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

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

Warner, James E.↗
NASA NTRS2004

Experiments with osteoblasts cultured under hypergravity conditions

To understand further the role of gravity in osteoblast attachment, osteoblasts were subjected to hypergravity conditions in vitro. Scanning electron microscopy of all confluent coverslips from FPA units show that the number of attached osteoblasts was similar among gravitational levels and growth durations (~90 cells/microscopic field). Specifically, confluent 1.0 G control cultures contained an average of 91 +/- 8 cells/field, 3.3 G samples had 88 +/- 8 cells/field, and 4.0 G cultures averaged 90 +/- 7 cells/field. The sparsely plated cultures assessed by immunohistochemistry also had similar numbers of cells at each time point (l.0 G was similar to 3.3 and 4.0 G), but cell number changed from one time point to the next as those cells proliferated. Immunohistochemistry of centrifuged samples showed an increase in number (up to 160% increase) and thickness (up to 49% increase) of actin fibers, a decrease in intensity of fibronectin fluorescence (18-23% decrease) and an increase in number of vinculin bulbs (202-374% increase in number of vinculin bulbs/area). While hypergravity exposure did not alter the number of attached osteoblasts, it did result in altered actin, fibronectin, and vinculin elements, changing some aspects of osteoblast- substrate adhesion.

NASA Program Fundamental Space Biology↗
DOE OSTI2024

Dynamic sparse x-ray nanotomography reveals ionomer hydration mechanism in polymer electrolyte fuel-cell catalyst

Tomographic imaging of time-evolving samples is a challenging yet important task for various research fields. At the nanoscale, current approaches face limitations of measurement speed or resolution due to lengthy acquisitions. We developed a dynamic nanotomography technique based on sparse dynamic imaging and 4D tomography modeling. We demonstrated the technique, using ptychographic x-ray computed tomography as its imaging modality, on resolving the in situ hydration process of polymer electrolyte fuel cell (PEFC) catalyst. The technique provides a 40-time increase in temporal resolution compared to conventional approaches, yielding 28 nm half-period spatial and 12 min temporal resolution. The results allow a quantitative characterization of the water intake process inside PEFC catalysts with nanoscale resolution, which is crucial for understanding their electrochemical mechanisms and optimizing their performance. Our technique enables high-speed operando nanotomography studies and paves the way for wider application of dynamic tomography at the nanoscale.

Science & Technology - Other Topics↗
DOE OSTI2017

Implicit sampling combined with reduced order modeling for the inversion of vadose zone hydrological data

Bayesian inverse modeling techniques are computationally expensive because many forward simulations are needed when sampling the posterior distribution of the parameters. Here, in this paper, we combine the implicit sampling method and generalized polynomial chaos expansion (gPCE) to significantly reduce the computational cost of performing Bayesian inverse modeling. There are three steps in this approach: (1) find the maximizer of the likelihood function using deterministic approaches; (2) construct a gPCE-based surrogate model using the results from a limited number of forward simulations; and (3) efficiently sample the posterior distribution of the parameters using implicit sampling method. The cost of constructing the gPCE-based surrogate model is further decreased by using sparse Bayesian learning to reduce the number of gPCE coefficients that have to be determined. We demonstrate the approach for a synthetic ponded infiltration experiment simulated with TOUGH2. The surrogate model is highly accurate with mean relative error that is < 0.035% in predicting saturation and < 0.25% in predicting the likelihood function. The posterior distribution of the parameters obtained using our proposed technique is nearly indistinguishable from the results obtained from either an implicit sampling method or a Markov chain Monte Carlo method utilizing the full mode.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Development and Demonstration of a Prototype Molten Salt Sampling System

Molten salt reactors (MSRs) offer potential operability and safety advantages when compared to commercial light water reactors (LWRs). However, operating experience with MSRs is sparse in comparison to what exists for LWRs. Further, the chemical and isotopic composition of the fuel and/or coolant salt is dynamic and difficult to characterize continuously, posing potential safety, operability, and safeguards unknowns that need to be addressed. A molten salt sampling system (MSSS) is regarded as a necessary subsystem within first generation MSRs used to obtain samples of salt for chemical and isotopic analysis in support of the need to monitor and control salt composition during operation. The MSSS is being developed using the Safety-in-Design (SiD) methodology, which incorporates incremental integration of safety analysis into the design process. The MSSS conceptual design emerging from the application of the early stages of the SiD methodology consists of a sample collection system and its housing, a freeze port, and inert gas control and delivery systems. This article describes the prototypes developed to test the functions of these MSSS subsystems, presents the results of testing in both dry and molten salt environments (including reliability data collection performed in accordance with the principles of SiD and the development of a semiquantitative fault tree model), and summarizes the opportunities for future design and testing enhancements based on the results of prototype testing.

molten salt reactor↗
DOE OSTI2016

Blind identification of full-field vibration modes of output-only structures from uniformly-sampled, possibly temporally-aliased (sub-Nyquist), video measurements

Enhancing the spatial and temporal resolution of vibration measurements and modal analysis could significantly benefit dynamic modelling, analysis, and health monitoring of structures. For example, spatially high-density mode shapes are critical for accurate vibration-based damage localization. In experimental or operational modal analysis, higher (frequency) modes, which may be outside the frequency range of the measurement, contain local structural features that can improve damage localization as well as the construction and updating of the modal-based dynamic model of the structure. In general, the resolution of vibration measurements can be increased by enhanced hardware. Traditional vibration measurement sensors such as accelerometers have high-frequency sampling capacity; however, they are discrete point-wise sensors only providing sparse, low spatial sensing resolution measurements, while dense deployment to achieve high spatial resolution is expensive and results in the mass-loading effect and modification of structure's surface. Non-contact measurement methods such as scanning laser vibrometers provide high spatial and temporal resolution sensing capacity; however, they make measurements sequentially that requires considerable acquisition time. As an alternative non-contact method, digital video cameras are relatively low-cost, agile, and provide high spatial resolution, simultaneous, measurements. Combined with vision based algorithms (e.g., image correlation or template matching, optical flow, etc.), video camera based measurements have been successfully used for experimental and operational vibration measurement and subsequent modal analysis. However, the sampling frequency of most affordable digital cameras is limited to 30–60 Hz, while high-speed cameras for higher frequency vibration measurements are extremely costly. This work develops a computational algorithm capable of performing vibration measurement at a uniform sampling frequency lower than what is required by the Shannon-Nyquist sampling theorem for output-only modal analysis. In particular, the spatio-temporal uncoupling property of the modal expansion of structural vibration responses enables a direct modal decoupling of the temporally-aliased vibration measurements by existing output-only modal analysis methods, yielding (full-field) mode shapes estimation directly. Then the signal aliasing properties in modal analysis is exploited to estimate the modal frequencies and damping ratios. Furthermore, the proposed method is validated by laboratory experiments where output-only modal identification is conducted on temporally-aliased acceleration responses and particularly the temporally-aliased video measurements of bench-scale structures, including a three-story building structure and a cantilever beam.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Knowledge Oriented Graph Unified Transformer (KOGUT) v0.1

KOGUT — Knowledge Oriented Graph Unified Transformer KOGUT implements the Relational Graph Transformer (RelGT) architecture for knowledge graph link prediction in biological domains, with a primary focus on microbial growth media prediction. While the original RelGT (arXiv:2505.10960) targets relational tables, time series, and multi-table databases, KOGUT adapts this architecture for heterogeneous biological knowledge graphs, providing first-in-class AI predictive models for microbial cultivation. Key Adaptations Beyond Original RelGT: - Knowledge Graph Focus: Applied to biological KGs with semantic node types (taxa, chemicals, media, phenotypes, environments) versus generic relational database tables, trained on the KG-Microbe knowledge graph (1.3M entities, 2.9M edges, 24 relation types). - Multimodal Node Encoding: Integrates node labels, categories, descriptions, and synonyms from KG metadata through learned embedding layers—adapting relational column features to graph node attributes with textual semantics. - Extended K-Hop Subgraph Strategy: Optimized neighborhood sampling (3-hop default, configurable up to 200 nodes) tuned for sparse biological networks, building on the original local-global attention framework with biological relation preservation. - Biolink Predicate Preservation: Type-specific transformations for 24 biological edge semantics (occurs_in, consumes, produces, has_phenotype, subclass_of) beyond standard relational foreign keys, enabling multi-relation link prediction. - Inductive Learning Support: Enables zero-shot predictions for novel taxa through feature-based embeddings (temperature, oxygen requirements, gram stain, cell shape), extending the original transductive relational benchmark scope to uncultured microorganisms. CheapSOTA Performance Optimizations (This Distribution): - VQ-EMA Centroid Attention: Vector quantization with exponential moving average for improved global context modeling (+5-10% MRR improvement). - HDF5 Precomputed Data Loading: One-time preprocessing of k-hop subgraphs to eliminate redundant graph traversals (2-5× training speedup). - Distributed Data Parallel Training: Multi-GPU support for scaling to larger knowledge graphs (tested on 4× NVIDIA A100 GPUs at NERSC Perlmutter). - Mixed Precision Training: Automatic mixed precision (AMP) for memory efficiency and faster training. Advantages Over Standard Knowledge Graph Embedding Models: Combines RelGT's proven multi-element tokenization (features, type, hop, structure) with graph-native biological representations, enabling interpretable link prediction across heterogeneous entities that standard embedding models (TransE, RotatE, ComplEx) and table-based transformers cannot directly model. Achieves near-perfect performance on microbial growth media prediction (MRR: 0.9966, Precision@1: 0.9932, Hit@10: 1.0000) while maintaining explainability through attention-based reasoning over biological pathways. Training Data: - KG-Microbe merged knowledge graph: 1,379,337 nodes, 2,960,472 edges - 24 biological relation types including taxonomic hierarchies, metabolic interactions, phenotype associations, and environmental relationships - Primary prediction task: Growth media suitability for microbial taxa (biolink:occurs_in, 50K edges) - Multi-relation capability: Predicts links for any of the 24 relation types, including chemical consumption/production, phenotype associations, and taxonomic classification Citation: Original RelGT Architecture: Dwivedi et al., "Relational Graph Transformer", arXiv:2505.10960, 2025 KOGUT Implementation: Knowledge Oriented Graph Unified Transformer for Microbial Growth Media Prediction Developed at Lawrence Berkeley National Laboratory (LBNL) Trained on NERSC Perlmutter supercomputer

Joachimiak, Marcin [Lawrence Berkeley National Lab↗
NASA NTRS1980

First Scientific Working Group Meeting of Airborne Doppler Lidar Wind Velocity Measurement Program, appendix C

The problem is to operate on two scalar fields to produce a vector field, to produce user products from the vector field, and to establish reliability of results. Data problems encountered include sparse measurements, irregular distribution, varying quality, imperfect orthogonality, aliasing due to sampling volume, and measurements not simultaneous. Desired algorithm characteristics, solution elements, and characteristics of the model are listed. The seven simulation elements, eight algorithm steps and the required user inputs are given.

Lee, R. W.↗
DOE OSTI2018

Compressed sensing with sparse corruptions: Fault-tolerant sparse collocation approximations

The recovery of approximately sparse or compressible coefficients in a polynomial chaos expansion is a common goal in many modern parametric uncertainty quantification (UQ) problems. However, relatively little effort in UQ has been directed toward theoretical and computational strategies for addressing the sparse corruptions problem, where a small number of measurements are highly corrupted. Such a situation has become pertinent today since modern computational frameworks are sufficiently complex with many interdependent components that may introduce hardware and software failures, some of which can be difficult to detect and result in a highly polluted simulation result. In this paper we present a novel compressive sampling-based theoretical analysis for a regularized t1 minimization algorithm that aims to recover sparse expansion coefficients in the presence of measurement corruptions. Our recovery results are uniform (the theoretical guarantees hold for all compressible signals and compressible corruptions vectors), and prescribe algorithmic regularization parameters in terms of a user-defined a priori estimate on the ratio of measurements that are believed to be corrupted. We also propose an iteratively reweighted optimization algorithm that automatically refines the value of the regularization parameter, and empirically produces superior results. Our numerical results test our framework on several medium-to-high dimensional examples of solutions to parameterized differential equations, and demonstrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2017

X-Ray Computed Tomography: The First Step in Mars Sample Return Processing

The Mars 2020 rover mission will collect and cache samples from the martian surface for possible retrieval and subsequent return to Earth. If the samples are returned, that mission would likely present an opportunity to analyze returned Mars samples within a geologic context on Mars. In addition, it may provide definitive information about the existence of past or present life on Mars. Mars sample return presents unique challenges for the collection, containment, transport, curation and processing of samples [1] Foremost in the processing of returned samples are the closely paired considerations of life detection and Planetary Protection. In order to achieve Mars Sample Return (MSR) science goals, reliable analyses will depend on overcoming some challenging signal/noise-related issues where sparse martian organic compounds must be reliably analyzed against the contamination background. While reliable analyses will depend on initial clean acquisition and robust documentation of all aspects of developing and managing the cache [2], there needs to be a reliable sample handling and analysis procedure that accounts for a variety of materials which may or may not contain evidence of past or present martian life. A recent report [3] suggests that a defined set of measurements should be made to effectively inform both science and Planetary Protection, when applied in the context of the two competing null hypotheses: 1) that there is no detectable life in the samples; or 2) that there is martian life in the samples. The defined measurements would include a phased approach that would be accepted by the community to preserve the bulk of the material, but provide unambiguous science data that can be used and interpreted by various disciplines. Fore-most is the concern that the initial steps would ensure the pristine nature of the samples. Preliminary, non-invasive techniques such as computed X-ray tomography (XCT) have been suggested as the first method to interrogate and characterize the cached samples without altering the materials [1,2]. A recent report [4] indicates that XCT may minimally alter samples for some techniques, and work is needed to quantify these effects, maximizing science return from XCT initial analysis while minimizing effects.

Welzenbach, L. C.↗
DOE OSTI2013

Results of Routine Strip Effluent Hold Tank and Decontaminated Salt Solution Hold Tank Samples from Modular Caustic-Side Solvent Extraction Unit during Macrobatch 5 Operations

Strip Effluent Hold Tank (SEHT) and Decontaminated Salt Solution Hold Tank (DSSHT) samples from several of the "microbatches" of Integrated Salt Disposition Project (ISDP) Salt Batch ("Macrobatch") 5 have been analyzed for 238 Pu, 90 Sr, 137 Cs, and by Inductively Coupled Plasma Emission Spectroscopy (ICPES). The results indicate good decontamination performance within process design expectations. While the data set is sparse, the results of this set and the previous set of results for Macrobatch 4 samples indicate generally consistent operations. The DSSHT samples show continued presence of titanium, likely from leaching of the monosodium titanate in the Actinide Removal process (ARP).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2018

A new synchrotron rapid-scanning X-ray fluorescence (SRS-XRF) imaging station at SSRL beamline 6-2

This paper describes a new large-range rapid-scan X-ray fluorescence (XRF) imaging station at beamline 6-2 at the Stanford Synchrotron Radiation Lightsource at SLAC National Accelerator Laboratory. This station uses a continuous rapid-scan system with a scan range of 1000 × 600 mm and a load capacity of up to 25 kg, capable of 25–100 µm resolution elemental XRF mapping and X-ray absorption spectroscopy (XAS) of a wide range of objects. XRF is measured using a four-element Hitachi Vortex ME4 silicon drift detector coupled to a Quantum Detectors Xspress3 multi-channel analyzer system. A custom system allows the X-ray spot size to be changed quickly and easily via pinholes ranging from 25 to 100 µm, and the use of a poly-capillary or axially symmetric achromatic optic may achieve a <10 µm resolution in the future. The instrument is located at wiggler beamline 6-2 which has an energy range of 2.1–17 keV, creating K emission for elements up to strontium, and L or M emission for all other elements. XAS can also be performed at selected sample positions within the same experiment, allowing for a more detailed chemical characterization of the elements of interest. Furthermore, sparse excitation energy XRF imaging can be performed over a wide range of incident X-ray energies. User friendliness has been emphasized in all stages of the experiment, including versatile sample mounts, He purged chambers for low- Z analyses, and intuitive visualization hardware and software. The station provides analysis capabilities for a wide range of materials and research fields including biological, chemical, environmental and materials science, paleontology, geology and cultural heritage.

47 OTHER INSTRUMENTATION↗
DOE OSTI2018

Sparse modeling of space- and time-varying diffraction response of a progressively loaded aluminum alloy

Highlights: • Plasticity induces crystal orientation and lattice spacing heterogeneity. • High energy x-ray diffraction spot broadening typically accompanies plasticity. • Method quantifies spot broadening in difficult, mixed microstructure data. • Algorithm finds sparse combination of entries from dictionary of peak functions. • Approach showed asymmetric plastic response in preprocessed AA7075 T651 sample. - Abstract: High energy X-ray diffraction data collected in situ during loading experiments permits probing of the crystal structure of a plastically deforming material sample. An elastoplastic deformation is associated with heterogeneity in both crystal orientation and lattice spacing—each manifesting as azimuthal broadening and radial broadening of diffraction peaks respectively. Quantifying the spreading effect is challenging, especially in cases where the sample has a granularity between that of a single crystal and fine grain or powder material. The approach developed in this paper begins by modeling the intensity signal in the vicinity of a Debye-Scherrer ring as a sparse, nonnegative superposition of Gaussian basis functions drawn from an over-complete dictionary. Processing automatically selects from the dictionary basis functions whose widths and amplitudes are representative of the data. The chosen basis functions are used to compute scalar measures of radial and azimuthal broadening for the set of diffraction peaks composing a Debye-Scherrer ring. To demonstrate the utility of the approach, we show that analysis of diffraction peak shape information from an aluminum alloy 7075 T651 (AA7075 T651) sample provides insight into the origin of material state that would have otherwise have been difficult if not impossible to extract using conventional methods. Furthermore, the extracted information revealed a deformation response linked to the processing history of the sample.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Graph decomposition techniques for solving combinatorial optimization problems with variational quantum algorithms

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum—in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly k-regular graphs, as k-regular graphs on n vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. In conclusion, while this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions

We propose a multi-element stochastic collocation method that can be applied in high-dimensional parameter space for functions with discontinuities lying along manifolds of general geometries. The key feature of the method is that the parameter space is decomposed into multiple elements defined by the discontinuities and thus only the minimal number of elements are utilized. On each of the resulting elements the function is smooth and can be approximated using high-order methods with fast convergence properties. The decomposition strategy is in direct contrast to the traditional multi-element approaches which define the sub-domains by repeated splitting of the axes in the parameter space. Such methods are more prone to the curse-of-dimensionality because of the fast growth of the number of elements caused by the axis based splitting. The present method is a two-step approach. Firstly a discontinuity detector is used to partition parameter space into disjoint elements in each of which the function is smooth. The detector uses an efficient combination of the high-order polynomial annihilation technique along with adaptive sparse grids, and this allows resolution of general discontinuities with a smaller number of points when the discontinuity manifold is low-dimensional. After partitioning, an adaptive technique based on the least orthogonal interpolant is used to construct a generalized Polynomial Chaos surrogate on each element. The adaptive technique reuses all information from the partitioning and is variance-suppressing. We present numerous numerical examples that illustrate the accuracy, efficiency, and generality of the method. When compared against standard locally-adaptive sparse grid methods, the present method uses many fewer number of collocation samples and is more accurate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Spatially resolved microlensing time-scale distributions across the Galactic bulge with the VVV survey

ABSTRACT We analyse 1602 microlensing events found in the VISTA Variables in the Via Lactea (VVV) near-infrared (NIR) survey data. We obtain spatially resolved, efficiency-corrected time-scale distributions across the Galactic bulge (|ℓ| < 10°, |b| < 5°), using a Bayesian hierarchical model. Spatially resolved peaks and means of the time-scale distributions, along with their marginal distributions in strips of longitude and latitude, are in agreement at a 1σ level with predictions based on the Besançon model of the Galaxy. We find that the event time-scales in the central bulge fields (|ℓ| < 5°) are on average shorter than the non-central (|ℓ| > 5°) fields, with the average peak of the lognormal time-scale distribution at 23.6 ± 1.9 d for the central fields and 29.0 ± 3.0 d for the non-central fields. Our ability to probe the structure of the bulge with this sample of NIR microlensing events is limited by the VVV survey’s sparse cadence and relatively small number of detected microlensing events compared to dedicated optical surveys. Looking forward to future surveys, we investigate the capability of the Roman telescope to detect spatially resolved asymmetries in the time-scale distributions. We propose two pairs of Roman fields, centred on (ℓ = ±9, 5°, b = −0.125°) and (ℓ = −5°, b = ±1.375°) as good targets to measure the asymmetry in longitude and latitude, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Towards A Geo-Data Science Method for Assessing Rare Earth Element and Critical Mineral Occurrences in Coal and Other Sedimentary Systems

While preliminary analyses of data from open-source resources (Ekmann, 2012) show promising concentrations of REE in individual coal samples from a number of sites and basins in the U.S., other sparse data for REE in domestic coal-related strata suggest that many occurrences are low, “subeconomic” concentrations. At present, there is no method for systematically assessing potential sedimentary occurrences of REE. However, the geologic processes responsible for REE occurrences in coal-related strata are systematic; the unpredictability of REE resources in coal-related strata is due to poorly quantified spatial resource trends and the lack of an exploration method tailored to these resources. Thus, there exists a need for a systematic assessment approach that incorporates knowledge of geological variation in the mechanisms of REE enrichment within coal basins to help minimize geologic uncertainty and reduce commercial exploration risk.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2018

Compressed Sensing with Sparse Corruptions: Fault-Tolerant Sparse Collocation Approximations

The recovery of approximately sparse or compressible coefficients in a polynomial chaos expansion is a common goal in many modern parametric uncertainty quantification (UQ) problems. However, relatively little effort in UQ has been directed toward theoretical and computational strategies for addressing the sparse corruptions problem, where a small number of measurements are highly corrupted. Such a situation has become pertinent today since modern computational frameworks are sufficiently complex with many interdependent components that may introduce hardware and software failures, some of which can be difficult to detect and result in a highly polluted simulation result. In this paper we present a novel compressive sampling--based theoretical analysis for a regularized $\ell^1$ minimization algorithm that aims to recover sparse expansion coefficients in the presence of measurement corruptions. Our recovery results are uniform (the theoretical guarantees hold for all compressible signals and compressible corruptions vectors) and prescribe algorithmic regularization parameters in terms of a user-defined a priori estimate on the ratio of measurements that are believed to be corrupted. We also propose an iteratively reweighted optimization algorithm that automatically refines the value of the regularization parameter and empirically produces superior results. Lastly, our numerical results test our framework on several medium to high dimensional examples of solutions to parameterized differential equations and demonstrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗