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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Physics-informed Karhunen-Loeve and Neural Network Approximations for Solving Inverse Differential Equation Problems

Here we present the PI-CKL-NN method for parameter estimation in differential equation (DE) models given sparse measurements of the parameters and states. In the proposed approach, the space- or time-dependent parameters are approximated by Karhunen-Loeve (KL) expansions that are conditioned on the parameters’ measurements, and the states are approximated by deep neural networks (DNNs). The unknown weights in the KL expansions and DNNs are found my minimizing the cost function that enforces the measurements of the states the DE constraint. Regularization is achieved by adding the l2 norm of the conditional KL coefficients into the loss function. Our approach assumes that the parameter fields are correlated in space or time and enforces the statistical knowledge (the mean and the covariance function) in addition to the DE constraints and measurements as opposed to the physics-informed neural network (PINN) and other similar physics-informed machine learning methods where only DE constraints and data are used for parameter estimation. We use the PI-CKL-NN method for parameter estimation in an ordinary differential equation with an unknown time-dependent parameter and the one- and two-dimensional partial differential diffusion equations with unknown space-dependent diffusion coefficients. We also demonstrate that PI-CKL-NN is more accurate than the PINN method, especially when the observations of the parameters are very sparse

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

Regional and seasonal estimates of fractional storm coverage based on station precipitation observations

Simulated climates using numerical atmospheric general circulation models (GCMs) have been shown to be highly sensitive to the fraction of GCM grid area assumed to be wetted during rain events. The model hydrologic cycle and land-surface water and energy balance are influenced by the parameter bar-kappa, which is the dimensionless fractional wetted area for GCM grids. Hourly precipitation records for over 1700 precipitation stations within the contiguous United States are used to obtain observation-based estimates of fractional wetting that exhibit regional and seasonal variations. The spatial parameter bar-kappa is estimated from the temporal raingauge data using conditional probability relations. Monthly bar-kappa values are estimated for rectangular grid areas over the contiguous United States as defined by the Goddard Institute for Space Studies 4 deg x 5 deg GCM. A bias in the estimates is evident due to the unavoidably sparse raingauge network density, which causes some storms to go undetected by the network. This bias is corrected by deriving the probability of a storm escaping detection by the network. A Monte Carlo simulation study is also conducted that consists of synthetically generated storm arrivals over an artificial grid area. It is used to confirm the bar-kappa estimation procedure and to test the nature of the bias and its correction. These monthly fractional wetting estimates, based on the analysis of station precipitation data, provide an observational basis for assigning the influential parameter bar-kappa in GCM land-surface hydrology parameterizations.

Gong, Gavin↗
DOE OSTI2026

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Discrete-Direct Model Calibration and Uncertainty Propagation Method Confirmed on Multi-Parameter Plasticity Model Calibrated to Sparse Random Field Data

A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures.

42 ENGINEERING↗
DOE OSTI2022

Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry

Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and complex logistics of direct bathymetry surveys, i.e, depth imaging, have encouraged the use of indirect measurements such as surface flow velocities. However, estimating high-resolution bathymetry from indirect measurements is an inverse problem that can be computationally challenging. Here, we propose a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE), a type of deep neural network with a narrow layer in the middle, to compress bathymetry and flow velocity information and accelerate bathymetry inverse problems from flow velocity measurements. In our application, the shallow-water equations (SWE) with appropriate boundary conditions (BCs), e.g., the discharge and/or the free surface elevation, constitute the forward problem, to predict flow velocity. Then, ROMs of the SWEs are constructed on a nonlinear manifold of low dimensionality through a variational encoder and the bathymetry inversion problem is derived on the low-dimensional latent space in a Hierarchical Bayesian setting. Further, the reformulation allows variational inference with a small number (e.g., $\mathscr{O}$ (100) of ROM runs and efficient uncertainty quantification. We have tested our inversion approach on a one-mile reach of the Savannah River, GA, USA. Once the neural network is trained (offline stage), the proposed technique can perform the inversion operation orders of magnitude faster than traditional inversion methods that are commonly based on linear projections, such as principal component analysis (PCA), or the principal component geostatistical approach (PCGA). Furthermore, tests show that the algorithm can estimate the bathymetry with good accuracy even with sparse flow velocity measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A deep learning hybrid predictive modeling (HPM) approach for estimating evapotranspiration and ecosystem respiration

Climate change is reshaping vulnerable ecosystems, leading to uncertain effects on ecosystem dynamics, including evapotranspiration (ET) and ecosystem respiration (R eco ). However, accurate estimation of ET and R eco still remains challenging at sparsely monitored watersheds, where data and field instrumentation are limited. In this study, we developed a hybrid predictive modeling approach (HPM) that integrates eddy covariance measurements, physically based model simulation results, meteorological forcings, and remote-sensing datasets to estimate ET and R eco in high space–time resolution. HPM relies on a deep learning algorithm and long short-term memory (LSTM) and requires only air temperature, precipitation, radiation, normalized difference vegetation index (NDVI), and soil temperature (when available) as input variables. We tested and validated HPM estimation results in different climate regions and developed four use cases to demonstrate the applicability and variability of HPM at various FLUXNET sites and Rocky Mountain SNOTEL sites in Western North America. To test the limitations and performance of the HPM approach in mountainous watersheds, an expanded use case focused on the East River Watershed, Colorado, USA. The results indicate HPM is capable of identifying complicated interactions among meteorological forcings, ET, and R eco variables, as well as providing reliable estimation of ET and R eco across relevant spatiotemporal scales, even in challenging mountainous systems. The study documents that HPM increases our capability to estimate ET and R eco and enhances process understanding at sparsely monitored watersheds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Data for A Hybrid Biophysical-Machine Learning Framework for Diurnal Surface Energy Flux Estimation Using Proximal Sensing

Thermal infrared-based remote sensing of surface energy fluxes has traditionally relied on high spatial resolution satellite data with revisit frequencies on the order of weeks. In this study, we evaluate a biophysics-based analytical surface energy balance model for predicting latent energy (LE) and sensible heat (H) fluxes using proximal sensing observations. The Surface Temperature Initiated Closure (STIC1.2) model has been extensively validated across a wide range of spatial and temporal scales using various satellite-derived thermal infrared data sets. Here we extend this validation by applying STIC at sub-hourly temporal resolution over multiple growing seasons for four distinct agricultural systems. We further develop and evaluate novel STIC variants that incorporate machine learning (ML) techniques to eliminate the need for surface energy balance observations, specifically net radiation and soil heat flux, thereby enhancing model applicability in data-sparse settings. The integration of a ML component to estimate surface available energy is shown to have strong predictive performance for both LE (R2 = 0.81–0.94) and H (R2 = 0.46–0.72) across all agricultural systems examined here, demonstrating the potential of hybrid biophysical-machine learning approaches for surface energy balance modeling with minimal data requirements. This study concludes with a novel application of explainable machine learning (exML) to diagnose sources of model error. This exML framework attributes residual prediction errors to both model input variables and environmental drivers not explicitly included in the simulation experiments. This approach provides a new pathway for improving model design and integrating previously overlooked yet influential variables into future model iterations.

AI/ML↗
DOE OSTI2024

ReLU, Sparseness, and the Encoding of Optic Flow in Neural Networks

Accurate self-motion estimation is critical for various navigational tasks in mobile robotics. Optic flow provides a means to estimate self-motion using a camera sensor and is particularly valuable in GPS- and radio-denied environments. The present study investigates the influence of different activation functions—ReLU, leaky ReLU, GELU, and Mish—on the accuracy, robustness, and encoding properties of convolutional neural networks (CNNs) and multi-layer perceptrons (MLPs) trained to estimate self-motion from optic flow. Our results demonstrate that networks with ReLU and leaky ReLU activation functions not only achieved superior accuracy in self-motion estimation from novel optic flow patterns but also exhibited greater robustness under challenging conditions. The advantages offered by ReLU and leaky ReLU may stem from their ability to induce sparser representations than GELU and Mish do. Our work characterizes the encoding of optic flow in neural networks and highlights how the sparseness induced by ReLU may enhance robust and accurate self-motion estimation from optic flow.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2009

Estimation of Faults in DC Electrical Power System

This paper demonstrates a novel optimization-based approach to estimating fault states in a DC power system. Potential faults changing the circuit topology are included along with faulty measurements. Our approach can be considered as a relaxation of the mixed estimation problem. We develop a linear model of the circuit and pose a convex problem for estimating the faults and other hidden states. A sparse fault vector solution is computed by using 11 regularization. The solution is computed reliably and efficiently, and gives accurate diagnostics on the faults. We demonstrate a real-time implementation of the approach for an instrumented electrical power system testbed, the ADAPT testbed at NASA ARC. The estimates are computed in milliseconds on a PC. The approach performs well despite unmodeled transients and other modeling uncertainties present in the system.

Gorinevsky, Dimitry↗
DOE OSTI2022

Source scaling comparison and validation in Central Italy: data intensive direct S waves versus the sparse data coda envelope methodology

SUMMARY Robustness of source parameter estimates is a fundamental issue in understanding the relationships between small and large events; however, it is difficult to assess how much of the variability of the source parameters can be attributed to the physical source characteristics or to the uncertainties of the methods and data used to estimate the values. In this study, we apply the coda method by Mayeda et al. using the coda calibration tool (CCT), a freely available Java-based code (https://github.com/LLNL/coda-calibration-tool) to obtain a regional calibration for Central Italy for estimating stable source parameters. We demonstrate the power of the coda technique in this region and show that it provides the same robustness in source parameter estimation as a data-driven methodology [generalized inversion technique (GIT)], but with much fewer calibration events and stations. The Central Italy region is ideal for both GIT and coda approaches as it is characterized by high-quality data, including recent well-recorded seismic sequences such as L'Aquila (2009) and Amatrice–Norcia–Visso (2016–2017). This allows us to apply data-driven methods such as GIT and coda-based methods that require few, but high-quality data. The data set for GIT analysis includes ∼5000 earthquakes and more than 600 stations, while for coda analysis we used a small subset of 39 events spanning 3.5 < Mw < 6.33 and 14 well-distributed broad-band stations. For the common calibration events, as well as an additional 247 events (∼1.7 < Mw < ∼5.0) not used in either calibration, we find excellent agreement between GIT-derived and CCT-derived source spectra. This confirms the ability of the coda approach to obtain stable source parameters even with few calibration events and stations. Even reducing the coda calibration data set by 75 per cent, we found no appreciable degradation in performance. This validation of the coda calibration approach over a broad range of event size demonstrates that this procedure, once extended to other regions, represents a powerful tool for future routine applications to homogeneously evaluate robust source parameters on a national scale. Furthermore, the coda calibration procedure can homogenize the Mw estimates for small and large events without the necessity of introducing any conversion scale between narrow-band measures such as local magnitude (ML) and Mw, which has been shown to introduce significant bias.

Morasca, Paola (ORCID:0000000265254867)↗
NASA NTRS2021

3D Shape Reconstruction of Small Bodies from Sparse Features

The autonomous approach of spacecraft to a small body (comet or asteroid) relies on using all available information at each phase of the approach. This paper presents new algorithms for global shape reconstructions from sparse tracked surface points. These methods leverage estimates from earlier phases, such as rotation pole, as well as a priori knowledge, such as a genus-0 body (i.e. without boundaries or topological holes). A mapping algorithm is proposed, which performs faithful reconstructions while enforcing genus-0 output through spherical parameterization. To estimate the shape of permanently shadowed regions of the body, a symmetry reconstruction method is added to the reconstruction algorithms. This method is shown to substantially increase the reconstruction accuracy but is subject to the symmetry of the body perpendicular to the rotation pole. The proposed mapping algorithm is compared to stateof- the-practice surface reconstruction algorithms, assessing their accuracy and ability to correctly generate genus-0 shape models for 2400 datasets and three small bodies. The proposed spherical parameterization algorithm performed consistently with the state-of-the-practice while being the only algorithm to always produce genus-0 shape models.

Nesnas, Issa↗
NASA NTRS2020

Underlying Fundamentals of Kalman Filtering for River Network Modeling

The grand challenge of producing hydrometeorological estimates every time and everywhere has motivated the fusion of sparse observations with dense numerical models, with a particular interest on discharge in river modeling. Ensemble methods are largely preferred as they enable the estimation of error properties, but at the expense of computational load and generally with underestimations. These imperfect stochastic estimates motivate the use of correction methods, that is, error localization and inflation, although the physical justifications for their optimality are limited. The purpose of this study is to use one of the simplest forms of data assimilation when applied to river modeling and reveal the underlying mechanisms impacting its performance. Our framework based on assimilating daily averaged in situ discharge measurements to correct daily averaged runoff was tested over a 4-yr case study of two rivers in Texas. Results show that under optimal conditions of inflation and localization, discharge simulations are consistently improved such that the mean values of Nash–Sutcliffe efficiency are enhanced from211.32 to 0.55 at observed gauges and from212.24 to21.10 at validation gauges. Yet, parameters controlling the inflation and the localization have a large impact on the performance. Further investigations of these sensitivities showed that optimal inflation occurs when compensating exactly for discrepancies in the magnitude of errors while optimal localization matches the distance traveled during one assimilation window. These results may be applicable to more advanced data assimilation methods as well as for larger applications motivated by upcoming river-observing satellite missions, such as NASA’s Surface Water and Ocean Topography mission.

Streamflow↗
NASA NTRS1982

Intercepted photosynthetically active radiation in wheat canopies estimated by spectral reflectance

The interception of photosynthetically active radiation (PAR) was evaluated relative to greenness and normalized difference (MSS 7-5/7+5) for five planting dates of wheat for 1978-79 and 1979-80 in Phoenix. Intercepted PAR was calculated from a model driven by leaf area index and stage of growth. Linear relationships were found between greenness and normalized difference with a separate model representing growth and senescence of the crop. Normalized difference was a significantly better model and would be easier to apply than the empirically derived greenness parameter. For the leaf area growth portion of the season the model between PAR interception and normalized difference was the same over years, however, for the leaf senescence the models showed more variability due to the lack of data on measured interception in sparse canopies. Normalized difference could be used to estimate PAR interception directly for crop growth models.

Hatfield, J. L.↗
NASA NTRS2013

Influence of Persistent Wind Scour on the Surface Mass Balance of Antarctica

Accurate quantification of surface snow accumulation over Antarctica is a key constraint for estimates of the Antarctic mass balance, as well as climatic interpretations of ice-core records. Over Antarctica, near-surface winds accelerate down relatively steep surface slopes, eroding and sublimating the snow. This wind scour results in numerous localized regions (< or = 200 sq km) with reduced surface accumulation. Estimates of Antarctic surface mass balance rely on sparse point measurements or coarse atmospheric models that do not capture these local processes, and overestimate the net mass input in wind-scour zones. Here we combine airborne radar observations of unconformable stratigraphic layers with lidar-derived surface roughness measurements to identify extensive wind-scour zones over Dome A, in the interior of East Antarctica. The scour zones are persistent because they are controlled by bedrock topography. On the basis of our Dome A observations, we develop an empirical model to predict wind-scour zones across the Antarctic continent and find that these zones are predominantly located in East Antarctica. We estimate that approx. 2.7-6.6% of the surface area of Antarctica has persistent negative net accumulation due to wind scour, which suggests that, across the continent, the snow mass input is overestimated by 11-36.5 Gt /yr in present surface-mass-balance calculations.

Antarctica↗
NASA NTRS1985

Utilization of satellite-derived cloud cover to improve the estimation of latent heat release in a winter extratropical cyclone

A simple scheme for utilizing satellite cloud pattern information to improve the estimation of parameterized stable and convective latent heat release is proposed and tested for an extratropical cyclone occurring over the United States during January 9-11, 1975. Calculations are done over the standard North American rawinsonde data region and over a sparse data region simulated by ignoring one-third of the original rawinsonde stations. Results indicate 15 percent and 30 percent improvements in latent heating estimates derived from the total and sparse data sets, respectively. A larger improvement was found using the sparse data set because the parameterized latent heat release estimates obtained using these data were poorer than those obtained using the total data set.

Lin, S.-J.↗
DOE OSTI2023

Statistical Learning for Nonlinear Model Reduction from Local Simulations of Stochastic and Particle- and Agent-Based Systems

Stochastic physical systems across the sciences that have very high-dimensional state spaces, with a large number of fast degrees of freedom that force direct simulators to proceed by integration steps that are orders of magnitude smaller than events of interests (e.g., particle collisions). Examples range from molecular motion to dynamics of large populations of cells. A grand challenge in the simulation and understanding of such systems is the systematic construction of accurate, interpretable, reduced models, enabling faster simulations, revealing fundamental properties of the dynamics, and predicting phenomena of interest that the original simulator could not reached with sufficient accuracy or within a given computational budget. In this projected we developed novel statistical estimation/machine learning techniques for analyzing and building empirical reduced models for important families of high-dimensional stochastic systems, in particular: - we developed techniques for estimating interaction kernels in interacting particle- and agent-based systems, which are ubiquitous in Physics, Biology and many other sciences, given observed trajectories of the system; - we developed techniques for nonlinear model reduction for high-dimensional stochastic systems that have a small number of unknown, nonlinear slow variables, and a large number of fast modes, that are possibly of large magnitude, given observed short trajectories of the system in the form of bursts of trajectories from different initial conditions; - we developed novel techniques for estimating linear dynamical systems on graphs when both the dynamics and the underlying graph are unknown, and we have a sparse set of space-time observations; - we considered the problem of estimating an unknown nonlinear observation function of a standard process (e.g. Brownian motion), so that we can recognized if an observed dynamics is "just" a nonlinear version of a known dynamics; we also developed benchmarks for learning algorithms aimed at learning and classifying diffusion processes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2019

Anthropogenic Nitrogen Inputs and Impacts on Oceanic N2O Fluxes in the Northern Indian Ocean: the Need for an Integrated Observation and Modelling Approach

Anthropogenically-derived nitrogen input to the northern Indian Ocean has increased significantly in recent decades, based on both observational and model derived estimates This external nutrient source is supplied by atmospheric deposition and riverine fluxes, and has the potential to affect the vulnerable biogeochemical systems of the Arabian Sea and Bay of Bengal, influencing productivity and oceanic production of the greenhouse-gas nitrous-oxide (N2O). We summarize current estimates of this external nitrogen source to the northern Indian Ocean from observations and models, highlight implications for regional marine N2O emissions using model-based analyses, and make recommendations for measurement and model needs to improve current estimates and future predictions of this impact. Current observationally-derived estimates of deposition and riverine nitrogen inputs are limited by sparse measurements and uncertainties on accurate characterization of nitrogen species composition. Ocean model assessments of the impact of external nitrogen sources on regional marine N2O production in the northern Indian Ocean estimate potentially significant changes but also have large associated uncertainties. We recommend an integrated program of basin-wide measurements combined with high-resolution modeling and more detailed characterization of nitrogen-cycle process to address these uncertainties and improve current estimates and predictions.

Parvadha Suntharalingam↗
NASA NTRS1986

Canopy reflectance modeling in a tropical wooded grassland

Geometric/optical canopy reflectance modeling and spatial/spectral pattern recognition are used to study the form and structure of savanna in West Africa. An invertible plant canopy reflectance model is tested for its ability to estimate the amount of woody vegetation cover in areas of sparsely wooded grassland from remotely sensed data. Dry woodlands and wooded grasslands, commonly referred to as savannas, are important ecologically and economically in Africa, and cover approximately forty percent of the continent by some estimates. The Sahelian and Sudanian savanna make up the important and sensitive transition zone between the tropical forests and the arid Saharan region. The depletion of woody cover, used for fodder and fuel in these regions, has become a very severe problem for the people living there. LANDSAT Thematic Mapper (TM) data is used to stratify woodland and wooded grassland into areas of relatively homogeneous canopy cover, and then by applying an invertible forest canopy reflectance model to estimate directly the height and spacing of the trees in the stands. Since height and spacing are proportional to biomass in some cases, a successful application of the segmentation/modeling techniques will allow direct estimation of woody biomass, as well as cover density, over significant areas of these valuable and sensitive ecosystems. Sahelian savanna sites in the Gourma area of Mali being used by the NASA/GIMMS project (Global Inventory Modeling and Monitoring System, at Goddard Space Flight Center), in conjunction with CIPEA/Mali (Centre International pour l'Elevage en Afrique) will be used for testing the canopy model. The model will also be tested in a Sudanian zone crop/woodland area in the Region of Segou, Mali.

Simonett, D.↗