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NASA NTRSDate not supplied

Compressive Sensing Based Data Acquisition Architecture for Transient Stellar Events in Crowded Star Fields

Compressive sensing is a mathematical technique for simultaneous data acquisition and compression. In this work, we show a CS based architecture for acquiring and reconstructing transient stellar events. This architecture recon-structs a differenced image itself, eliminating the need for any sparse domain transforms, otherwise required for traditional CS reconstruction. The resulting reconstructed differenced image is of critical importance as the information required for generating a time-series photometric light curve is obtained only from a differenced image. Hence, reconstructing a crowded star spatial image, followed by differencing is wasteful. This architecture eliminates the need to 1.) transform an image to a sparse domain, 2.) Reconstruct a dense field, and then apply differencing on the image to obtain the image of critical value. We study the case of microlensing to depict a star source experiencing magnification in time. Our results show that this architecture is able to reconstruct star source magnitudes with magnification factors greater than 1 for clean images with error less than 2% using only 10% of the Nyquist rate samples.

Compressive Sensing, Data acquisition, Image diffe↗
NASA NTRSDate not supplied

Compressive Sensing Based Data Acquisition Architecture for Transient Stellar Events in Crowded Star Fields

Compressive sensing is a mathematical technique for simultaneous data acquisition and compression. In this work, we show a CS based architecture for acquiring and reconstructing transient stellar events. This architecture recon-structs a differenced image itself, eliminating the need for any sparse domain transforms, otherwise required for traditional CS reconstruction. The resulting reconstructed differenced image is of critical importance as the information required for generating a time-series photometric light curve is obtained only from a differenced image. Hence, reconstructing a crowded star spatial image, followed by differencing is wasteful. This architecture eliminates the need to 1.) transform an image to a sparse domain, 2.) Reconstruct a dense field, and then apply differencing on the image to obtain the image of critical value. We study the case of microlensing to depict a star source experiencing magnification in time. Our results show that this architecture is able to reconstruct star source magnitudes with magnification factors greater than 1 for clean images with error less than 2% using only 10% of the Nyquist rate samples.

Asmita Korde-patel↗
DOE OSTI2014

A convex pseudolikelihood framework for high dimensional partial correlation estimation with convergence guarantees

Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either parametric likelihoods, or regularized regression/pseudolikelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudolikelihood-based objective functions have provable convergence guarantees, it is not clear whether corresponding estimators exist or are even computable, or if they actually yield correct partial correlation graphs. We propose a new pseudolikelihood-based graphical model selection method that aims to overcome some of the shortcomings of current methods, but at the same time retain all their respective strengths. In particular, we introduce a novel framework that leads to a convex formulation of the partial covariance regression graph problem, resulting in an objective function comprised of quadratic forms. The objective is then optimized via a coordinate wise approach. The specific functional form of the objective function facilitates rigorous convergence analysis leading to convergence guarantees; an important property that cannot be established by using standard results, when the dimension is larger than the sample size, as is often the case in high dimensional applications. These convergence guarantees ensure that estimators are well defined under very general conditions and are always computable. In addition, the approach yields estimators that have good large sample properties and also respect symmetry. Furthermore, application to simulated and real data, timing comparisons and numerical convergence is demonstrated. We also present a novel unifying framework that places all graphical pseudolikelihood methods as special cases of a more general formulation, leading to important insights.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics-Informed Sparse Gaussian Process for Probabilistic Stability Analysis of Large-Scale Power System with Dynamic PVs and Loads

This work proposes a physics-informed sparse Gaussian process (SGP) for probabilistic stability assessment of large-scale power systems in the presence of uncertain dynamic PVs and loads. The differential and algebraic equations considering uncertainties from dynamic PVs and loads are reformulated to a nonlinear mapping relationship that allows the application of SGP. Thanks to the nonparametric characteristic of Gaussian process, the proposed framework does not require distributions of uncertain inputs and this distinguishes it from existing approaches. As the original Gaussian process is not scalable to large-scale systems with high dimensional uncertain inputs, this paper develops the SGP with a stochastic variational inference technique. It leads to approximately two orders of complex reduction. A data pre-processing step is also introduced to tackle the coexistence of stable and unstable cases by sample clustering and constructing separate SGPs. The probabilistic transient stability index is analyzed to assess system stability under different uncertain dynamics loads and PVs. Comparisons are performed with the sampling-based, the polynomial chaos expansion-based, and traditional Gaussian process-based methods on the modified IEEE 118-bus and Texas 2000-bus systems under various scenarios, including different levels of uncertainties and the existence of nonlinear correlations among dynamic PVs. The impacts of data quality and quantity issues are also investigated. It is shown that the proposed SGP achieves significantly improved computational efficiency while maintaining high accuracy with a limited number of data.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2014

Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis

The demand for accurate and computationally affordable sensitivity and uncertainty techniques is constantly on the rise and has become especially pressing in the nuclear field with the shift to Best Estimate Plus Uncertainty methodologies in the licensing of nuclear installations. Besides traditional, already well developed methods – such as first order perturbation theory or Monte Carlo sampling – Polynomial Chaos Expansion (PCE) has been given a growing emphasis in recent years due to its simple application and good performance. This paper presents new developments of the research done at TU Delft on such Polynomial Chaos (PC) techniques. Our work is focused on the Non-Intrusive Spectral Projection (NISP) approach and adaptive methods for building the PCE of responses of interest. Recent efforts resulted in a new adaptive sparse grid algorithm designed for estimating the PC coefficients. The algorithm is based on Gerstner's procedure for calculating multi-dimensional integrals but proves to be computationally significantly cheaper, while at the same it retains a similar accuracy as the original method. More importantly the issue of basis adaptivity has been investigated and two techniques have been implemented for constructing the sparse PCE of quantities of interest. Not using the traditional full PC basis set leads to further reduction in computational time since the high order grids necessary for accurately estimating the near zero expansion coefficients of polynomial basis vectors not needed in the PCE can be excluded from the calculation. Moreover the sparse PC representation of the response is easier to handle when used for sensitivity analysis or uncertainty propagation due to the smaller number of basis vectors. The developed grid and basis adaptive methods have been implemented in Matlab as the Fully Adaptive Non-Intrusive Spectral Projection (FANISP) algorithm and were tested on four analytical problems. These show consistent good performance both in terms of the accuracy of the resulting PC representation of quantities and the computational costs associated with constructing the sparse PCE. Basis adaptivity also seems to make the employment of PC techniques possible for problems with a higher number of input parameters (15–20), alleviating a well known limitation of the traditional approach. The prospect of larger scale applicability and the simplicity of implementation makes such adaptive PC algorithms particularly appealing for the sensitivity and uncertainty analysis of complex systems and legacy codes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

El-CID: a filter for gravitational-wave electromagnetic counterpart identification

ABSTRACT As gravitational-wave (GW) interferometers become more sensitive and probe ever more distant reaches, the number of detected binary neutron star mergers will increase. However, detecting more events farther away with GWs does not guarantee corresponding increase in the number of electromagnetic counterparts of these events. Current and upcoming wide-field surveys that participate in GW follow-up operations will have to contend with distinguishing the kilonova (KN) from the ever increasing number of transients they detect, many of which will be consistent with the GW sky-localization. We have developed a novel tool based on a temporal convolutional neural network architecture, trained on sparse early-time photometry and contextual information for Electromagnetic Counterpart Identification (El-CID). The overarching goal for El-CID is to slice through list of new transient candidates that are consistent with the GW sky localization, and determine which sources are consistent with KNe, allowing limited target-of-opportunity resources to be used judiciously. In addition to verifying the performance of our algorithm on an extensive testing sample, we validate it on AT2017gfo – the only EM counterpart of a binary neutron star merger discovered to date – and AT2019npv – a supernova that was initially suspected as a counterpart of the GW event, GW190814, but was later ruled out after further analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Application of Compressed Sensing to 2-D Ultrasonic Propagation Imaging System data

The Ultrasonic Propagation Imaging (UPI) System is a unique, non-contact, laser-based ultrasonic excitation and measurement system developed for structural health monitoring applications. The UPI system imparts laser-induced ultrasonic excitations at user-defined locations on a structure of interest. The response of these excitations is then measured by piezoelectric transducers. By using appropriate data reconstruction techniques, a time-evolving image of the response can be generated. A representative measurement of a plate might contain 800x800 spatial data measurement locations and each measurement location might be sampled at 500 instances in time. The result is a total of 640,000 measurement locations and 320,000,000 unique measurements. This is clearly a very large set of data to collect, store in memory and process. The value of these ultrasonic response images for structural health monitoring applications makes tackling these challenges worthwhile. Recently compressed sensing has presented itself as a candidate solution for directly collecting relevant information from sparse, high-dimensional measurements. The main idea behind compressed sensing is that by directly collecting a relatively small number of coefficients it is possible to reconstruct the original measurement. The coefficients are obtained from linear combinations of (what would have been the original direct) measurements. Often compressed sensing research is simulated by generating compressed coefficients from conventionally collected measurements. The simulation approach is necessary because the direct collection of compressed coefficients often requires compressed sensing analog front-ends that are currently not commercially available. The ability of the UPI system to make measurements at user-defined locations presents a unique capability on which compressed measurement techniques may be directly applied. The application of compressed sensing techniques on this data holds the potential to reduce the number of required measurement locations, reduce the time to make measurements, reduce the memory required to store the measurements, and possibly reduce the computational burden to classify the measurements. This work considers the appropriate selection of the signal dictionary used for signal reconstruction, and performs an evaluation of compressed sensing technique's ability to reconstruct ultrasonic images using fewer measurements than would be needed using traditional Nyquist-limited data collection techniques.

42 ENGINEERING↗
NASA NTRS2001

Validation of Ocean Color Satellite Data Products in Under Sampled Marine Areas

The planktonic marine cyanobacterium, Trichodesmium sp., is broadly distributed throughout the oligotrophic marine tropical and sub-tropical oceans. Trichodesmium, which typically occurs in macroscopic bundles or colonies, is noteworthy for its ability to form large surface aggregations and to fix dinitrogen gas. The latter is important because primary production supported by N2 fixation can result in a net export of carbon from the surface waters to deep ocean and may therefore play a significant role in the global carbon cycle. However, information on the distribution and density of Trichodesmium from shipboard measurements through the oligotrophic oceans is very sparse. Such estimates are required to quantitatively estimate total global rates of N2 fixation. As a result current global rate estimates are highly uncertain. Thus in order to understand the broader biogeochemical importance of Trichodesmium and N2 fixation in the oceans, we need better methods to estimate the global temporal and spatial variability of this organism. One approach that holds great promise is satellite remote sensing. Satellite ocean color sensors are ideal instruments for estimating global phytoplankton biomass, especially that due to episodic blooms, because they provide relatively high frequency synoptic information over large areas. Trichodesmium has a combination of specific ultrastructural and biochemical features that lend themselves to identification of this organism by remote sensing. Specifically, these features are high backscatter due to the presence of gas vesicles, and absorption and fluorescence of phycoerythrin. The resulting optical signature is relatively unique and should be detectable with satellite ocean color sensors such as the Sea-Viewing Wide Field-of-view Sensor (SeaWiFS).

Subramaniam, Ajit↗
DOE OSTI2023

Spatial and temporal variation in forest transpiration across a forested boreal peatland complex

Transpiration is a globally important component of evapotranspiration. Careful upscaling of transpiration from point measurements is thus crucial for quantifying water and energy fluxes. In spatially heterogeneous landscapes common across the boreal biome, upscaled transpiration estimates are difficult to determine due to variation in local environmental conditions (e.g., basal area, soil moisture, permafrost). Here, we sought to determine stand-level attributes that influence transpiration scalars for a forested boreal peatland complex consisting of sparsely treed wetlands and densely treed permafrost plateaus as land cover types. The objectives were to quantify spatial and temporal variability in stand-level transpiration, and to identify sources of uncertainty when scaling point measurements to the stand-level. Using heat ratio method sap flow sensors, we determined sap velocity for black spruce and tamarack for 2-week periods during peak growing season in 2013, 2017 and 2018. We found greater basal area, drier soils, and the presence of permafrost increased daily sap velocity in individual trees, suggesting that local environmental conditions are important in dictating sap velocity. When sap velocity was scaled to stand-level transpiration using gridded 20 × 20 m resolution data across the ~10 ha Scotty Creek ForestGEO plot, we observed significant differences in daily plot transpiration among years (0.17–0.30 mm), and across land cover types. Daily transpiration was lowest in grid-cells with sparsely treed wetlands compared to grid-cells with well-drained and densely treed permafrost plateaus, where daily transpiration reached 0.80 mm, or 30% of the daily evapotranspiration. When transpiration scalars (i.e., sap velocity) were not specific to the different land cover types (i.e., permafrost plateaus and wetlands), scaled stand-level transpiration was overestimated by 42%. To quantify the relative contribution of tree transpiration to ecosystem evapotranspiration, we recommend that sampling designs stratify across local environmental conditions to accurately represent variation associated with land cover types, especially with different hydrological functioning as encountered in rapidly thawing boreal peatland complexes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

The Global Aerosol Synthesis and Science Project (GASSP): Measurements and Modeling to Reduce Uncertainty

The largest uncertainty in the historical radiative forcing of climate is caused by changes in aerosol particles due to anthropogenic activity. Sophisticated aerosol microphysics processes have been included in many climate models in an effort to reduce the uncertainty. However, the models are very challenging to evaluate and constrain because they require extensive in situ measurements of the particle size distribution, number concentration, and chemical composition that are not available from global satellite observations. The Global Aerosol Synthesis and Science Project (GASSP) aims to improve the robustness of global aerosol models by combining new methodologies for quantifying model uncertainty, to create an extensive global dataset of aerosol in situ microphysical and chemical measurements, and to develop new ways to assess the uncertainty associated with comparing sparse point measurements with low-resolution models. GASSP has assembled over 45,000 hours of measurements from ships and aircraft as well as data from over 350 ground stations. The measurements have been harmonized into a standardized format that is easily used by modelers and nonspecialist users. Available measurements are extensive, but they are biased to polluted regions of the Northern Hemisphere, leaving large pristine regions and many continental areas poorly sampled. The aerosol radiative forcing uncertainty can be reduced using a rigorous model–data synthesis approach. Nevertheless, our research highlights significant remaining challenges because of the difficulty of constraining many interwoven model uncertainties simultaneously. Although the physical realism of global aerosol models still needs to be improved, the uncertainty in aerosol radiative forcing will be reduced most effectively by systematically and rigorously constraining the models using extensive syntheses of measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale twodimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. In conclusion, employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1994

MME-based attitude dynamics identification and estimation for SAMPEX

A method is described for obtaining optimal attitude estimation algorithms for spacecraft lacking attitude rate measurement devices (rate gyros), and then demonstrated using actual flight data from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) spacecraft. SAMPEX does not have on-board rate sensing, and relies on sun sensors and a three-axis magnetometer for attitude determination. Problems arise since typical attitude estimation is accomplished by filtering measurements of both attitude and attitude rates. Rates are nearly always sampled much more densely than are attitudes. Thus, the absence/loss of rate data normally reduces both the total amount of data available and the sampling density (in time) by a substantial fraction. As a result, the sensitivity of the estimates to model uncertainty and to measurement noise increases. In order to maintain accuracy in the attitude estimates, there is increased need for accurate models of the rotational dynamics. The proposed approach is based on the minimum model error (MME) optimal estimation strategy, which has been successfully applied to estimation of poorly modeled dynamic systems which are relatively sparsely and/or noisily measured. The MME estimates may be used to construct accurate models of the system dynamics (i.e. perform system model identification). Thus, an MME-based approach directly addresses the problems created by absence of attitude rate measurements.

Depena, Juan↗
DOE OSTI2023

Estimation of hydraulic conductivity in a watershed using sparse multi-source data via Gaussian process regression and Bayesian experimental design

Enhanced water management systems depend on accurate estimation of subsurface hydraulic properties. However, geologic formations can vary significantly, so information from a single source (e.g., widely spaced boreholes) is insufficient in characterizing subsurface aquifer properties. Therefore, multiple sources of information are needed to complement the hydrogeology understanding of a region. Here, this study presents a numerical framework in which information from different measurement sources is combined to characterize the 3D random field in a multi-fidelity prediction model. Coupled with the model, a Bayesian experimental design was used to determine the best future sampling locations. The Upper Sangamon watershed in east-central Illinois was selected as the case study site, where the multi-fidelity Gaussian process model was used to estimate the hydraulic conductivity in the region of interest. Multi-source observation data were obtained from electrical resistivity and borehole pumping tests. The accuracy of the model prediction is dependent on the locations and the distribution of both high- and low-fidelity data. Furthermore, the multi-fidelity model was compared with the single-fidelity model. The uncertainties and confidence in the measurements and parameter estimates were quantified and used to design future cycles of data collection to further improve the confidence intervals.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

OPEN CLUSTERS AS PROBES OF THE GALACTIC MAGNETIC FIELD. I. CLUSTER PROPERTIES

Stars in open clusters are powerful probes of the intervening Galactic magnetic field via background starlight polarimetry because they provide constraints on the magnetic field distances. We use 2MASS photometric data for a sample of 31 clusters in the outer Galaxy for which near-IR polarimetric data were obtained to determine the cluster distances, ages, and reddenings via fitting theoretical isochrones to cluster color–magnitude diagrams. The fitting approach uses an objective χ{sup 2} minimization technique to derive the cluster properties and their uncertainties. We found the ages, distances, and reddenings for 24 of the clusters, and the distances and reddenings for 6 additional clusters that were either sparse or faint in the near-IR. The derived ranges of log(age), distance, and E(B−V) were 7.25–9.63, ∼670–6160 pc, and 0.02–1.46 mag, respectively. The distance uncertainties ranged from ∼8% to 20%. The derived parameters were compared to previous studies, and most cluster parameters agree within our uncertainties. To test the accuracy of the fitting technique, synthetic clusters with 50, 100, or 200 cluster members and a wide range of ages were fit. These tests recovered the input parameters within their uncertainties for more than 90% of the individual synthetic cluster parameters. These results indicate that the fitting technique likely provides reliable estimates of cluster properties. The distances derived will be used in an upcoming study of the Galactic magnetic field in the outer Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

An Online Approach to Solve the Dynamic Vehicle Routing Problem with Stochastic Trip Requests for Paratransit Services

Many transit agencies operating paratransit and microtransit services have to respond to trip requests that arrive in real-time, which entails solving hard combinatorial and sequential decision-making problems under uncertainty. To avoid decisions that lead to significant inefficiency in the long term, vehicles should be allocated to requests by optimizing a non-myopic utility function or by batching requests together and optimizing a myopic utility function. While the former approach is typically offline, the latter can be performed online. We point out two major issues with such approaches when applied to paratransit services in practice. First, it is difficult to batch paratransit requests together as they are temporally sparse. Second, the environment in which transit agencies operate changes dynamically (e.g., traffic conditions can change over time), causing the estimates that are learned offline to become stale. To address these challenges, we propose a fully online approach to solve the dynamic vehicle routing problem (DVRP) with time windows and stochastic trip requests that is robust to changing environmental dynamics by construction. We focus on scenarios where requests are relatively sparse—our problem is motivated by applications to paratransit services. We formulate DVRP as a Markov decision process and use Monte Carlo tree search to evaluate actions for any given state. Accounting for stochastic requests while optimizing a non-myopic utility function is computationally challenging; indeed, the action space for such a problem is intractably large in practice. To tackle the large action space, we leverage the structure of the problem to design heuristics that can sample promising actions for the tree search. Our experiments using real-world data from our partner agency show that the proposed approach outperforms existing state-of-the-art approaches both in terms of performance and robustness.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2010

Transfer of Satellite Rainfall Uncertainty from Gauged to Ungauged Regions at Regional and Seasonal Timescales

Hydrologists and other users need to know the uncertainty of the satellite rainfall data sets across the range of time/space scales over the whole domain of the data set. Here, uncertainty' refers to the general concept of the deviation' of an estimate from the reference (or ground truth) where the deviation may be defined in multiple ways. This uncertainty information can provide insight to the user on the realistic limits of utility, such as hydrologic predictability, that can be achieved with these satellite rainfall data sets. However, satellite rainfall uncertainty estimation requires ground validation (GV) precipitation data. On the other hand, satellite data will be most useful over regions that lack GV data, for example developing countries. This paper addresses the open issues for developing an appropriate uncertainty transfer scheme that can routinely estimate various uncertainty metrics across the globe by leveraging a combination of spatially-dense GV data and temporally sparse surrogate (or proxy) GV data, such as the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar and the Global Precipitation Measurement (GPM) mission Dual-Frequency Precipitation Radar. The TRMM Multi-satellite Precipitation Analysis (TMPA) products over the US spanning a record of 6 years are used as a representative example of satellite rainfall. It is shown that there exists a quantifiable spatial structure in the uncertainty of satellite data for spatial interpolation. Probabilistic analysis of sampling offered by the existing constellation of passive microwave sensors indicate that transfer of uncertainty for hydrologic applications may be effective at daily time scales or higher during the GPM era. Finally, a commonly used spatial interpolation technique (kriging), that leverages the spatial correlation of estimation uncertainty, is assessed at climatologic, seasonal, monthly and weekly timescales. It is found that the effectiveness of kriging is sensitive to the type of uncertainty metric, time scale of transfer and the density of GV data within the transfer domain. Transfer accuracy is lowest at weekly timescales with the error doubling from monthly to weekly.However, at very low GV data density (<20% of the domain), the transfer accuracy is too low to show any distinction as a function of the timescale of transfer.

Tang, Ling↗
DOE OSTI2017

Quantum algorithms for Gibbs sampling and hitting-time estimation

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2 ), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗