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DOE OSTI2022

Learning Distributed Geometric Koopman Operator for Sparse Networked Dynamical Systems

Koopman operator theory provides an alternative to study nonlinear networked dynamical systems by mapping the state space to an abstract higher dimensional space where the system evolution is linear. Recent works show the application of graph neural networks (GNNs) to learn state to object-centric embeddings and achieve centralized block-wise computation of Koopman operator (KO) under additional assumptions on the underlying agents properties and constraints on the KO structure. However, the computational complexity of learning the Koopman increases exponentially for networked systems where the number of possible system states grows in a combinatorial fashion with the number of nodes. The learning challenge is further amplified for sparse networks by two factors: 1) sample sparsity for learning the Koopman operator in the non-linear space, and 2) the divergence in the dynamics of individual nodes or from one subgraph to another. Our work aims to address these challenge by formulating the representation learning of networked dynamical systems into a multi-agent paradigm and learning the Koopman operator in a distributive manner. The computational as well as performance advantages of distributed Koopman is predominant for sparse networks whereas for fully connected networks, it is shown to coincide with the centralized one. The empirical study on rope system, network of oscillators and a synthetic power system show comparable and superior performance along with computational benefits with the state-of-the-art methods.

Mukherjee, Sayak↗

DOE OSTI2023

FAST (FAST AUTONOMOUS SCANNING TOOLKIT)

SF-23-006 FAST (FAST AUTONOMOUS SCANNING TOOLKIT)The software is deployed on an edge computing device at the beamline computer attached to a scanning microscope. It iteratively analyzes the data collected, then identifies new scan positions to scan next and directs the positioners that move the sample (or probe beam) to these positions. Overall, it identifies a sparse set of scan positions that are sufficient to image the full sample. This can reduce the scan time by >60%.

KANDEL, SAUGAT↗

DOE OSTI2015

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ{sub 1}-minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence on the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids

We present a new approach to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed: (1) stochastic collocation based on dimension-adaptive sparse grids (SGs), which approximates the stochastic objective function with a limited number of quadrature nodes, and (2) projection-based reduced-order models (ROMs), which generate efficient approximations to PDE solutions. These two sources of inexactness lead to inexact objective function and gradient evaluations, which are managed by a trust-region method that guarantees global convergence by adaptively refining the SG and ROM until a proposed error indicator drops below a tolerance specified by trust-region convergence theory. A key feature of the proposed method is that the error indicator---which accounts for errors incurred by both the SG and ROM---must be only an asymptotic error bound, i.e., a bound that holds up to an arbitrary constant that need not be computed. This allows the approach to be applicable to a wide range of problems, including those where sharp, computable error bounds are not available; this distinguishes the proposed method from previous works. Numerical experiments performed on a model problem from optimal flow control under uncertainty verify global convergence of the method and demonstrate the method's ability to outperform previously proposed alternatives.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Uncertainty Quantification in Dynamic Simulations of Large-scale Power System Models using the High-Order Probabilistic Collocation Method on Sparse Grids

This paper proposes a probabilistic collocation method (PCM) to quantify the uncertainties with dynamic simulations in power systems. The appraoch was tested on a single-machine-infinite-bus system and the over 15,000 -bus Western Electricity Coordinating Council (WECC) system. Comparing to classic Monte-Carlo (MC) method, the proposed PCM applies the Smolyak algorithm to reduce the number of simulations that have to be performed. Therefore, the computational cost can be greatly reduced using PCM. The algorithm and procedures are described in the paper. Comparison was made with MC method on the single machine as well as the WECC system. The simulation results shows that using PCM only a small number of sparse grid points need to be sampled even when dealing with systems with a relatively large number of uncertain parameters. PCM is, therefore, computationally more efficient than MC method.

Uncertainty quantification, parameter estimation, ↗

DOE OSTI2019

Algorithms for X-Ray Imaging of Single Particles

Our group develops image reconstruction algorithms and applies them to data collected with x-ray sources (synchrotron, XFEL) and electron microscopes. Some of the challenges we face are (1) extremely low signal levels and noise, (2) missing information (phase, sample orientation), and (3) large, very sparse datasets. We have made significant progress in all three of these areas in our DOE project. This final report highlights two results produced during the extension of the project that proved to be spectacular successes. Publications and software products generated over the entire project period are listed at the end of the report.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Measurements of peroxyacetyl nitrate (PAN) and peroxypropionyl nitrate (PPN) at selected urban, rural and remote sites

PAN and PPN were measured in a series of eight field studies performed at urban, rural and remote locations in the contiguous U.S. during 1983-1985. Seven of the eight studies were performed in the winter/spring period, a period of sparsely available data. Nearly 2000 air samples were analyzed during these studies. Mean PAN and PPN levels in the range of 45-1600 ppt (max. 7.9 ppb) and 5-230 ppt (max. 0.9 ppb), respectively, were measured. Despite a great deal of observed variability, PAN and PPN showed virtually identical behavior at all sites and in all seasons, supporting the view that these nitrogenous compounds are produced and destroyed by very similar mechanisms. On the average PPN concentrations were about 8 percent (range 3-14 percent) of PAN values. It is inferred that PPN/PAN ratio is highest in urban areas and declines as polluted air masses are transported over long distances.

Singh, Hanwant B.↗

NASA NTRS2007

High-Resolution N-Band Observations of the Nova RS Ophiuchi with the Keck Interferometer Nuller

We report new observations of the nova RS Ophiuchi (RS Oph) using the Keck Interferometer Nulling Instrument, approximately 3.8 days following the most recent outburst that occurred on 2006 February 12. The Keck Interferometer Nuller (KIN) operates in K-band from 8 to 12.5 pm in a nulling mode, which means that the central broad-band interference fringe is a dark fringe - with an angular width of 25 mas at mid band - rather than the bright fringe used ill a conventional optical interferometer. In this mode the stellar light itself is suppressed by the destructive fringe, effectively enhancing the contrast of the circumstellar material located near the star. By subsequently shifting the neighboring bright fringe onto the center of the source brightness distribution and integrating, a second spatial regime dominated by light from the central portion of the source is almost simultaneously sampled. The nulling technique is the sparse aperture equivalent of the conventional corongraphic technique used in filled aperture telescopes. By fitting the unique KIK inner and outer spatial regime data, we have obtained an angular size of the mid-infrared continuum of 6.2, 4.0. or 5.4 mas for a disk profile, gaussian profile (fwhm), and shell profile respectively. The data show evidence of enhanced neutral atomic hydrogen emission located in the inner spatial regime relative to the outer regime. There is also evidence of a 9.7 micron silicate feature seen outside of this region. Importantly, we see spectral lines excited by the nova flash in the outer region before the blast wave reaches these regions. These lines are from neutral, weakly excited atoms which support the following interpretation. We discuss the present results in terms of a unifying model of the system that includes an increase in density in the plane of the orbit of the two stars created by a spiral shock wave caused by the motion of the stars through the cool wind of the red giant star. These data show the power and potential of the nulling technique which has been developed for the detection of Earth-like planets around nearby stars for the Terrestrial Planet Finder Mission and Darwin missions.

Barry, R. K.↗

DOE OSTI2020

Stochastic AC optimal power flow: A data-driven approach

There is an emerging need for efficient solutions to stochastic AC Optimal Power Flow (AC-OPF) to ensure optimal and reliable grid operations in the presence of increasing demand and generation uncertainty. Herein this paper presents a highly scalable data-driven algorithm for stochastic AC-OPF that has extremely low sample requirement. The novelty behind the algorithm’s performance involves an iterative scenario design approach that merges information regarding constraint violations in the system with data-driven sparse regression. Compared to conventional methods with random scenario sampling, our approach is able to provide feasible operating points for realistic systems with much lower sample requirements. Furthermore, multiple sub-tasks in our approach can be easily paralleled and based on historical data to enhance its performance and application. We demonstrate the computational improvements of our approach through simulations on different test cases in the IEEE PES PGLib-OPF benchmark library.

42 ENGINEERING↗

DOE OSTI2021

Scalable Techniques for Stochastic Power Flow Problems (Final Report)

The proposed research focuses on developing scalable algorithms for two-stage security-constrained OPF problems with AC power flow constraints, a class of problems complicated by (i) scale arising from a scenario representation; and (ii) the presence of nonlinearity, nonconvexity, and possibly second-stage discreteness or complementarity. Unfortunately, most existing solvers cannot contend with both challenges simultaneously; accordingly, the proposed research focuses on developing solution techniques that can both scale with the number of scenarios and contend with nonconvexity and second-stage complementarity. We consider three avenues for addressing such problems: (i) Variable sample-size SQP (VS-SQP) methods that combine sparse Quasi-Newton updates with a scalable variance-reduced stochastic gradient scheme for stochastic QP subproblems, allowing for contending with second-stage complementarity via regularization; (ii) Variable sample-size stochastic Interior-point (VS-sIP) schemes that propose a sampling-based regularized (to allow for contending with complementarity) interior-point schemes in which a Schur-complement technique is employed for decomposing the Newton direction computation step; (iii) Variable sample-size tractable ADMM (VS-tADMM) schemes combine variable sample-sizes with carefully designed techniques for resolving each of the nonconvex updates (by leveraging the QCQP structures). We intend to compare the three schemes using performance profiles in terms of solution quality, scalability, etc. and then select one scheme which will then be developed and further refined in Python for purposes of the GO competition.

42 ENGINEERING↗

DOE OSTI2012

LUMINOSITY FUNCTIONS OF SPITZER-IDENTIFIED PROTOSTARS IN NINE NEARBY MOLECULAR CLOUDS

We identify protostars in Spitzer surveys of nine star-forming (SF) molecular clouds within 1 kpc: Serpens, Perseus, Ophiuchus, Chamaeleon, Lupus, Taurus, Orion, Cep OB3, and Mon R2, which combined host over 700 protostar candidates. These clouds encompass a variety of SF environments, including both low-mass and high-mass SF regions, as well as dense clusters and regions of sparsely distributed star formation. Our diverse cloud sample allows us to compare protostar luminosity functions in these varied environments. We combine near- and mid-infrared photometry from the Two Micron All Sky Survey and Spitzer to create 1-24 {mu}m spectral energy distributions (SEDs). Using protostars from the c2d survey with well-determined bolometric luminosities, we derive a relationship between bolometric luminosity, mid-IR luminosity (integrated from 1-24 {mu}m), and SED slope. Estimations of the bolometric luminosities for protostar candidates are combined to create luminosity functions for each cloud. Contamination due to edge-on disks, reddened Class II sources, and galaxies is estimated and removed from the luminosity functions. We find that luminosity functions for high-mass SF clouds (Orion, Mon R2, and Cep OB3) peak near 1 L{sub Sun} and show a tail extending toward luminosities above 100 L{sub Sun }. The luminosity functions of the low-mass SF clouds (Serpens, Perseus, Ophiuchus, Taurus, Lupus, and Chamaeleon) do not exhibit a common peak, however the combined luminosity function of these regions peaks below 1 L{sub Sun }. Finally, we examine the luminosity functions as a function of the local surface density of young stellar objects. In the Orion molecular clouds, we find a significant difference between the luminosity functions of protostars in regions of high and low stellar density, the former of which is biased toward more luminous sources. This may be the result of primordial mass segregation, although this interpretation is not unique. We compare our luminosity functions to those predicted by models and find that our observed luminosity functions are best matched by models that invoke competitive accretion, although we do not find strong agreement between the high-mass SF clouds and any of the models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Stacked reverberation mapping of high-redshift quasars in DESI. I. Feasibility analysis

The broad-line region of quasars has long been probed by reverberation mapping techniques that measure time lags between continuum and broad emission-line variations. Stacked reverberation mapping has been proposed as a less observationally expensive alternative to traditional methods. This ensemble approach also reduces biases from small-number statistics. The Dark Energy Spectroscopic Instrument (DESI) is conducting the most extensive spectroscopic survey of quasars to date. We create mock light curves emulating expected DESI quasar observations at redshifts $1.48\lt z\lt 5.2$ and luminosities $44.68 \le \log \lambda L_{1350 \mathring{\rm A}{}} / \mathrm{erg\, s^{-1}} \le 45.99$ to test stacked reverberation mapping feasibility using sparse spectroscopic data paired with well-sampled photometric data. The pipeline, using the lag estimation code JAVELIN (Just Another Vehicle for Estimating Lags In Nuclei), successfully recovers the simulated C IV lags within 1σ of the true values using spectroscopic light curves composed of only a few spectral epochs (2–10) with irregular cadences. We investigate how observational factors, including C IV flux error magnitude, number of stacked quasars, and spectral epoch count, affect performance. This work motivates a pathway for future stacked reverberation mapping projects with large-scale spectroscopic surveys of quasars having $\ge 2$ spectroscopic observations. Our results suggest an economical alternative for constraining and extending the radius–luminosity relation to higher redshifts and luminosities. Subsequently, this relation can be employed more reliably in single-epoch black hole mass measurements and quasar cosmology in these distant regimes.

quasars: general, quasars: supermassive black hole↗

DOE OSTI2012

The plug-based nanovolume Microcapillary Protein Crystallization System (MPCS)

The Microcapillary Protein Crystallization System (MPCS) embodies a new semi-automated plug-based crystallization technology which enables nanolitre-volume screening of crystallization conditions in a plasticware format that allows crystals to be easily removed for traditional cryoprotection and X-ray diffraction data collection. Protein crystals grown in these plastic devices can be directly subjected to in situ X-ray diffraction studies. The MPCS integrates the formulation of crystallization cocktails with the preparation of the crystallization experiments. Within microfluidic Teflon tubing or the microfluidic circuitry of a plastic CrystalCard, {approx}10-20 nl volume droplets are generated, each representing a microbatch-style crystallization experiment with a different chemical composition. The entire protein sample is utilized in crystallization experiments. Sparse-matrix screening and chemical gradient screening can be combined in one comprehensive 'hybrid' crystallization trial. The technology lends itself well to optimization by high-granularity gradient screening using optimization reagents such as precipitation agents, ligands or cryoprotectants.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

A Bayesian Approach for Extracting Fluorescence Lifetimes from Sparse Data Sets and Its Significance for Imaging Experiments

The measurement of fluorescence lifetimes, especially in small sample volumes, presents the dual challenge of probing a small number of fluorophores and fitting the concomitant sparse data set to the appropriate excited-state decay function. A common method of analysis, such as the maximum likelihood (ML) technique, assumes a uniform probability distribution of the parameters describing the fluorescence decay function. An improvement is thus suggested by implementing a suitable nonuniform distribution, as is provided by a Bayesian framework, where the distribution of parameters is obtained from both their prior knowledge and the evidence-based likelihood of an event for a given set of parameters. We have also considered the Dirichlet prior distribution, whose mathematical form enables analytical solutions of the fitting parameters to be rapidly obtained. If Gaussian and exponential prior distributions are judiciously chosen, they reproduce the experimental target lifetime to within 20% with as few as 20 total photon counts for the data set, as does the Dirichlet prior distribution. But because of the analytical solutions afforded by the Dirichlet prior distribution, it is proposed to employ a Dirichlet prior to search parameter space rapidly to provide, if necessary, appropriate parameters for subsequent employment of a Gaussian or exponential prior distribution

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Assessing the limitations of commercial sensors and models for supporting marine carbon dioxide removal monitoring: a case study

Several unknowns remain surrounding marine Carbon Dioxide Removal (mCDR) monitoring, reporting, and verification (MRV) practices and capabilities. Current in-situ sensor technology is limited (primarily pH and pCO 2 ), requiring calculations and assumptions to estimate changes in carbonate chemistry parameters, including total alkalinity (TA). Considering that cost, energy consumption, and accuracy of commercial sensors can vary by orders of magnitude, understanding how well existing sensors perform in an mCDR context is important for this emerging community. Likewise, documenting sensor limitations and how relatively simple models can optimize sensor deployments will improve MRV efforts and support protocol development. Here we (1) compare performance a variety of commercially available sensors in a blind mesocosm experiment simulating ocean alkalinity enhancement (OAE), and how sensor performance impacted carbonate chemistry estimates; (2) evaluate if sensors can distinguish the OAE signal from natural variability during a small scale OAE field test in Sequim Bay, WA, USA, and (3) use an idealized ocean biogeochemistry model to explore optimal sensor network design based on (1) and (2). Our mesocosm results indicate that correctly constraining pH uncertainty will be critical for accurate TA estimates with current sensor technology compared to the less impactful variation caused by uncertainty in pCO 2 (pH data that are presented throughout are reported on the total scale (pH T ) unless otherwise noted). Our pilot field test demonstrated that sensors were capable of distinguishing mCDR signatures from natural variability under optimal real-world conditions. Idealized modeling simulations of the field test showed that a range of sparse and dense (3 to 100) sensors sampling areas of detectable increases will underestimate the net change in surface pH by at least 35–55%, at both realistic and highly elevated alkalinity input levels. We also highlight the limitations of current sensing technology for MRV, and the importance of ocean biogeochemistry models as critical tools for predicting when and where mCDR signals will be detectable using available sensors. Overall, our findings suggest that commercially available pCO 2 sensors and some pH sensors will form an important backbone for mCDR MRV tasks, though complete MRV characterization will require these data to be used in combination with other tools.

OAE↗

NASA NTRS2001

Determining Greenland Ice Sheet Accumulation Rates from Radar Remote Sensing

An important component of NASA's Program for Arctic Regional Climate Assessment (PARCA) is a mass balance investigation of the Greenland Ice Sheet. The mass balance is calculated by taking the difference between the snow accumulation and the ice discharge of the ice sheet. Uncertainties in this calculation include the snow accumulation rate, which has traditionally been determined by interpolating data from ice core samples taken throughout the ice sheet. The sparse data associated with ice cores, coupled with the high spatial and temporal resolution provided by remote sensing, have motivated scientists to investigate relationships between accumulation rate and microwave observations.

Jezek, Kenneth C.↗

NASA NTRSDate not supplied

Biological Research and Space Health Enabled by Machine Learning to Support Deep Space Missions

A key science goal of the NASA “Moon to Mars” campaign is to understand how biology responds to the Lunar, Martian, and deep space environments in order to advance fundamental knowledge, reduce risk, and support safe, productive human space missions. Through the powerful emerging computer science approaches of artificial intelligence (AI) and machine learning (ML), a paradigm shift has begun in biomedical science and engineered astronaut health systems, to enable Earth-independence and autonomy of mission operations. We present a decadal view of AI/ML architecture to support deep space mission goals, developed in concert with leaders in the field. We describe current AI/ML methods to support 1) fundamental biology, 2) in situ analytics, 3) high performance computing hardware, 4) automated science, 5) self-driving labs, 6) remote data management, 7) integrated real-time mission biomonitoring, and 8) a Precision Space Health system. Cutting-edge AI/ML approaches that can be integrated to support these domains include active learning, explainable AI, adaptive learning, causal inference, knowledge graphs, federated learning, transfer learning, and large language models. Finally, we present results from several current ML projects that are underway in the field to address key challenges of small sample n, high feature count, heterogeneity, and sparse data. These include 1) connecting omics data to phenotypic data using an ensemble model to infer causality of spaceflight rodent liver health disruption, 2) usage of explainable ML to interrogate the muscular underpinnings of spaceflight muscle atrophy, 3) ML models analyzing and determining directed acyclic graphs of human space health risk leveraging rodent bone datasets, 4) usage of large pre-trained models connecting biomedical knowledgebases with small spaceflight datasets to understand gene-to-gene interaction networks, and 5) a suite of benchmarked open science datasets (spaceflight mouse liver; radiation DNA damage) enabling programmers to identify the best ML algorithms to answer space biological science questions.

space biology↗

NASA NTRSDate not supplied

Biological Research and Space Health Enabled by Machine Learning to Support Deep Space Missions

A key science goal of the NASA “Moon to Mars” campaign is to understand how biology responds to the Lunar, Martian, and deep space environments in order to advance fundamental knowledge and support human space missions. Through artificial intelligence (AI) and machine learning (ML), a paradigm shift has begun in space biosciences and engineered astronaut health systems, to enable Earth-independence and mission operations autonomy. We describe current AI/ML methods to support 1) fundamental biology, 2) in situ analytics, 3) high performance computing, 4) automated science, 5) self-driving labs, 6) remote data management, 7) integrated mission biomonitoring, and 8) a Precision Space Health system. AI/ML approaches that can be integrated to support these domains include active learning, explainable AI, adaptive learning, causal inference, knowledge graphs, federated learning, transfer learning, and large language models. Finally, we present results from several current ML projects that are underway in the space biology field to address key challenges of small sample n, high feature count, heterogeneity, and sparse data. These include 1) connecting omics to phenotypic data using an ensemble model to infer causality of rodent liver health disruption, 2) usage of explainable ML to interrogate muscular underpinnings of muscle atrophy, 3) ML models analyzing and determining directed acyclic graphs of human health risk leveraging rodent bone datasets, 4) usage of large pre-trained models connecting biomedical knowledgebases with small spaceflight datasets to understand gene-to-gene interactions, and 5) a suite of benchmarked open science datasets enabling programmers to identify best algorithms to answer space biology questions.

space biology↗