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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
DOE OSTI2022

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO 2 sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 10 6 because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Astrometric results of 1978-1985 Deep Space Network radio interferometry - The JPL 1987-1 extragalactic source catalog

An astrometric radio reference frame has been determined from intercontinental dual-frequency radio interferometric measurements. These measurements were carried out on a regular basis during 1978-1985 between NASA's Deep Space Network stations in California, Spain, and Australia. Analysis of 6800 pairs of delay and delay-rate observations made during 51 sessions produced estimates of 1300 parameters. The most significant of these are geophysical quantities and positions of extragalactic sources. The source catalog resulting from this analysis includes 106 sources fairly uniformly distributed over the celestial sphere, north of -45 deg declination. Almost all of the resulting source positions have formal uncertainties between 0.5 and 3 milliarcseconds (mas), with rms values of 2 mas in both angular coordinates. Internal consistency checks, as well as comparisons with independently determined source catalogs of comparable quality, indicate that relative source coordinates determined by VLBI contain systematic errors at the level of 1 to 2 mas.

Sovers, O. J.↗
NASA NTRS2019

Comparison of high-resolution airborne soil moisture retrievals to SMAP soil moisture during the SMAP validation experiment 2016 (SMAPVEX16)

The NASA's Soil Moisture Active Passive (SMAP) mission conducted a field experiment with its partners over two 40-km agricultural domains in Iowa and Manitoba in the summer of 2016 to address concerns observed in SMAP soil moisture (SM) retrievals over agricultural areas. The experiment featured airborne Passive Active L-band System (PALS) flights over each domain with intensive ground measurements and dense networks of SM monitoring stations. With two intensive observation periods separated in time (May 28–June 20 and July 14–August 16), the flights captured both early-season/low vegetation and later-season/high-vegetation conditions. The comparison of the PALS brightness temperature (TB) measurements to the SMAP TB observed over the sites resulted in root mean square difference (RMSD) of 2.8 K and 4.0 K for vertical and horizontal polarizations, respectively. The subsequent SM analysis rescaled the PALS TB with the SMAP TB to allow equitable comparisons between the SM retrievals from the two instruments. The PALS SM retrieval algorithm used the SM sampled by the ground teams during the overpass days for tuning, and was parameterized by a high-resolution vegetation water content product calibrated using vegetation samples collected during the experiment. The tuning process was not able to find a satisfactory result with a temporally constant set of parameters in the single channel algorithm for the two intensive observation periods of the experiment. This result indicated that the rapid change in the vegetation structure during the growth stages and likely variation in the surface roughness conditions were not compatible with rigid parameterization over the entire period. However, using seasonally variable parameters we found that it was possible to retrieve soil moisture with satisfactory accuracy. Comparative analysis with the SMAP SM product included aggregation of the PALS SM to the SMAP pixel-scale. The RMSD between the PALS SM and the aggregated manual field samples was <0.04 m3/m3 with Pearson correlation >0.85 for both sites. The comparison between different in situ sources indicated that the soil moisture network measurements were not the source of the large biases observed for SMAP over the sites reported in earlier studies. Therefore, the results suggested the rapidly growing vegetation and the early-season surface condition changes not captured by the SMAP algorithm caused the SMAP retrieval errors. In addition, the significant deviations of the vegetation water content used by the SMAP product from the calibrated vegetation water content obtained during the experiment compounds the problem.

Andreas Colliander↗
DOE OSTI2022

Effects-Based Monitoring of Geomagnetically-Induced Current Using a Convolutional Neural Network

Geomagnetically-induced current (GIC) due to space weather can flow in the power grid causing undesirable effects such as transformer overheating, misoperation of protection devices, and potential blackouts. It is therefore important to monitor GIC in the power grid to improve online situational awareness and decision-making of system operators during a geomagnetic disturbance. To avoid the costly installation of GIC monitors at transformers’ neutrals, it is desirable to find correlations between GIC and already-monitored parameters. Hence, this work proposed the use of a convolutional neural network (CNN) to compute GIC amplitudes from learned patterns in the time-series data of transformer even harmonic currents. Using an electromagnetic transient program, GIC injection simulations were performed for a modeled Dominion Energy Virginia (DEV) substation with two 504 MVA, 500/230 kV transformers. Data collected from these offline simulations were used to train the CNN to provide online GIC monitoring. Testing the CNN performance involved using real GIC measurements from published literature and from a physical GIC monitor in the DEV area. Finally, the results showed that the proposed method was able to provide GIC readings with a root mean squared error of 1.56 A/phase (equivalent to an average accuracy of 94%) for these real GIC waveforms.

42 ENGINEERING↗
NASA NTRS1993

Investigation of Mars Rotational Dynamics Using Earth-based Radio Tracking of Mars Landers

The development of space geodetic techniques over the past two decades has made it possible to measure the rotational dynamics of the Earth at the milliarcsecond level, improving our geophysical models of the Earth 's interior and the interactions between the solid Earth and its atmosphere. We have found that the rotational dynamics of Mars can be determined to nearly the same level of accuracy by acquiring Earth-based two-way radio tracking observations of three or more landers globally distributed on the surface of Mars. Our results indicate that the precession and long-term obliquity changes of the Mars pole direction can be determined to an angular accuracy corresponding to about 15 cm/yr at the planet's surface. In addition, periodic nutations of the pole and seasonal variations in the spin rate of the planet can be determined to 10 cm or less. Measuring the rotation of Mars at this accuracy would greatly improve the determination of the planet' s moment of inertia and would resolve the size of a planetary fluid core, providing a valuable constraint on Mars interior models. Detecting seasonal variations in the spin rate of Mars would provide global constraints on atmospheric angular momentum changes due to sublimation of the Mars CO2 polar ice caps. Finally, observation of quasisecular changes in Mars obliquity would have significant implications for understanding long-term climatic change. The key to achieving these accuracies is a globally distributed network of Mars landers with stable, phase-coherent radio transponders. By simultaneously acquiring coherent two-way carrier phase observations between a single Earth tracking station and multiple Mars landers, Earth media errors are essentially eliminated, providing an extremely sensitive measure of changes in the differential path lengths between the Earth tracking station and the Mars landers due to Mars rotation. Time variability of the instrumental phase delay through the radio transponder may represent the limiting error source for this technique. Calibration of the transponder stability to about 0.1 ns or less, over a single tracking arc of up to 12 hr, is sufficient to provide the decimeter-level determination of Mars orientation parameters quoted above. We will provide a detailed description of the multilander tracking technique and the requirements it imposes on both the lander radio system and the Earth-based ground-tracking system. This concept is currently part of the strawman science plan for the Mars Environmental Survey (MESUR) mission and complements many of the other MESUR science goals.

Edwards, C. D., Jr.↗
DOE OSTI2025

GeoLoRA: Geometric integration for parameter efficient fine-tuning

Low-Rank Adaptation (LoRA) has become a widely used method for parameter-efficient fine-tuning of large-scale, pre-trained neural networks. However, LoRA and its extensions face several challenges, including the need for rank adaptivity, robustness, and computational efficiency during the fine-tuning process. We introduce GeoLoRA, a novel approach that addresses these limitations by leveraging dynamical low-rank approximation theory. GeoLoRA requires only a single backpropagation pass over the small-rank adapters, significantly reducing computational cost as compared to similar dynamical low-rank training methods and making it faster than popular baselines such as AdaLoRA. This allows GeoLoRA to efficiently adapt the allocated parameter budget across the model, achieving smaller low-rank adapters compared to heuristic methods like AdaLoRA and LoRA, while maintaining critical convergence, descent, and error-bound theoretical guarantees. The resulting method is not only more efficient but also more robust to varying hyperparameter settings. We demonstrate the effectiveness of GeoLoRA on several state-of-the-art benchmarks, showing that it outperforms existing methods in both accuracy and computational efficiency.

Schotthoefer, Steffen [ORNL] (ORCID:00000002156965↗
DOE OSTI2023

Emulating aerosol optics with randomly generated neural networks

Abstract. Atmospheric aerosols have a substantial impact on climate and remain one of the largest sources of uncertainty in climate prediction. Accurate representation of their direct radiative effects is a crucial component of modern climate models. However, direct computation of the radiative properties of aerosol populations is far too computationally expensive to perform in a climate model, so optical properties are typically approximated using a parameterization. This work develops artificial neural networks (ANNs) capable of replacing the current aerosol optics parameterization used in the Energy Exascale Earth System Model (E3SM). A large training dataset is generated by using Mie code to directly compute the optical properties of a range of atmospheric aerosol populations given a large variety of particle sizes, wavelengths, and refractive indices. Optimal neural architectures for shortwave and longwave bands are identified by evaluating ANNs with randomly generated wirings. Randomly generated deep ANNs are able to outperform conventional multilayer-perceptron-style architectures with comparable parameter counts. Finally, the ANN-based parameterization produces significantly more accurate bulk aerosol optical properties than the current parameterization when compared with direct Mie calculations using mean absolute error. The success of this approach makes possible the future inclusion of much more sophisticated representations of aerosol optics in climate models that cannot be captured by extension of the existing parameterization scheme and also demonstrates the potential of random-wiring-based neural architecture search in future applications in the Earth sciences.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1994

Enhanced orbit determination filter sensitivity analysis: Error budget development

An error budget analysis is presented which quantifies the effects of different error sources in the orbit determination process when the enhanced orbit determination filter, recently developed, is used to reduce radio metric data. The enhanced filter strategy differs from more traditional filtering methods in that nearly all of the principal ground system calibration errors affecting the data are represented as filter parameters. Error budget computations were performed for a Mars Observer interplanetary cruise scenario for cases in which only X-band (8.4-GHz) Doppler data were used to determine the spacecraft's orbit, X-band ranging data were used exclusively, and a combined set in which the ranging data were used in addition to the Doppler data. In all three cases, the filter model was assumed to be a correct representation of the physical world. Random nongravitational accelerations were found to be the largest source of error contributing to the individual error budgets. Other significant contributors, depending on the data strategy used, were solar-radiation pressure coefficient uncertainty, random earth-orientation calibration errors, and Deep Space Network (DSN) station location uncertainty.

Estefan, J. A.↗
NASA NTRS2021

Synthesizing Disparate LiDAR and Satellite Datasets through Deep Learning to Generate Wall-to-Wall Regional Inventories for the Complex, Mixed-Species Forests of the Eastern United States

Light detection and ranging (LiDAR) has become a commonly-used tool for generating remotely-sensed forest inventories. However, LiDAR-derived forest inventories have remained uncommon at a regional scale due to varying parameters among LiDAR data acquisitions and the availability of sufficient calibration data. Here, we present a model using a 3-D convolutional neural network (CNN), a form of deep learning capable of scanning a LiDAR point cloud, combined with coincident satellite data (spectral, phenology, and disturbance history). We compared this approach to traditional modeling used for making forest predictions from LiDAR data (height metrics and random forest) and found that the CNN had consistently lower uncertainty. We then applied the CNN to public data over six New England states in the USA, generating maps of 14 forest attributes at a 10 m resolution over 85% of the region. Aboveground biomass estimates produced a root mean square error of 36 Mg ha−1 (44%) and were within the 97.5% confidence of independent county-level estimates for 33 of 38 or 86.8% of the counties examined. CNN predictions for stem density and percentage of conifer attributes were moderately successful, while predictions for detailed species groupings were less successful. The approach shows promise for improving the prediction of forest attributes from regional LiDAR data and for combining disparate LiDAR datasets into a common framework for large-scale estimation.

Elias Ayrey↗
DOE OSTI2024

Improving River Routing Using a Differentiable Muskingum‐Cunge Model and Physics‐Informed Machine Learning

Recently, rainfall-runoff simulations in small headwater basins have been improved by methodological advances such as deep neural networks (NNs) and hybrid physics-NN models—particularly, a genre called differentiable modeling that intermingles NNs with physics to learn relationships between variables. However, hydrologic routing simulations, necessary for simulating floods in stem rivers downstream of large heterogeneous basins, had not yet benefited from these advances and it was unclear if the routing process could be improved via coupled NNs. We present a novel differentiable routing method (δMC-Juniata-hydroDL2) that mimics the classical Muskingum-Cunge routing model over a river network but embeds an NN to infer parameterizations for Manning's roughness (n) and channel geometries from raw reach-scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. Synthetic experiments show that while the channel geometry parameter was unidentifiable, n can be identified with moderate precision. With real-world data, the trained differentiable routing model produced more accurate long-term routing results for both the training gage and untrained inner gages for larger subbasins (>2,000 km2) than either a machine learning model assuming homogeneity, or simply using the sum of runoff from subbasins. The n parameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned n pattern was consistent with literature expectations, demonstrating the framework's potential for knowledge discovery, but the absolute values can vary depending on training periods. The trained n parameterization can be coupled with traditional models to improve national-scale hydrologic flood simulations.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2024

Noise Reduction for Solar-Induced Fluorescence Retrievals Using Machine Learning and Principal Component Analysis: Simulations and Applications to GOME-2 Satellite Retrievals

We use a spectral-based approach that employs principal component analysis along with a relatively shallow artificial neural network (NN) to substantially reduce noise and other artifacts in terrestrial chlorophyll solar-induced fluorescence (SIF) retrievals. SIF is a very small emission at red and far-red wavelengths that is difficult to measure and is highly sensitive to random errors and systematic artifacts. Our approach relies upon an assumption that a trained NN can effectively reconstruct the total SIF signal from a relatively small number of leading principal components of the satellite-observed far-red radiance spectra without using information from the trailing modes that contain most of the random errors. We test the approach with simulated reflectance spectra produced with a full atmospheric and surface radiative transfer model using different observing and geophysical parameters and various noise levels. Resulting noisy and noise-reduced retrieved SIF values are compared with true values to assess performance. We then apply our noise reduction approach to SIF derived from two different satellite spectrometers. For evaluation, since the truth in this case is unknown, we compare SIF retrievals from two independent sensors with each other. We also compare the noise-reduced SIF temporal variations with those from an independent gross primary product (GPP) product that should display similar variations. Results show that our noise reduction approach improves capture of SIF seasonal and inter-annual variability. Our approach should be applicable to many noisy data products derived from spectral measurements. Our methodology does not replace the original retrieval algorithms; rather the original noisy retrievals are needed as the target for the NN training process.

noise reduction, solar-induced fluorescence, SIF, ↗
NASA NTRSDate not supplied

Early Information Parameter-Set Analysis for Satellite Close Approaches using Machine Learning

Understanding orbital mechanics is essential in space flight and navigation applications, and leveraging modern force models for flight path projection remains an important aspect in space mission design and operation. However, force models do not capture all the dynamics or perturbations in the space environment and thus are subject to errors in predicting the state vectors. The further out the predicted miss distance between spacecraft is from the time of closest approach (TCA), the larger the propagated errors in the predicted miss distance at TCA is. The dependency on these force models for spacecraft flight state prediction calls for a more reliable method that can quantify, or even reduce, these propagated errors. With recent advances in the field artificial intelligence, specifically in machine and deep learning algorithms, a model that implements these approaches can improve on the modern force model approach. The goal for this work is to provide an early-information decision-making threshold, in order to prioritize risk assessment implementation, given the ongoing increase of space objects. In analyzing the relationship of several parameters from conjunction data messages(CDMs) and solar information, early information becomes viable in miss distance prediction with unsupervised learning techniques, which learn the parameters that are linked together with miss distance and probability of collision (Pc) variables. Another approach implemented for identifying relationships within CDMs is supervised learning, in which a shallow neural network binary classifier learns to distinguish events with Pc values¡108. These parameters detected in the unsupervised process are then applied to a regression neural network, which predicts the miss distance at TCA for a specific event within a given uncertainty bound. For the regression neural network, a Long Short Term Memory (LSTM) neural network is implemented, which yields memory about each time step in an event. Using an LSTM network, the model learns to predict miss distance within 0.2km of the value measured at TCA. Although there is a limited amount of "close miss" data to train a network, the network learns to associate parameters, like large energy dissipation rates with the secondary object, with an elevated Pc

Brianna I. Robertson↗
NASA NTRS1981

Space shuttle launch era spacecraft injection errors and DSN initial acquisition

The initial acquisition of a spacecraft by the Deep Space Network (DSN) is a critical mission event. This results from the importance of rapidly evaluating the health and trajectory of a spacecraft in the event that immediate corrective action might be required. Further, the DSN initial acquisition is always complicated by the most extreme tracking rates of the mission. The DSN initial acquisition characteristics will change considerably in the upcoming space shuttle launch era. How given injection errors at spacecraft separation from the upper stage launch vehicle (carried into orbit by the space shuttle) impact the DSN initial acquisition, and how this information can be factored into injection accuracy requirements to be levied on the Space Transportation System (STS) is addressed. The approach developed begins with the DSN initial acquisition parameters, generates a covariance matrix, and maps this covariance matrix backward to the spacecraft injection, thereby greatly simplifying the task of levying accuracy requirements on the STS, by providing such requirements in a format both familiar and convenient to STS.

Khatib, A. R.↗
NASA NTRS1985

Navigation systems

The elements of the measurement and communications network comprising the global deep space navigation system (DSN) for NASA missions are described. Among the measurement systems discussed are: VLBI, two-way Doppler and range measurements, and optical measurements carried out on board the spacecraft. Processing of navigation measurement is carried out using two modules: an N-body numerical integration of the trajectory (and state transition partial derivatives) based on pre-guessed initial conditions; and partial derivatives of simulated observables corresponding to each actual observation. Calculations of velocity correction parameters is performed by precise modelling of all physical phenomena influencing the observational measurements, including: planetary motions; tracking station locations, gravity field structure, and transmission media effects. Some of the contributions to earth-relative orbit estimate errors for the Doppler/range system on board Voyager are discussed in detail. A line drawing of the DSN navigation system is provided.

Jordan, J. F.↗
NASA NTRS1996

Multilevel Algorithm for Atmospheric Data Assimilation

A multiscale algorithm for the problem of optimal statistical interpolation of observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w(sup a) by the formula: w(sup a) = w(sup f) + P(sup f) H(sup T) y, where the quantity y is defined by the equation (H P(sup f) H(sup T) + R)y = w(sup o) - H w(sup f), using the given model forecast first guess w(sup f) and the vector of observations w(sup o); H is an interpolation operator from the regular grid to the observation network, P(sup f) is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P(sup f) is assumed to be given by the formula P(sub ij)(sup f) = sigma(sub i)(sup f) mu(sub ij) sigma(sub j)(sub f), where mu(sub ij) is a smooth, decreasing function of the distance between the i-th and the j-th points. In this paper we describe a multiscale iterative process based on a multiresolution, simultaneous displacement technique and a localized variational calculation of iteration parameters.

Brandt, Achi↗
NASA NTRSDate not supplied

Development of Neural Network for X-59 Air Data Probe Calibration

Two wind tunnel tests were conducted in the NASA Glenn Research Center (GRC) 8- by 6-Foot Supersonic Wind Tunnel to calibrate the nose-mounted air data probe for the X-59. The probe will be the primary instrument for the flight test of the X-59 for determining angle of attack, angle of sideslip, airspeed, and pressure altitude of the aircraft in flight. This paper documents the development of several neural net algorithms that can be used to relate air data probe port pressures from those tests to relevant X-59 flight parameters, such as angle of attack, angle of sideslip, mach number, and static and dynamic pressure. These calibration algorithms address accuracy effects for significant real-world conditions, such as initial sensor measurement uncertainties, assumed parameter constraints on NN modelling errors, and malfunctioning or plugged ports. Resultant integrated uncertainties are provided for each algorithm; these uncertainties are then used to estimate the effects on relevant X-59 mission parameters.

Kurtis Roy Long↗