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NASA NTRS2003

Case for Deploying Complex Systems Utilizing Commodity Components

When the International Space Station (ISS) finally reached an operational state, many of the Payload Operations and Integration Facility (POIF) hardware components were reaching end of life, COTS product costs were soaring, and the ISS budget was becoming severely constrained. However, most requirement development was complete. In addition, the ISS program is a fully functioning program with at least fifteen years of operational life remaining. Therefore it is critical that any upgrades, refurbishments, or enhancements be accomplished in realtime with minimal disruptions to service. For these and other reasons, it was necessary to ensure the viability of the POIF. Due to the to the breadth of capability of the POIF (a NASA ground station), it is believed that the lessons to be learned by other complex systems are applicable and any solutions garnered by the POIF are applicable to other complex systems as well. With that in mind, a number of new approaches have been investigated to increase the portability of the POIF and reduce the cost of refurbishment, operations, and maintenance. These new approaches were directed at the Total Cost of Ownership (TCO); not only the refurbishment but also current operational difficulties, licensing, and anticipation of the next refurbishment. Our basic premise is that technology had evolved dramatically since the concept of the POIF ground system and we should leverage our experience on this new technological landscape. Fortunately, Moore's law and market forces have changed the landscape considerably. These changes are manifest in five (5) ways that are particularly relevant to POIF: 1. Complex Instruction Set Computing (CISC) processors have advanced to unprecedented levels of compute capacity with a dramatic cost break, 2. Linux has become a major operating system supported by most vendors on a broad range of platforms, 3. Windows(TradeMark) based desktops are pervasive in the office environment, 4. Stable and affordable WindowsTM development environments and tools are available and offer a rich set of capabilities, 5. The WindowsTM 2000 provides a stable client platform, Therefore, five studies were proposed, developed, and are in the current process of deployment which dramatically reduces the cost of operations, maintenance, refurbishment, and deployment of a ground system. Restating and refining the basic premise stated earlier, it is possible to enhance operations through the replacement of hardware and software components with commodity based items wherever applicable. This will dramatically reduce the overall lifecycle cost of the project. The first study leveraged the POIF S secure, three-tier, web architecture to replace the client workstations with lower cost PC platforms. A second study initiated a review of COTS products to examine the level of added value of each product. This study included replacement of some COTS products with custom code, deletions, substitutions, and consolidation of COTS products. Studies three and four reviewed the server architectures of the data distribution systems and Enhanced HOSC System (EHS) command and telemetry system to propose migration to new platforms, both software and hardware. The final study reviewed current IP communication technologies, developed an operational model for flight operations, and demonstrated that voice over IP was practical and could be integrated into operations.

Bryant, Barry S.↗
NASA NTRS2004

The Investigation Of Carbon Contamination And Sputtering Effects Of Xenon Ion Thrusters

The Electro-Physics Branch of the NASA Glenn Research Center investigates the effect of atomic oxygen, environmental durability of high performance power materials and surfaces, and low earth orbit. One of its current projects involves the analysis of ion thrusters. Ion thrusters are devices that initiate a beam of ions to a target area. The type of ion thruster that I have been working with this Summer of 2004 emits positively charged Xenon (Xe(+)) atoms through two grids, the screen grid and the accelerator grid, after it enters an ionization chamber. Insulators are used to mechanically hold and separate these two grids. A propellant isolator, an instrument that closely resembles insulators, is placed in front of the ionization chamber. Both the insulator and isolator are made with a ceramic compound and filled with insulating beads. The main difference between the two devices is that the propellant isolator allows gas to flow through, in this case, the gas is Xe(+) and the insulators do not. In order to avoid carbon deposits and other contaminating chemicals to settle on the insulators and propellant isolator, a metal shadow shield is placed around them. These shadow shields function as a protectant and can be shaped in numerous configurations. Part of my job responsibility this summer is to investigate the effectiveness of different shadow shields that are utilized on three different ion engines: the NSTAR (NASA Solar Electric Propulsion Technology Application Readiness), JIMO (Jupiter Icy Moons Orbiter), and NEXIS (Nuclear Electric Xenon Ion System). Using calculus and other mathematical tactics, I was asked to find the total flux of carbon contamination that was able to pass the protectant shadow shield. I familiarized myself with the software program, MathCad2004, to help perform some mathematical computations such as complex integration. Another method of studying the probability of contamination is by experimental simulation. After attaining the precise parameters of the actual shadow shields, I created replicas of three types of shadow shielding to be used to undergo testing. It will be placed in a machine that produces carbon atoms at a high temperature of 200 C. or beam is aimed at a targeted material. As a result of this collision, atoms and other particles are ejected out of the target surface. Another part of my internship consisted of research on sputter ejection, or the angle distribution of sputtered material. This research entailed finding the past results of sputter ejection investigation as well as creating another type of mock simulation. Other minor projects include calculating the path of Xe(+) gas through the insulating beads of the isolators and assisting my mentor in collecting data for his paper for the Joint Propulsion Conference & Exhibit to be held July 11-14,2004 in Fort Lauderdale, Florida.

Prak, Moline K.↗
NASA NTRS2005

Data management in the mission data system

As spacecraft evolve from simple embedded devices to become more sophisticated computing platforms with complex behaviors it is increasingly necessary to model and manage the flow of data, and to provide uniform models for managing data that promote adaptability, yet pay heed to the physical limitations of the embedded and space environments.

mission data system (MDS)↗
NASA NTRS2011

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b , where A is an m by x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as 4x(sub 1) + 6x(sub 2) + 5x (sub 3) = 10, where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or a minimum norm solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.

Sen, Syamal K.↗
NASA NTRS2011

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b, where A is an m x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as an equation 4x(sub 1) + 6x(sub 2) + 5x(sub 3) = 10 , where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. It is assumed that at least one information, i.e. one equation is known to be correct and which will be our first equation. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The . error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.

Sen, Syamal K.↗
NASA NTRS2014

Spinoff 2013

Topics covered include: Innovative Software Tools Measure Behavioral Alertness; Miniaturized, Portable Sensors Monitor Metabolic Health; Patient Simulators Train Emergency Caregivers; Solar Refrigerators Store Life-Saving Vaccines; Monitors Enable Medication Management in Patients' Homes; Handheld Diagnostic Device Delivers Quick Medical Readings; Experiments Result in Safer, Spin-Resistant Aircraft; Interfaces Visualize Data for Airline Safety, Efficiency; Data Mining Tools Make Flights Safer, More Efficient; NASA Standards Inform Comfortable Car Seats; Heat Shield Paves the Way for Commercial Space; Air Systems Provide Life Support to Miners; Coatings Preserve Metal, Stone, Tile, and Concrete; Robots Spur Software That Lends a Hand; Cloud-Based Data Sharing Connects Emergency Managers; Catalytic Converters Maintain Air Quality in Mines; NASA-Enhanced Water Bottles Filter Water on the Go; Brainwave Monitoring Software Improves Distracted Minds; Thermal Materials Protect Priceless, Personal Keepsakes; Home Air Purifiers Eradicate Harmful Pathogens; Thermal Materials Drive Professional Apparel Line; Radiant Barriers Save Energy in Buildings; Open Source Initiative Powers Real-Time Data Streams; Shuttle Engine Designs Revolutionize Solar Power; Procedure-Authoring Tool Improves Safety on Oil Rigs; Satellite Data Aid Monitoring of Nation's Forests; Mars Technologies Spawn Durable Wind Turbines; Programs Visualize Earth and Space for Interactive Education; Processor Units Reduce Satellite Construction Costs; Software Accelerates Computing Time for Complex Math; Simulation Tools Prevent Signal Interference on Spacecraft; Software Simplifies the Sharing of Numerical Models; Virtual Machine Language Controls Remote Devices; Micro-Accelerometers Monitor Equipment Health; Reactors Save Energy, Costs for Hydrogen Production; Cameras Monitor Spacecraft Integrity to Prevent Failures; Testing Devices Garner Data on Insulation Performance; Smart Sensors Gather Information for Machine Diagnostics; Oxygen Sensors Monitor Bioreactors and Ensure Health and Safety; Vision Algorithms Catch Defects in Screen Displays; and Deformable Mirrors Capture Exoplanet Data, Reflect Lasers.

Source record↗
NASA NTRS2009

Sequential Principal Component Analysis -An Optimal and Hardware-Implementable Transform for Image Compression

This paper presents the JPL-developed Sequential Principal Component Analysis (SPCA) algorithm for feature extraction / image compression, based on "dominant-term selection" unsupervised learning technique that requires an order-of-magnitude lesser computation and has simpler architecture compared to the state of the art gradient-descent techniques. This algorithm is inherently amenable to a compact, low power and high speed VLSI hardware embodiment. The paper compares the lossless image compression performance of the JPL's SPCA algorithm with the state of the art JPEG2000, widely used due to its simplified hardware implementability. JPEG2000 is not an optimal data compression technique because of its fixed transform characteristics, regardless of its data structure. On the other hand, conventional Principal Component Analysis based transform (PCA-transform) is a data-dependent-structure transform. However, it is not easy to implement the PCA in compact VLSI hardware, due to its highly computational and architectural complexity. In contrast, the JPL's "dominant-term selection" SPCA algorithm allows, for the first time, a compact, low-power hardware implementation of the powerful PCA algorithm. This paper presents a direct comparison of the JPL's SPCA versus JPEG2000, incorporating the Huffman and arithmetic coding for completeness of the data compression operation. The simulation results show that JPL's SPCA algorithm is superior as an optimal data-dependent-transform over the state of the art JPEG2000. When implemented in hardware, this technique is projected to be ideally suited to future NASA missions for autonomous on-board image data processing to improve the bandwidth of communication.

Duong, Tuan A.↗
NASA NTRS2015

Regolith and Environment Science and Oxygen and Lunar Volatile Extraction (RESOLVE): Lunar Advanced Volatile Analysis (LAVA) Capillary Fluid Dynamic Restriction Effects on Gas Chromatography

The Resource Prospector (RP) mission with the Regolith and Environment Science and Oxygen Lunar Volatile Extraction (RESOLVE) payload aims to show the presence of water in lunar regolith, and establish a proving ground for NASAs mission to Mars. One of the analysis is performed by the Lunar Advanced Volatiles Analysis (LAVA) subsystem, which consists of a fluid network that facilitates the transport of volatile samples to a gas chromatograph and mass spectrometer (GC-MS) instrument. The understanding of fluid dynamics directed from the GC to the MS is important due to the influence of flow rates and pressures that affect the accuracy of and prevent the damage to the overall GC-MS instrument. The micro-scale capillary fluid network within the GC alone has various lengths and inner-diameters; therefore, determination of pressure differentials and flow rates are difficult to model computationally, with additional complexity from the vacuum conditions in space and lack of a lunar atmosphere. A series of tests were performed on an experimental set-up of the system where the inner diameters of the GC transfer line connecting to the MS were varied. The effect on chromatography readings were also studied by applying these lines onto a GC instrument. It was found that a smaller inner diameter transfer line resulted in a lower flow rate, as well as a lower pressure differential across the thermal conductivity detector (TCD) unit of the GC and a negligible pressure drop across the mock-up capillary column. The chromatography was affected with longer retention times and broader peak integrations. It was concluded that a 0.050 mm inner diameter line still proved most suitable for the systems flow rate preferences. In addition, it was evident that this small transfer line portrayed some expense to GC signal characteristics and the wait time for steady-state operation.

RESOLVE↗
NASA NTRS2017

Reconfigurable Model Execution in the OpenMDAO Framework

NASA's OpenMDAO framework facilitates constructing complex models and computing their derivatives for multidisciplinary design optimization. Decomposing a model into components that follow a prescribed interface enables OpenMDAO to assemble multidisciplinary derivatives from the component derivatives using what amounts to the adjoint method, direct method, chain rule, global sensitivity equations, or any combination thereof, using the MAUD architecture. OpenMDAO also handles the distribution of processors among the disciplines by hierarchically grouping the components, and it automates the data transfer between components that are on different processors. These features have made OpenMDAO useful for applications in aircraft design, satellite design, wind turbine design, and aircraft engine design, among others. This paper presents new algorithms for OpenMDAO that enable reconfigurable model execution. This concept refers to dynamically changing, during execution, one or more of: the variable sizes, solution algorithm, parallel load balancing, or set of variables-i.e., adding and removing components, perhaps to switch to a higher-fidelity sub-model. Any component can reconfigure at any point, even when running in parallel with other components, and the reconfiguration algorithm presented here performs the synchronized updates to all other components that are affected. A reconfigurable software framework for multidisciplinary design optimization enables new adaptive solvers, adaptive parallelization, and new applications such as gradient-based optimization with overset flow solvers and adaptive mesh refinement. Benchmarking results demonstrate the time savings for reconfiguration compared to setting up the model again from scratch, which can be significant in large-scale problems. Additionally, the new reconfigurability feature is applied to a mission profile optimization problem for commercial aircraft where both the parametrization of the mission profile and the time discretization are adaptively refined, resulting in computational savings of roughly 10% and the elimination of oscillations in the optimized altitude profile.

Hwang, John T.↗
NASA NTRS2019

A Composite Damage Tolerance Simulation Technique to Augment the Building Block Approach

Aerospace structures comprised of composite materials are traditionally certified empirically via the Building Block Approach (BBA). While this approach has been performed successfully in the past, it is expensive and time consuming. One means to improve the overall efficiency of composite structural certification is to reduce the cost of the BAA by eliminating the need for some tests by incorporating damage analysis tools. For an analysis to replace a given test, the tool must first be validated using other similar test data. The subject of this paper is a description of an analysis technique for simulating compression after damage strength of a solid laminate. The analysis technique is one that is practical for use in an applied engineering context due to efforts to minimize necessary computational resources and complexity of the model.

McElroy, Mark↗
NASA NTRS2019

A Composite Damage Tolerance Simulation Technique to Augment the Building Block Approach

Aerospace structures comprised of composite materials are traditionally certified empirically via the Building Block Approach (BBA). While this approach has been performed successfully in the past, it is expensive and time-consuming. One means to improve the overall efficiency of composite structural certification is to reduce the cost of the BBA by eliminating the need for some tests by incorporating damage analysis tools. For an analysis to replace a given test, the tool must first be validated using other similar test data. The subject of this paper is a description of an efficient analysis technique for simulating compression after damage strength of a solid laminate. The analysis technique is one that is practical for use in an applied engineering context due to efforts to minimize necessary computational resources and complexity of the model.

McElroy, Mack↗
NASA NTRS1996

Implementation of a Very Large Atmospheric Correction Lookup Table for ASTER Using a Relational Database Management System

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER)is designed to provide a high resolution map of the Earth in both visible, near-infrared, and thermal spectral regions of the electromagnetic spectrum. The ASTER Science Team has developed several standard data product algorithms, but the most complex aod computing-intensive of these is the estimation of surface radiance and reflectance values, which is done by modeling and correcting for the effects of the atmosphere. The algorithm for atmospheric correction in the visible bands sensed by ASTER calls for use of a very large Atmospheric Correction Look Up Table (ACLUT).

ASTER↗
NASA NTRSDate not supplied

Agent-based modeling of microbes in space

Space is tough on organisms. Microorganisms traveling to space experience stress from environmental features such as ionizing radiation and lack of normal microgravity; however, much remains unknown about the mechanisms by which those environmental features affect microbial physiology. Microbes experience changes in gravity not directly but rather through changes in their fluid environment, and deep-space particle radiation causes cell damage that is complex but rare. Computational modeling at the single-cell level (agent-based modeling) can allow us to probe the spatially heterogeneous processes that characterize space stresses, to gain insight into the relationships of microbial cells with their environments and with each other. Here we present two software packages for simulating microbial population dynamics in space conditions: CAMDLES and AMMPER. Microbes growing in liquid culture medium in the microgravity of an orbital space station experience a quiescent, poorly-mixed fluid environment. CAMDLES (CFD-DEM Artificial Microgravity Developments for Living Ecosystem Simulation) simultaneously simulates biological, chemical, and mechanical processes to predict microbial ecological dynamics in microgravity, and in the rotating culture vessels used to create an artificial microgravity environment in the lab. Initial results demonstrate that the growth of a cross-feeding microbial consortium, dependent on the exchange of soluble metabolites, is sensitive to the initial spatial distribution of cells, and grows differently in real versus artificial microgravity. Microbial populations exposed to deep-space radiation experience spatially and temporally heterogeneous damage from the traversal of high-energy particles. AMMPER (Agent-Based Model for Microbial Populations Exposed to Radiation) pairs a 3d model of energy deposition along a radiation particle track with a microbial population growth and damage model to predict the effects of localized radiation damage on population-level responses. It includes a user-friendly graphical interface. AMMPER results agree with experimental data indicating that indirect effects of radiation (reactive oxygen species generation, metabolic impairment) have a greater impact on microorganisms than direct effects (DNA damage).

Jessica A Lee↗
NASA NTRS2022

Agent-Based Modeling of Microbes in Space

Space is tough on organisms. Microorganisms traveling to space experience stress from environmental features such as ionizing radiation and lack of normal gravity, and much remains unknown about the mechanisms by which those environmental features affect microbial physiology. Microbes experience changes in gravity not directly but rather through changes in their fluid environment, and deep-space particle radiation causes cell damage that is complex but rare. Computational modeling at the single-cell level (agent-based modeling) can allow us to probe the spatially heterogeneous processes that characterize space stresses, to gain insight into the relationships of microbial cells with their environments and with each other. Here we present two software packages for simulating microbial population dynamics in space conditions: CAMDLES and AMMPER. Microbes growing in liquid culture medium in the microgravity of an orbital space station experience a quiescent, poorly-mixed fluid environment. CAMDLES (CFD-DEM Artificial Microgravity Developments for Living Ecosystem Simulation) simultaneously simulates biological, chemical, and mechanical processes to predict microbial ecological dynamics in microgravity, and in the rotating culture vessels used to create an artificial microgravity environment in the lab. Initial results demonstrate that the growth of a cross-feeding microbial consortium, dependent on the exchange of soluble metabolites, is sensitive to the initial spatial distribution of cells, and grows differently in real versus artificial microgravity. Microbial populations exposed to deep-space radiation experience spatially and temporally heterogeneous damage from the traversal of high-energy particles. AMMPER (Agent-Based Model for Microbial Populations Exposed to Radiation) pairs a 3d model of energy deposition along a radiation particle track with a microbial population growth and damage model to predict the effects of localized radiation damage on population-level responses. It includes a user-friendly graphical interface. AMMPER growth curves recapitulate experimental results, and allow comparison between direct effects (DNA damage) and indirect effects (reactive oxygen species generation, metabolic impairment) of radiation.

microbiology↗
DOE OSTI2020

Analytic Modeling of a Deep Shielding Problem

Previous generations of scientists would make tremendous efforts to simplify non-tractable problems and generate simpler models that preserved the fundamental physics. This process involved applying assumptions and simplifications to reduce the complexity of the problem until it reached a solvable form. Each assumption and simplification was chosen and applied with the intent to preserve the essential physics of the problem, since, if the core physics of the problem were eliminated, the simplified model served no purpose. Moreover, if done correctly, solutions to the reduced model would serve as useful approximations to the original problem. In a sense, solving the simple models laid the ground-work for and provided insight into the more complex problem. Today, however, the affordability of high performance computing has essentially replaced the process for analyzing complex problems. Rather than \building up" a problem by understanding smaller, simpler models, a user generally relies on powerful computational tools to directly arrive at solutions to complex problems. As computational resources grow, users continue trying to simulate new, more complex, or more detailed problems, resulting in continual stress on both the code and computational resources. When these resources are limited, the user will have to make concessions by simplifying the problem while trying to preserve important details. In the context of MCNP, simplifications typically come as reductions in geometry, or by using variance reduction techniques. Both approaches can influence the physics of the problem, leading to potentially inaccurate or non-physical results. Errors can also be introduced as a result of faulty input into a computational tool: something as simple as transposing numbers in a tally input can result in incorrect answers.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Circuit complexity near critical points

Here, we consider the Bose–Hubbard model in two and three spatial dimensions and numerically compute the quantum circuit complexity of the ground state in the Mott insulator and superfluid phases using a mean field approximation with additional quadratic fluctuations. After mapping to a qubit system, the result is given by the complexity associated with a Bogoliubov transformation applied to the reference state taken to be the mean field ground state. In particular, the complexity has peaks at the O(2) critical points where the system can be described by a relativistic quantum field theory. Given that we use a Gaussian approximation, near criticality the numerical results agree with a free field theory calculation. To go beyond the Gaussian approximation we use general scaling arguments that imply that, as we approach the critical point t → t c , there is a non-analytic behavior in the complexity c 2 (t) of the form |c 2 (t) – c 2 (t c )| ~ |t – t c | νd , up to possible logarithmic corrections. Here d is the number of spatial dimensions and ν is the usual critical exponent for the correlation length ξ ~ |t – t c | –ν . As a check, for d = 2 this agrees with the numerical computation if we use the Gaussian critical exponent $v=\frac{1}{2}$. Finally, using AdS/CFT methods, we study higher dimensional examples and confirm this scaling argument with non-Gaussian exponent ν for strongly interacting theories that have a gravity dual.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Online Learning of Effective Turbine Wind Speed in Wind Farms

To develop better wind farm controllers that can meet more complex objectives, methods of modeling the wind turbine wakes at low computational expense are needed. Gaussian process (GP) regression offers a computationally inexpensive framework for learning complex functions from noisy measurements with very few datapoints. In this work, an online learning approach is presented to learn the rotor-averaged wind velocity at downstream wind turbines with GPs, using the available datastream of wind field measurements and wind turbine control set-points. This framework can readily be integrated into model-based controls methods because the model a) is updated online at low computational expense, b) assumes a mathematically favorable Gaussian form, and c) explicitly quantifies the stochastic nature of the wake field so that the trade-off between exploration and exploitation, and the uncertainty in the prediction, can be utilized. We show that a GP-learned model can match true values with errors within 0.5% on average, with as few as 5 training data points.

Gaussian process↗