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Leveraging Physics-based Surrogates for Efficient Density Estimation of Sparse Observable Data on Low-dimensional Manifolds.
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Efficient Reconstruction of Resonant Cavity Fields from Sparse Sensor Data
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Preliminary results of an assessment of FGGE 'special effort' data and its impact on GLAS model analyses and forecasts
Attempts to improve the handling of satellite temperature and cloud-derived data during the FGGE experiment are compared with results gained during the trials. The satellite data were edited by assigning quality indicators to temperature soundings by means of the IR TV camera on the Tiros-N spacecraft, and to cloud-tracked wind data from GEO satellites. The data quality were assayed on the basis of horizontal, vertical, and temporal consistency of observed synoptic conditions. The data interpreter-operator retrieved all available data for an area, determined which regions were data-sparse, then used data-rich areas nearby to supply smoothed gradients into the zones with insufficient data. Results are presented for measurements taken during Jan.-Feb., and May 1979 over Alaska. It was found that enhanced and operational IR soundings were mostly equivalent. Some improvements were implemented in the 1000-300 mb layer thickness and intensification of atmospheric thermal gradients. Interactive processing was concluded to be an aid to processing Tiros-N data. The data-improvements treatment was found to significantly modify large scale analyses.
Orbit Determination During Spacecraft Emergencies with Sparse Tracking Data - THEMIS and TDRS-3 Lessons Learned
This paper provides an overview of the lessons learned from the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center s (GSFC) Flight Dynamics Facility s (FDF) support of the Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft emergency in February 2007, and the Tracking and Data Relay Satellite-3 (TDRS-3) spacecraft emergency in March 2006. A successful and timely recovery from both of these spacecraft emergencies depended on accurate knowledge of the orbit. Unfortunately, the combination of each spacecraft emergency with very little tracking data contributed to difficulties in estimating and predicting the orbit and delayed recovery efforts in both cases. In both the THEMIS and TDRS-3 spacecraft emergencies, numerous factors contributed to problems with obtaining nominal tracking data measurements. This paper details the various causative factors and challenges. This paper further enumerates lessons learned from FDF s recovery efforts involving the THEMIS and TDRS-3 spacecraft emergencies and scant tracking data, as well as recommendations for improvements and corrective actions. In addition, this paper describes the broad range of resources and complex navigation methods employed within the FDF for supporting critical navigation activities during all mission phases, including launch, early orbit, and on-orbit operations.
Development of the variational SEASAT data analysis technique
Surface winds are closely associated with the surface pressure gradient. The variational SEASAT data analysis technique was designed to improve the sea level pressure analysis in the data sparse areas. The SEASAT-derived surface wind data were compared with observations from the Joint Air Sea Interaction Experiment (JASIN) and it was found that the satellite-derived sea surface wind has an accuracy of up to + or - 2 m/s in speed and + or - 20 deg in direction. These numbers are considered characteristic of the retrieved SEASAT wind field. By combining the densely spaced SEASAT-derived wind data with the sparsely distributed sea-level pressure observation via a variational adjustment technique subject to some appropriate physical constraint(s), an improvement in the sea-level pressure analysis is expected. It is demonstrated that a simple marine boundary layer scheme in conjunction with a variational adjustment technique can be developed to help improve the sea-level pressure analysis by the SEASAT-derived wind of a limited-area domain in the ocean.
Bayesian Physics Informed Spatio-Temporal Network for Streamflow Data Imputation
Reliable reconstruction of incomplete streamflow records is critical for improving hydrological forecasting, flood preparedness, and water resource management. However, large observational gaps and uncertainties in governing physical parameters limit the accuracy of traditional statistical and machinelearning imputation frameworks. To address these challenges, we develop a Bayesian Physics-Informed Spatio-Temporal Network (BPI-STNet) that jointly captures spatial and temporal dependencies while enforcing hydrologic consistency through embedded physical constraints. The framework integrates a GraphSAGE-LSTM architecture to model spatial connectivity across gauges and temporal flow dynamics, coupled with a Bayesian update mechanism to estimate uncertain parameters in a simplified water-balance framework. Unlike conventional physics-informed networks that rely on sampling-based posterior estimation, BPI-STNet derives an analytic solution to the inverse problem, allowing closed-form Bayesian updates of uncertain parameters Λ={α,β,k} using Gaussian priors and likelihoods. Applied to daily observations from the Susquehanna River Basin (1980-2022), BPI-STNet achieves substantial improvements over a purely data-driven RGNN baseline, which reduced RMSE by 23 % and MAE by 9 %, and achieving an average NSE values up to 0.96. The results demonstrate that coupling Bayesian inference with physics-informed learning yields physically consistent, uncertainty-aware reconstructions that preserve the temporal persistence and statistical distribution of observed flows. The proposed framework establishes a generalizable paradigm for data-sparse hydrologic systems where both data fidelity and physical interpretability are essential.
Bayesian Approach to Estimation of Water Table Elevations Using Historical Rasters as Prior Information 2019 - 20430
In cases of complex but only partially known geology and a lack of spatial control in observation well locations, water table elevation estimation is very challenging. In some cases, auxiliary information, such as observations of the movement of tracers, operation of injection and extraction wells, and calibration of groundwater models against the historical elevation data, can be combined with expert judgement to estimate flow directions in areas of sparse data and to aid in the production of more reliable contour maps (and associated rasters) than could be produced by relying on sparse well elevation data alone. Given a historical sequence of these raster maps, the question arises how to automate, to the extent possible, the process of producing new raster maps to reflect data from previous times, the current data and the operation of expert judgement. One solution is to adopt a Bayesian point of view and to regard the historical well elevation data, auxiliary information and historical raster maps as prior information. The well elevations for water table wells, as well as those for injection/extraction wells and the data associated with other relevant variables, can be viewed as predictors for the raster surface. From this prior information, we can, conditional on the values of these predictors for a new time period, compute an expected value map and a standard deviation map for the new raster. These then can be taken to specify a prior predictive distribution for the pixels in the new raster map. Then we condition the pixels, corresponding to water level observation wells within the raster, on the observed values in those wells (which in general will differ from the regression estimate) for the new time period. Given the smoothness of the water table surface, we then smooth the surface of deviations from the mean surface, based on the variograms of the historical rasters, and add this smoothed surface to the regression mean surface. The error structure of the produced raster map is defined by the regression error structure and the error due to smoothing based on the estimated variograms. This methodology has been developed and is being further refined for groundwater monitoring and remediation at LANL. It is a very flexible method that can also be applied with a variety of other predictors applied to model the water level wells in the area of interest over the historical record. The smoothness of the spatial process and its possible evolution over time can then be estimated from the residuals from this regression. This can be augmented by expert hydrogeological opinion based on site topography and hydrogeology. (authors)
Multiscale Modeling Meets Machine Learning: What Can We Learn?
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learn- ing to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.
Operator learning for predicting multiscale bubble growth dynamics
We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.
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.
Development of a variational SEASAT data analysis technique
Oceans are data-sparse areas in terms of conventional weather observations. The surface pressure field obtained solely by analyzing the conventional weather data is not expected to possess high accuracy. On the other hand, in entering asynoptic data such as satellite-derived temperature soundings into an atmospheric prediction system, an improved surface analysis is crucial for obtaining more accurate weather predictions because the mass distribution of the entire atmosphere will be better represented in the system as a result of the more accurate surface pressure field. In order to obtain improved surface pressure analyses over the oceans, a variational adjustment technique was developed to help blend the densely distributed surface wind data derived from the SEASAT-A radar observations into the sparsely distributed conventional pressure data. A simple marine boundary layer scheme employed in the adjustment technique was discussed. In addition, a few aspects of the current technique were determined by numerical experiments.
Famine Early Warning Systems Network (FEWS NET) Land Data Assimilation System (LDAS) and Other Assimilated Hydrological Data at NASA GES DISC
The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) provides science support for several data sets relevant to agriculture and food security, including the Famine Early Warning Systems Network (FEWS NET) Land Data Assimilation System (LDAS), or FLDAS data set. The GES DISC is one of twelve NASA Earth Observing System (EOS) data centers that process, archive, document, and distribute data from Earth science missions and related projects. The GES DISC hosts a wide range of remote sensing and model data, and provides reliable and robust data access and other services to users worldwide. Beyond data archive and access, the GES DISC offers many services to visualize and analyze the data. This presentation provides a summary of the hydrological data available at the GES DISC, along with an overview of related data services. Specifically, the FLDAS data set has been adapted to work with domains, data streams, and monitoring and forecast requirements associated with food security assessment in data-sparse, developing country settings. The FLDAS global monthly data have a 0.1 x 0.1 degree spatial resolution covering the period from January 1982 to present. Global FLDAS monthly anomaly and monthly climatology data are also available at the GES DISC to evaluate how current conditions compare to averages over the FLDAS 35-year period. Several case studies using the FLDAS soil moisture, evapotranspiration, rainfall, runoff, and surface temperature data will be presented.
A Brief Assessment of the Impact of Nearly 40 Years of Assimilated Observations Over the Amazon Basin
Adding a Forecast Sensitivity-based Observation Impact component to Version 2 of the Modern Era Retrospective-analysis for Research and Applications, the present study provides an assessment of the impact of nearly 40 years of observations on short-range (24-hr) forecasts over the Amazon basin. Under self-verification, forecast errors are found to slightly increase from the early data-sparse days to the more recent years, when data dramatically increase. Throughout the reanalysis, satellite radiances dominate in volume, but only before 1999 they dominate the impacts. Beyond 1999, over 50% of forecast error reduction is associated with conventional observations (radiosondes). Atmospheric Motion Vectors are also found to be large contributors to error reduction, but their contribution reduces in dry periods. In opposition to Atmospheric Motion Vectors, satellite radiances tend to contribute more in the dry season. Results provide motivation for additional conventional observations and the use of all-sky treatment of radiances.
Quantum block encoding for one-pair semiseparable matrices
Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE has mostly focused on sparse matrices; less effort has been devoted to data-sparse (e.g., rank-structured) matrices. In this work we examine a particular case of rank structure, namely, one-pair semiseparable matrices. We present a new block encoding approach that relies on a suitable factorization of the given matrix as the product of triangular and diagonal factors. To encode the matrix, the algorithm needs $2\log(N)+7$ ancillary qubits. Assuming that the data input oracles can be implemented with polylogarithmic depth, or that a QRAM input model is available, our proposed method requires $\mathcal{O}({\rm polylog} (N))$ time and has an error of $\mathcal{O}(N^2)$, where $N$ is the matrix size.
Results of a statistical approach to rainfall estimation using Nimbus 5 6.7 micrometers and 11.5 micrometers THIR data
Nimbus 5 6.7 mm and 11.5 mm temperature humidity infrared radiometer (THIR) data were used in a simple multiple regression scheme to test the feasibility of using these data to estimate hourly rainfall. Throughout the test area (85 W to 105 W and 45 N to 30 N) subareas (8 deg x 6 deg) were chosen from which point to point and areal statistics were obtained. Four subsets of data were used. The first consisted of only those surface stations indicating precipitation whose latitude and longitude coincided with the THIR grid points. A second used surface stations 0.1 degree from the THIR grid points. The third was a combination of subsets one and two. A reciprocal distance weighting scheme was used to derive precipitation values in data sparse areas. A fourth subset was made using these data combined with the data from subsets one and two. Point estimates resulted in negative correlations between estimated and grid derived "surface" precipitation. One degree areal estimates showed a slight improvement with a correlation coefficient of approximately 0.11. Single regression areal estimates resulted in correlations of approximately 0.11 and 0.20 for the 6.7 mm and 11.5 mm data respectively. These poor results were attributed to problems which are inherent in the satellite data (location errors, short temporal span of data, wavelength of sensors, etc.) and the lack of sufficient surface data to better verify the satellite estimate.
Tropical cyclone track and genesis forecasting using satellite microwave sounder data
Although many dynamical and statistical prediction schemes are available to forecasters, tropical cyclone track errors are still large. One primary difficulty is that tropical cyclones exist over the data-sparse tropical oceans. Satellite sounders, however, routinely provide numerous data over these areas. Mean layer temperatures from the Scanning Microwave Spectrometer on board the Nimbus 6 satellite are decomposed using empirical orthogonal functions, and the expansion coefficients are related to deviations from the persistence forecast location, to speed change, to direction change and to intensity change. The significance of the regression equations is tested by a null hypothesis of zero correlation coefficient. It appears that significant information about tropical cyclone motion exists in the satellite-estimated mean layer temperatures, especially at upper levels. A physical interpretation of the statistical results is offered, and a one-storm-out independent test is used to test the stability of the equations. Finally, some further work is suggested.
Integrating Applied Energy and BER Smart Data Capabilities to Develop a DOE Data Fabric for Energy-Water R&D
Focal Area(s): 1) Data acquisition and assimilation enabled by machine learning, AI, and advanced methods including experimental/network design/optimization, unsupervised learning (including deep learning), and hardware-related efforts involving AI (e.g., edge computing). Science Challenge: DOE R&D, including DOE’s Basic Energy Research (BER)’s Environmental Systems Science Division (EESSD) program and DOE’s applied energy research (AER) programs (EERE, FE, and NE) are producers and consumers of Earth systems datasets. This white paper focuses on the first topic area from the call in relation to how crosscutting resources and innovations from DOE’s EESSD and AER can be brought to bear to mutual benefit and more efficient energy-water, Earth system data resources through improved. The overarching challenge posed by this call focuses on how DOE can directly leverage artificial intelligence (AI) to engineer a substantial (paradigm-changing) improvement in Earth System Predictability? While stemming from DOE BER’s EESSD program, this is a challenge that is faced and also being addressed by DOE’s AER programs. Over the past decade plus, FE, EERE, and NE programs have made important strides towards addressing this need. These strides are in many ways highly complementary to EESSD’s MODEX efforts. Energy water systems spanning metocean to groundwater to surface water systems all are data driven whether for basic energy or applied energy. These are remote, multi-variate, complex natural, and in many cases engineered, systems. Key needs and challenges of both EESSD and AER include developing data-focused tools to enhance data search and discovery to fill in knowledge gaps (address sparse data challenge), and rapidly transform datasets, including disparate and multi-source data. Leveraging DOE on-premise computing (HPC, exascale) infrastructure supports the computing-intensive algorithms required to execute these data acquisition and transformation processes to derive enriched knowledge and data, driving AI/ML and big data analytics for these systems. The opportunity lies in combining BER and AER efforts to provide a more robust, advanced, efficient and complete computing data fabric to address energy-water data acquisition and assimilation needs which currently pose significant impediments to AI/ML predictions and research.