stress. OSDAS is a fully functional PC-based system with 48 channels of 24-bit, high-sample-rate input channels, phase synchronized, with an onboard storage capacity of over 1/2-terabyte of solid-state storage. This recording system takes a novel approach to the problem of recording multiple channels of instrumentation, integrated with the test article itself, packaged in a compact/rugged form factor, consuming limited power, all while rotating at high turbine speeds.

Pedings, Marc↗

NASA NTRS2013

An Offload NIC for NASA, NLR, and Grid Computing

This work addresses distributed data management and access dynamically configurable high-speed access to data distributed and shared over wide-area high-speed network environments. An offload engine NIC (network interface card) is proposed that scales at nX10-Gbps increments through 100-Gbps full duplex. The Globus de facto standard was used in projects requiring secure, robust, high-speed bulk data transport. Novel extension mechanisms were derived that will combine these technologies for use by GridFTP, bandwidth management resources, and host CPU (central processing unit) acceleration. The result will be wire-rate encrypted Globus grid data transactions through offload for splintering, encryption, and compression. As the need for greater network bandwidth increases, there is an inherent need for faster CPUs. The best way to accelerate CPUs is through a network acceleration engine. Grid computing data transfers for the Globus tool set did not have wire-rate encryption or compression. Existing technology cannot keep pace with the greater bandwidths of backplane and network connections. Present offload engines with ports to Ethernet are 32 to 40 Gbps f-d at best. The best of ultra-high-speed offload engines use expensive ASICs (application specific integrated circuits) or NPUs (network processing units). The present state of the art also includes bonding and the use of multiple NICs that are also in the planning stages for future portability to ASICs and software to accommodate data rates at 100 Gbps. The remaining industry solutions are for carrier-grade equipment manufacturers, with costly line cards having multiples of 10-Gbps ports, or 100-Gbps ports such as CFP modules that interface to costly ASICs and related circuitry. All of the existing solutions vary in configuration based on requirements of the host, motherboard, or carriergrade equipment. The purpose of the innovation is to eliminate data bottlenecks within cluster, grid, and cloud computing systems, and to add several more capabilities while reducing space consumption and cost. Provisions were designed for interoperability with systems used in the NASA HEC (High-End Computing) program. The new acceleration engine consists of state-ofthe- art FPGA (field-programmable gate array) core IP, C, and Verilog code; novel communication protocol; and extensions to the Globus structure. The engine provides the functions of network acceleration, encryption, compression, packet-ordering, and security added to Globus grid or for cloud data transfer. This system is scalable in nX10-Gbps increments through 100-Gbps f-d. It can be interfaced to industry-standard system-side or network-side devices or core IP in increments of 10 GigE, scaling to provide IEEE 40/100 GigE compliance.

Awrach, James↗

DOE OSTI2023

Single-Point Extrapolation to the Complete Basis Set Limit through Deep Learning

Machine learning (ML) offers an attractive method for making predictions about molecular systems while circumventing the need to run expensive electronic structure calculations. Once trained on ab initio data, the promise of ML is to deliver accurate predictions of molecular properties that were previously computationally infeasible. In this work, we develop and train a graph neural network model to correct the basis set incompleteness error (BSIE) between a small and large basis set at the RHF and B3LYP levels of theory. Our results show that, when compared to fitting to the total potential, an ML model fitted to correct the BSIE is better at generalizing to systems not seen during training. We test this ability by training on single molecules while evaluating on molecular complexes. We also show that ensemble models yield better behaved potentials in situations where the training data is insufficient. However, even when only fitting to the BSIE, acceptable performance is only achieved when the training data sufficiently resemble the systems one wants to make predictions on. As a result, the test error of the final model trained to predict the difference between the cc-pVDZ and cc-pV5Z potential is 0.184 kcal/mol for the B3LYP density functional, and the ensemble model accurately reproduces the large basis set interaction energy curves on the S66x8 dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Additive Manufacture of Plasma Diagnostic Components Final Report Phase II

There is now a well-established set of plasma diagnostics (see e.g. [3]), but these remain some of the most expensive assemblies in fusion systems since for every system they have to be custom built, and time for diagnostic development can pace the project. Additive manufacturing (AM) has the potential to decrease production cost and significantly lower design time of fusion diagnostic subsystems, which would realize significant cost reduction for standard diagnostics. In some cases, these basic components can be additively manufactured for less than 1/100th costs of conventional manufacturing.In our DOE Phase II SBIR, we examined the impact that AM can have on plasma diagnostic cost by taking 15 separate diagnostics through an engineering design using Conventional Manufacturing (CM) techniques, then optimizing the design to exploit the benefits of AM. The impact of AM techniques on cost is found to be in several areas. First, the cost of materials falls because AM parts can be manufactured with little to no waste, and engineered to use less material than CM. Next, the cost of fabrication falls for AM parts relative to CM since the fabrication time can be computed exactly, and often no post-processing is required for the part to be functional. We find that AM techniques are well suited for plasma diagnostics since typical diagnostic complexity comes at no additional cost. Cooling channels, for example, can be builtin to plasma-facing components at no extra cost. Fabrication costs associated with assembly are lower for AM parts because many components can be combined and printed as monoliths, thereby mitigating the need for alignment or calibration. Finally, the cost of engineering is impacted by exploiting AM design tools that allow standard components to be customized through web-interfaces. Furthermore, we find that concept design costs can be impacted by scripting interfaces for online engineering design tools.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least $\mathscr{C}$ 1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. Finally, the method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1998

Development of a Probabilistic Dynamic Synthesis Method for the Analysis of Nondeterministic Structures

Accounting for the statistical geometric and material variability of structures in analysis has been a topic of considerable research for the last 30 years. The determination of quantifiable measures of statistical probability of a desired response variable, such as natural frequency, maximum displacement, or stress, to replace experience-based "safety factors" has been a primary goal of these studies. There are, however, several problems associated with their satisfactory application to realistic structures, such as bladed disks in turbomachinery. These include the accurate definition of the input random variables (rv's), the large size of the finite element models frequently used to simulate these structures, which makes even a single deterministic analysis expensive, and accurate generation of the cumulative distribution function (CDF) necessary to obtain the probability of the desired response variables. The research presented here applies a methodology called probabilistic dynamic synthesis (PDS) to solve these problems. The PDS method uses dynamic characteristics of substructures measured from modal test as the input rv's, rather than "primitive" rv's such as material or geometric uncertainties. These dynamic characteristics, which are the free-free eigenvalues, eigenvectors, and residual flexibility (RF), are readily measured and for many substructures, a reasonable sample set of these measurements can be obtained. The statistics for these rv's accurately account for the entire random character of the substructure. Using the RF method of component mode synthesis, these dynamic characteristics are used to generate reduced-size sample models of the substructures, which are then coupled to form system models. These sample models are used to obtain the CDF of the response variable by either applying Monte Carlo simulation or by generating data points for use in the response surface reliability method, which can perform the probabilistic analysis with an order of magnitude less computational effort. Both free- and forced-response analyses have been performed, and the results indicate that, while there is considerable room for improvement, the method produces usable and more representative solutions for the design of realistic structures with a substantial savings in computer time.

Brown, A. M.↗

DOE OSTI2017

ROBUST ONLINE MONITORING FOR CALIBRATION ASSESSMENT OF TRANSMITTERS AND INSTRUMENTATION

Robust online monitoring (OLM) technologies are expected to enable the extension or elimination of periodic sensor calibration intervals in operating and new reactors. Specifically, the next generation of OLM technology is expected to include newly developed advanced algorithms that improve monitoring of sensor/system performance and enable the use of plant data to derive information that currently cannot be measured. These advances in OLM technologies will improve the safety and reliability of current and planned nuclear power systems through improved accuracy and increased reliability of sensors used to monitor key parameters. In this paper, we discuss an overview of research being performed within the Nuclear Energy Enabling Technologies (NEET)/Advanced Sensors and Instrumentation (ASI) program, for the development of OLM algorithms to use sensor outputs and, in combination with other available information, 1) determine whether one or more sensors are out of calibration or failing and 2) replace a failing sensor with reliable, accurate sensor outputs. Algorithm development is focused on the following OLM functions: • Signal validation – fault detection and selection of acceptance criteria • Virtual sensing – signal value prediction and acceptance criteria • Response-time assessment – fault detection and acceptance criteria selection A GP-based uncertainty quantification (UQ) method previously developed for UQ in OLM, was adapted for use in sensor-fault detection and virtual sensing. For signal validation, the various components to the OLM residual (which is computed using an AAKR model) were explicitly defined and modeled using a GP. Evaluation was conducted using flow loop data from multiple sources. Results using experimental data from laboratory-scale flow loops indicate that the approach, while capable of detecting sensor drift, may be incapable of discriminating between sensor drift and model inadequacy. This may be due to a simplification applied in the initial modeling, where the sensor degradation is assumed to be stationary. In the case of virtual sensors, the GP model was used in a predictive mode to estimate the correct sensor reading for sensors that may have failed. Results have indicated the viability of using this approach for virtual sensing. However, the GP model has proven to be computationally expensive, and so alternative algorithms for virtual sensing are being evaluated. Finally, automated approaches to performing noise analysis for extracting sensor response time were developed. Evaluation of this technique using laboratory-scale data indicates that it compares well with manual techniques previously used for noise analysis. Moreover, the automated and manual approaches for noise analysis also compare well with the current “gold standard”, hydraulic ramp testing, for response time monitoring. Ongoing research in this project is focused on further evaluation of the algorithms, optimization for accuracy and computational efficiency, and integration into a suite of tools for robust OLM that are applicable to monitoring sensor calibration state in nuclear power plants.

calibration interval extension↗

DOE OSTI2025

LDRD Abbreviated report: High-Order General-Discrete-Ordinates Method Enabling Efficient Deterministic Transport in Hydrodynamic Simulations

Deterministic transport simulations for national-security and energy applications often operate in high-dimensional phase-space, where accuracy and cost both become major challenges. A common numerical artifact in such problems is the “ray-effect,” which appears as unphysical streaks. Beyond misinterpretation, these artifacts can contaminate tightly coupled physics, such as fluid dynamics, radiation-hydrodynamics, and laser-plasma interactions, eroding the predictive capability of entire multiphysics workflows. Our objective was to make high-dimension studies practical on modern hardware while mitigating the ray-effect without relying on prohibitively expensive sampling approaches such as Monte Carlo methods. We developed the Generic Discretization Library (GenDiL), a Graphics Processing Unit (GPU)-first framework that uses high-order Discontinuous Galerkin (DG) methods and matrix-free algorithms to reduce memory usage and improve computational efficiency, critical for phase-space simulations. GenDiL supports phase-space adaptivity in both mesh size and polynomial order (hp-adaptivity) to place resolution only where it is needed. A central capability is Local Dimensional Refinement (LDR), which couples lower-dimension continuum models to higher-dimension kinetic models through stable and conservative interfaces, so that high-fidelity physics is applied only in regions where it is essential. Building on the GenDiL framework, we developed the General SN (GSN) family of algorithms as a true generalization of the polar SN approach (discrete ordinates, often denoted SN). Rather than tying discrete ordinates to a specific polar change of coordinates, GSN formulates transport on an arbitrary change of coordinates chosen to reduce ray-effect. We studied two complementary variants: an analytic variant, where the coordinate map is prescribed in advance by a closed-form function; and a data-driven variant, where a quantity of interest, such as the net flux, guides the coordinate system. GenDiL provides the library infrastructure for efficient GPU execution, but the GSN concept is algorithmic and independent of any one library. Across representative high-dimension tests, including non-symmetric solutions, both variants delivered strong ray-effect mitigation at practical cost, moving four- to six-dimensional analysis toward repeatable, routine studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Sequential Learning of Active Subspaces

This study shows that in recent years, active subspace methods (ASMs) have become a popular means of performing subspace sensitivity analysis on black-box functions. Naively applied, however, ASMs require gradient evaluations of the target function. In the event of noisy, expensive, or stochastic simulators, evaluating gradients via finite differencing may be infeasible. In such cases, often a surrogate model is employed, on which finite differencing is performed. When the surrogate model is a Gaussian process (GP), we show that the ASM estimator is available in closed form, rendering the finite-difference approximation unnecessary. We use our closed-form solution to develop acquisition functions focused on sequential learning tailored to sensitivity analysis on top of ASMs. We also show that the traditional ASM estimator may be viewed as a method of moments estimator for a certain class of GPs. We demonstrate how uncertainty on GP hyperparameters may be propagated to uncertainty on the sensitivity analysis, allowing model-based confidence intervals on the active subspace. Our methodological developments are illustrated on several examples.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Quasiclassical Computations of Compton-Scattered Spectra

Quality X-ray sources are crucial to fundamental physics research, medical radiology, humanities research, and materials science. While synchrotron radiation (SR) facilities produce the state-of-the-art emissions with respect to brilliance and frequency tunability, the great expense required to build, maintain, and operate these structures greatly limits their accessibility to researchers. Much of the research conducted at SR facilities, however, may be conducted with inverse Compton sources (ICS). Accelerator-based Compton scattering light sources generate high-energy, high-brilliance emissions. Compton scattering is the process by which a photon scatters o? an electron. ICS offer an affordable, in-lab alternative to SR facilities. Even though SR facilities produce greater intensity emissions, Compton sources provide the same frequency tunability at the intensities suitable for the purposes of many researchers currently fighting for time at SR facilities, i.e., ICS provides intensities suitable for contrast imaging, X-ray fluorescence, X-ray-diffraction, and X-ray spectroscopy. The focus of this work is to create computational models to simulate Compton-scattered spectra. These models have been used to build a theoretical basis for methods of improving the quality of future Compton sources and to preform diagnostic analysis of existing light sources. The theoretical basis of each model is derived from first principles. The numerical methods employed by each model are defined. A full description of the various functionalities of each code will be addressed. Furthermore, an in-depth analysis of spectral bandwidth sources is discussed. The complex physics arising from an extremely high-intensity, nonlinear laser pulse is explored in detail. Methods of frequency modulation of the incident laser, i.e., a method for correcting the nonlinear broadening effects on the scattered spectrum, will also be discussed. The work will conclude with a an exploration of the ongoing research efforts regarding regimes of operation outside of the limits of these current models.

Johnson, Erik↗

DOE OSTI2022

Screening of bimetallic electrocatalysts for water purification with machine learning

Electrocatalysis provides a potential solution to NO 3 - pollution in wastewater by converting it to innocuous N 2 gas. However, materials with excellent catalytic activity are typically limited to expensive precious metals, hindering their commercial viability. Here, in response to this challenge, we have conducted the most extensive computational search to date for electrocatalysts that can facilitate NO 3 - reduction reaction, starting with 59 390 candidate bimetallic alloys from the Materials Project and Automatic-Flow databases. Using a joint machine learning- and computation-based screening strategy, we evaluated our candidates based on corrosion resistance, catalytic activity, N 2 selectivity, cost, and the ability to synthesize. We found that only 20 materials will satisfy all criteria in our screening strategy, all of which contain varying amounts of Cu. Our proposed list of candidates is consistent with previous materials investigated in the literature, with the exception of Cu–Co and Cu–Ag based compounds that merit further investigation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

A novel energy balance approach for a verifiable and accurate solution of radiation extinction in purely absorbing particle clouds

Here we consider the problem of radiation transport through purely absorbing particle clouds. The gold-standard solution of particle-resolved Monte Carlo ray-tracing method to this problem is computationally expensive and therefore solving the radiation transport equation (specifically, the Beer-Bouguer law (BB-law)) on a Eulerian mesh is often preferred. While the absorption coefficient in the real problem is infinite, the BB-law approximates it to be a finite number in the form of number density through a set of assumptions. For particle clouds that do not obey these assumptions, the BB-law predicts an incorrect exponential decay. Also, when the number density is computed using the nearest-neighbor approach, the BB-law solution diverges when the Eulerian mesh size becomes closer to or smaller than the particle size. This numerical divergence is due to the homogenization error. Although the filtering strategy for number density minimizes the homogenization error, it still converges to an incorrect exponential decay for particle clouds that break the BB-law constraints and the cost of the filtering is equivalent to that of the gold-standard solution. In this study, we develop a novel, highly accurate, verifiable and cost-effective solution to the radiation transport equation on a Eulerian domain using an energy balance approach where we derive an expression for the absorption coefficient as a function of particle and Eulerian mesh sizes. We apply our new method to Poisson and turbulent particle clouds that violate all the BB-law constraints and show that the solution is converging upon the mesh refinement, and eventually, we recover the same gold-standard solution for a much cheaper computational cost.

42 ENGINEERING↗

NASA NTRS1989

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Meade, Andrew James, Jr.↗

NASA NTRS2011

Fault-Tolerant, Radiation-Hard DSP

Commercial digital signal processors (DSPs) for use in high-speed satellite computers are challenged by the damaging effects of space radiation, mainly single event upsets (SEUs) and single event functional interrupts (SEFIs). Innovations have been developed for mitigating the effects of SEUs and SEFIs, enabling the use of very-highspeed commercial DSPs with improved SEU tolerances. Time-triple modular redundancy (TTMR) is a method of applying traditional triple modular redundancy on a single processor, exploiting the VLIW (very long instruction word) class of parallel processors. TTMR improves SEU rates substantially. SEFIs are solved by a SEFI-hardened core circuit, external to the microprocessor. It monitors the health of the processor, and if a SEFI occurs, forces the processor to return to performance through a series of escalating events. TTMR and hardened-core solutions were developed for both DSPs and reconfigurable field-programmable gate arrays (FPGAs). This includes advancement of TTMR algorithms for DSPs and reconfigurable FPGAs, plus a rad-hard, hardened-core integrated circuit that services both the DSP and FPGA. Additionally, a combined DSP and FPGA board architecture was fully developed into a rad-hard engineering product. This technology enables use of commercial off-the-shelf (COTS) DSPs in computers for satellite and other space applications, allowing rapid deployment at a much lower cost. Traditional rad-hard space computers are very expensive and typically have long lead times. These computers are either based on traditional rad-hard processors, which have extremely low computational performance, or triple modular redundant (TMR) FPGA arrays, which suffer from power and complexity issues. Even more frustrating is that the TMR arrays of FPGAs require a fixed, external rad-hard voting element, thereby causing them to lose much of their reconfiguration capability and in some cases significant speed reduction. The benefits of COTS high-performance signal processing include significant increase in onboard science data processing, enabling orders of magnitude reduction in required communication bandwidth for science data return, orders of magnitude improvement in onboard mission planning and critical decision making, and the ability to rapidly respond to changing mission environments, thus enabling opportunistic science and orders of magnitude reduction in the cost of mission operations through reduction of required staff. Additional benefits of COTS-based, high-performance signal processing include the ability to leverage considerable commercial and academic investments in advanced computing tools, techniques, and infra structure, and the familiarity of the science and IT community with these computing environments.

Czajkowski, David↗