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DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗

DOE OSTI2025

Turbulent Processes that Influence Boundary-Layer Cloud Structure (Final Technical Report)

Many models of the atmosphere simulate vertical profiles of observable fields, such as temperature, moisture, and vertical velocity. To assess the realism of such model output, it is important to evaluate the modeled profiles against observations. However, many extant evaluations consist of comparing time averaged profiles from the model and the observations. Such time averages can smooth out unrealistic features that appear in instantaneous profiles. In this way, the time averages may obscure certain model errors from detection. For instance, many models misrepresent turbulent processes, leading to profiles that are too smoothed out or too noisy. E.g., if a model has coarse vertical resolution and overly strong diffusion, then the model may be unable to produce observed sharp peaks. On the other hand, a model may have artificial approximations that produce spurious jumps in the vertical. Much can be learned by browsing through instantaneous snapshots of model output. But the volume of output produced by a global model is far too great to rely purely on visual inspection. In addition, we need a way to statistically characterize the profiles, so that anomalies can be detected more conveniently.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1973

ASTP ranging system mathematical model

A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.

Ellis, M. R.↗

NASA NTRS1975

Application of the CINGEN program a thermal network data generator

The application of the CINGEN computer program and two of its supporting programs for the evaluation of structural and thermal performance of physical systems was described. The CINGEN program was written and implemented to avoid the duplication effort of performing a finite element approach for structural analysis and a finite differencing technique for thermal analysis, as well as the desire for a geometrical representation of the thermal model to reduce modeling errors. The program simplifies the thermal modeling process by performing all of the capacitance and conductance calculations normally done by the analyst. Each solid element is divided into five tetrahedrons, allowing the total volume to be calculated precisely. A sample problem was illustrated.

Shultz, W. E.↗

NASA NTRS1988

Human error in aviation operations

The role of human error in commercial and general aviation accidents and the techniques used to evaluate it are reviewed from a human-factors perspective. Topics addressed include the general decline in accidents per million departures since the 1960s, the increase in the proportion of accidents due to human error, methods for studying error, theoretical error models, and the design of error-resistant systems. Consideration is given to information acquisition and processing errors, visually guided flight, disorientation, instrument-assisted guidance, communication errors, decision errors, debiasing, and action errors.

Nagel, David C.↗

NASA NTRS1991

Simulator evaluation of system identification with on-line control law update for the controls and astrophysics experiment in space

A procedure for optimizing the performance of large flexible spacecraft that require active vibration suppression to achieve required performance is presented. The procedure is to conduct on-orbit testing and system identification followed by a control system design. It is applied via simulation to a spacecraft configuration currently being considered for flight test by NASA - the Controls, Astrophysics, and Structures Experiment in Space (CASES). The system simulator is based on a NASTRAN finite element structural model. A finite number of modes is used to represent the structural dynamics. The system simulator also includes models of the electronics, actuators, sensors, the digital controller, and the internal and external disturbances. Nonlinearities caused by quantization are included in the study to examine tolerance of the procedure to modelling errors. Disturbance and sensor noise is modelled as a Gaussian process. For system identification, the system is excited using sinusoidal inputs at the resonant frequencies of the structure using each actuator. Mode shapes, frequencies, and damping ratios are identified from the unforced response sensor data after each excitation. Then, the excitation data is used to identify the actuator influence coefficients. The results of the individual parameter identification analyses are assembled into an aggregate system model. The control design is accomplished based only on the identified model using multi-input/output linear quadratic Gaussian theory. Its performance is evaluated based on time-to-damp as compared with the uncontrolled structure.

Montgomery, Raymond C.↗

NASA NTRS1994

Stellar populations in edge-on galaxies from deep CCD surface photometry, 1: NGC 5907

We present extremely deep charge coupled device (CCD) surface photometry of the edge-on Sc galaxy NGC 5907. Our data reach reliably to a surface brightness of R=27 mag/sq arcsec, some two magnitudes fainter than any previous work. We obtained this improvement using a 2048X2048 CCD with a wide (approximately 24 min) field, which made it possible to sky subtract directly from the galaxy frame, and by taking many dark sky flatfields. Our analysis of these data, using a full 2D model fitting procedure with a detailed error model, confirm the thin disk parameters of van der Kruit & Searle (1981). In particular, we confirm that the galaxy's disk has a radial cutoff and a constant scale height with radius. We find evidence for a stellar warp in this system, which has the same orientation as the H I warp. Our deep data also confirm that NGC 5907 has no thick disk. This suggests that theories of thick disk formation from star formation in the early stages of disk collapse, or by secular heating mechanisms, are unlikely to be correct, because they would predict that every galaxy would have a thick disk. Thick disk formation from the accretion of satellite galaxies is more likely.

Morrison, Heather L.↗

NASA NTRS1995

Fine-resolution imaging of solar features using Phase-Diverse Speckle

Phase-diverse speckle (PDS) is a novel imaging technique intended to overcome the degrading effects of atmospheric turbulence on fine-resolution imaging. As its name suggests, PDS is a blend of phase-diversity and speckle-imaging concepts. PDS reconstructions on solar data were validated by simulation, by demonstrating internal consistency of PDS estimates, and by comparing PDS reconstructions with those produced from well accepted speckle-imaging processing. Several sources of error in data collected with the Swedish Vacuum Solar Telescope (SVST) were simulated: CCD noise, quantization error, image misalignment, and defocus error, as well as atmospheric turbulence model error. The simulations demonstrate that fine-resolution information can be reliably recovered out to at least 70% of the diffraction limit without significant introduction of image artifacts. Additional confidence in the SVST restoration is obtained by comparing its spatial power spectrum with previously-published power spectra derived from both space-based images and earth-based images corrected with traditional speckle-imaging techniques; the shape of the spectrum is found to match well the previous measurements. In addition, the imagery is found to be consistent with, but slightly sharper than, imagery reconstructed with accepted speckle-imaging techniques.

Paxman, Richard G.↗

NASA NTRS2000

Calibration of a Spacecraft Gyro Quadruplet

This work presents a new approach to gyro calibration where, in addition to being used for computing attitude that is needed in the calibration process, the gyro outputs are also used as measurements in a Kalman filter. Gyro calibration as well as calibration of other instruments occurs in two steps. In the first step, the instrument error parameters are estimated. During the second stage, those errors are continuously removed from the gyro readings. In the classical approach to gyro calibration, the gyro outputs are used to maintain or compute body orientation rather than being used as measurements in the context of filtering. In inertial navigation, for example, gyro errors cause erroneous computation of velocity and position, and then when the latter are compared to measured velocity and position, a great portion of the computed velocity and position errors can be determined. The latter errors are then fed into a Kalman filter (KF) that uses the INS error model to infer on the gyro errors. Similarly, when applying the classical approach to spacecraft (SC) altitude determination, the gyro outputs are used to compute the attitude and then attitude measurements are used to determine the attitude errors, which again using a KF, indicates what the gyro errors are. In the approach adopted in this work the gyro outputs are used as angular rate measurements and are compared to estimated angular rate measurements. However, this approach requires the knowledge of the angular rate. In the past, the estimated angular rate was computed in a rather simplistic way assuming that the rate was constant. In the present work, the estimated angular rate is derived using a KF whose input can be any kind of attitude measurement, therefore the angular rate experienced by the SC can be continuously changing, and yet a good estimate of the rate, necessary for calibration, can be obtained.

Harman, Richard R.↗

NASA NTRS2019

Impact of GMI All-Sky Radiance Assimilation in the NASA GEOS Forecast System

The assimilation of cloud- and precipitation-affected ("all-sky") radiances has become an important focus of development at most numerical weather prediction centers. Efforts at the Global Modeling and Assimilation Office (GMAO) have focused on all-sky assimilation of GPM Microwave Imager (GMI) radiances, which became operational in the GEOS real-time production system in July 2018. Implementation of the all-sky capability required several upgrades to the GEOS hybrid 4D-EnVar assimilation infrastructure including the addition of control variables for cloud liquid, cloud ice, rain and snow, enhancements to the radiative transfer model, new hybrid background and observational error models, and modified quality control and bias correction procedures. This talk describes the impact of GMI all-sky radiance assimilation on GEOS analyses and forecasts as determined from examination of various metrics including statistics of background departures and analysis increments, forecast skill scores, and forecast sensitivity observation impact (FSOI) calculations. It is shown that in addition to the hydrometeors themselves, the initial wind, temperature and pressure fields all undergo significant dynamic adjustment in response to the analyzed cloud and precipitation features. Assimilation of GMI radiances leads to improved forecasts of lower tropospheric wind, temperature and humidity, especially in the tropics. The largest forecast improvements occur during the first 48 hours, with diminishing impact thereafter. However, combining GMI all-sky assimilation with improvements to the GEOS model physics as in the recent implementation of the real-time production system, extends these forecast improvements well in to the medium range. FSOI results based on a 24-hr moist global energy norm show that GMI radiances provide nearly uniform beneficial impact throughout the tropics, with more mixed impacts in the subtropics. While the overall impact of GMI is smaller than that of other, much more numerous microwave and hyperspectral infrared radiance types, its impact is among the largest of all radiance types on a per-observation basis.

Gelaro, Ron↗

NASA NTRS2023

Developing a Radar Signal Simulator for the Community Radiative Transfer Model

Active radar instruments provide vertically resolved clouds and precipitation measurements that cannot be provided by the passive instruments. These active measurements are not conventionally assimilated into the data assimilation systems because of the lack of fast forward radiative transfer models and also difficulties in the error modelling of the measurements. This paper describes the development, evaluation, and sensitivity analysis for a forward radar model implemented in the Community Radiative Transfer Model (CRTM). The scattering properties required by the forward model are provided by the hydrometeor lookup tables that were generated using the discrete dipole approximation. The model is able to calculate both the reflectivity and the attenuated reflectivity for any given radar instrument at any given zenith angles as long as CRTM instrument specific coefficients are available. The evaluation using CloudSat measurements shows a very good agreement between the simulations and measurements as long as the input profiles of hydrometeors are consistent with the measured reflectivity profiles. Major sources contributing to the differences between the measured and simulated reflectivities are input hydrometeor profiles, scattering lookup tables, lack of melting layer in the forward model, CRTM scattering solvers, and attenuation calculations. In addition to the forward model, both Tangent Linear and Adjoint of the model are also implemented and tested within CRTM. These components may be required by some data assimilation systems for the assimilation of radar measurements.

radar↗

NASA NTRS2019

The Badhwar-O'Neill 2020 Model

The Badhwar-O'Neill (BON) model has been used for some time to describe the galactic cosmic ray (GCR) environment encountered in deep space by astronauts and sensitive electronics. The most recent version of the model, BON2014, was calibrated to available measurements to reduce model errors for particles and energies of significance to astronaut exposure. Although subsequent studies showed the model to be reasonably accurate for such applications, modifications to the sunspot number (SSN) classification system and a large number of new high precision measurements suggested the need to develop an improved and more capable model. In this work, the BON2020 model is described. The new model relies on daily integral flux from the Advanced Composition Explorer Cosmic Ray Isotope Spectrometer (ACE/CRIS) to describe solar activity. For time periods not covered by ACE/CRIS, the updated international SSN database is used. Parameters in the new model are calibrated to available data, which includes the new Alpha Magnetic Spectrometer (AMS-02) and Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) high-precision measurements. It is found that the BON2020 model is a significant improvement over BON2014. Systematic errors associated with BON2014 have been removed. The average relative error of the BON2020 model compared to all available measurements is found to be <1%, and BON2020 is found to be within ±15% of a large fraction of the available measurements (26,269 of 27,646 → 95%).

Slaba, Tony C.↗

NASA NTRS2020

The Badhwar-O'Neill 2020 Model

The Badhwar-O’Neill (BON) model has been used for some time to describe the galactic cosmic ray (GCR) environment encountered in deep space by astronauts and sensitive electronics. The most recent version of the model, BON2014, was calibrated to available measurements to reduce model errors for particles and energies of significance to astronaut exposure. Although subsequent studies showed the model to be reasonably accurate for such applications, modifications to the sunspot number (SSN) classification system and a large number of new high-precision measurements suggested the need to develop an improved and more capable model. In this work, the BON2020 model is described. The new model relies on daily integral flux from the Advanced Composition Explorer Cosmic Ray Isotope Spectrometer (ACE/CRIS) to describe solar activity. For time periods not covered by ACE/CRIS, the updated international SSN database is used. Parameters in the new model are calibrated to available data, which includes the new Alpha Magnetic Spectrometer (AMS-02) and Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) high-precision measurements. It is found that the BON2020 model is a significant improvement over BON2014. Systematic errors associated with BON2014 have been removed. The average relative error of the BON2020 model compared to all available measurements is found to be <1%, and BON2020 is found to be within +15% of a large fraction of the available measurements (26,269 of 27,646  95%.

T C Slaba↗

DOE OSTI2023

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

Here we investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the k eff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2012

A Fast and Efficient Version of the TwO-Moment Aerosol Sectional (TOMAS) Global Aerosol Microphysics Model

This study develops more computationally efficient versions of the TwO-Moment Aerosol Sectional (TOMAS) microphysics algorithms, collectively called Fast TOMAS. Several methods for speeding up the algorithm were attempted, but only reducing the number of size sections was adopted. Fast TOMAS models, coupled to the GISS GCM II-prime, require a new coagulation algorithm with less restrictive size resolution assumptions but only minor changes in other processes. Fast TOMAS models have been evaluated in a box model against analytical solutions of coagulation and condensation and in a 3-D model against the original TOMAS (TOMAS-30) model. Condensation and coagulation in the Fast TOMAS models agree well with the analytical solution but show slightly more bias than the TOMAS-30 box model. In the 3-D model, errors resulting from decreased size resolution in each process (i.e., emissions, cloud processing wet deposition, microphysics) are quantified in a series of model sensitivity simulations. Errors resulting from lower size resolution in condensation and coagulation, defined as the microphysics error, affect number and mass concentrations by only a few percent. The microphysics error in CN70CN100 (number concentrations of particles larger than 70100 nm diameter), proxies for cloud condensation nuclei, range from 5 to 5 in most regions. The largest errors are associated with decreasing the size resolution in the cloud processing wet deposition calculations, defined as cloud-processing error, and range from 20 to 15 in most regions for CN70CN100 concentrations. Overall, the Fast TOMAS models increase the computational speed by 2 to 3 times with only small numerical errors stemming from condensation and coagulation calculations when compared to TOMAS-30. The faster versions of the TOMAS model allow for the longer, multi-year simulations required to assess aerosol effects on cloud lifetime and precipitation.

Lee, Yunha↗

NASA NTRS2008

Similarity Metrics for Closed Loop Dynamic Systems

To what extent and in what ways can two closed-loop dynamic systems be said to be "similar?" This question arises in a wide range of dynamic systems modeling and control system design applications. For example, bounds on error models are fundamental to the controller optimization with modern control design methods. Metrics such as the structured singular value are direct measures of the degree to which properties such as stability or performance are maintained in the presence of specified uncertainties or variations in the plant model. Similarly, controls-related areas such as system identification, model reduction, and experimental model validation employ measures of similarity between multiple realizations of a dynamic system. Each area has its tools and approaches, with each tool more or less suited for one application or the other. Similarity in the context of closed-loop model validation via flight test is subtly different from error measures in the typical controls oriented application. Whereas similarity in a robust control context relates to plant variation and the attendant affect on stability and performance, in this context similarity metrics are sought that assess the relevance of a dynamic system test for the purpose of validating the stability and performance of a "similar" dynamic system. Similarity in the context of system identification is much more relevant than are robust control analogies in that errors between one dynamic system (the test article) and another (the nominal "design" model) are sought for the purpose of bounding the validity of a model for control design and analysis. Yet system identification typically involves open-loop plant models which are independent of the control system (with the exception of limited developments in closed-loop system identification which is nonetheless focused on obtaining open-loop plant models from closed-loop data). Moreover the objectives of system identification are not the same as a flight test and hence system identification error metrics are not directly relevant. In applications such as launch vehicles where the open loop plant is unstable it is similarity of the closed-loop system dynamics of a flight test that are relevant.

Whorton, Mark S.↗

DOE OSTI2019

Listening to the Forest: An Artificial Neural Network‐Based Model of Carbon Uptake at Harvard Forest

Abstract The terrestrial biosphere strongly modulates atmospheric CO 2 mixing ratios, whose inexorable rise propels anthropogenic climate change. Modeling and mechanistically understanding C uptake by the terrestrial biosphere are thus of broad societal concerns. Yet despite considerable progress, scaling up point observations to landscape and larger scales continues to frustrate analyses of the anthropogenically perturbed global C cycle. While that up‐scaling is our overarching motivation, here we focus on one of its elements, modeling C uptake at a given site. We devise a novel artificial neural network (ANN)‐based model of C uptake at Harvard Forest that combines locally observed and remotely sensed variables. Most of our model predictors are those used by an established ecosystem C uptake model, the Vegetation Photosynthesis and Respiration Model (VPRM), easing comparisons. To those, we add observed cumulative antecedent precipitation and soil temperature. We find that model errors are much larger in winter, indicating that better understanding and modeling of respiration will likely discernibly improve model performance. Comparing the ANN and VPRM results reveals errors attributed to unrealistic treatment of temperature in the VPRM formulation, indicating that better representation of temperature dependencies is also likely to enhance model skill. By judiciously comparing VPRM and ANN errors we thus overcome ANNs' notoriety for concealing the mechanisms underlying their predictive skills. We demonstrate their ability to identify outstanding ecosystem science knowledge gaps and particularly fruitful corresponding model development directions, improving site specific and up‐scaling flux modeling and understanding of the climate impacts of the northern forest.

Eshel, Gidon↗

DOE OSTI2021

Doppler-Lidar Evaluation of HRRR-Model Skill at Simulating Summertime Wind Regimes in the Columbia River Basin during WFIP2

Complex-terrain locations often have repeatable near-surface wind patterns, such as synoptic gap flows and local thermally forced flows. An example is the Columbia River Valley in east-central Oregon-Washington, a significant wind-energy-generation region and the site of the Second Wind-Forecast Improvement Project (WFIP2). Data from three Doppler lidars deployed during WFIP2 define and characterize summertime wind regimes and their large-scale contexts, and provide insight into NWP model errors by examining differences in the ability of a model [NOAA’s High-Resolution Rapid-Refresh (HRRR-version1)] to forecast wind-speed profiles for different regimes. Seven regimes were identified based on daily time series of the lidar-measured rotor-layer winds, which then suggested two broad categories. First, in three regimes the primary dynamic forcing was the large-scale pressure gradient. Second, in two regimes the dominant forcing was the diurnal heating-cooling cycle (regional sea-breeze-type dynamics), including the marine intrusion previously described, which generates strong nocturnal winds over the region. The other two included a hybrid regime and a non-conforming regime. For the large-scale pressure-gradient regimes, HRRR had wind-speed biases of ~1 m s -1 and RMSEs of 2-3 m s -1 . Errors were much larger for the thermally forced regimes, owing to the premature demise of the strong nocturnal flow in HRRR. Thus, the more dominant the role of surface heating in generating the flow, the larger the errors. Major errors could result from surface heating of the atmosphere, boundary-layer responses to that heating, and associated terrain interactions. Finally, measurement/modeling research programs should be aimed at determining which modeled processes produce the largest errors, so those processes can be improved and errors reduced.

17 WIND ENERGY↗