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NASA NTRSDate not supplied

Estimation With Range Dependent Sensor Model

This paper focuses on the improvement of target tracking accuracy taking into account the sensor’s reading degradation as the relative range increases. The approach is based on the assumption that range measurement error depends on the actual range. Specifically, we model the measurement error as a proportional to the actual range term plus a zero-mean, Gaussian distributed, and uncorrelated process. We present two approaches to tracking a target with constant velocity model. The first approach uses Extended Kalman Filter (EKF) framework to estimate target's states and the unknown proportionality coefficient with linearization on the observation model on the predicted states at each time step. The second one uses a measurement conversion method to estimate the target's scaled by the unknown constant term states, which is shown to be unbiased. This conversion results in linear state and observation models, hence the standard Kalman filter can be applied. The actual target state is computed by application of back scaling with the estimate of unknown scale factor. We evaluate the approaches in desktop simulations.

Target tracking↗
NASA NTRS2023

AI-3000K Infrared Line List for Hot CO 2

AI-3000K is a semi-empirical IR line list constructed for hot CO 2 spectra analysis and simulation up to 3000 – 4000 K. Compared to previously published Ames-1000K and UCL-4000, it represents a major upgrade, utilizing a new algorithm for optimization and including the latest improvements in potential energy surface (PES), dipole moment surface (DMS), and room temperature IR line list (Ames-2021 296K). To maximize the success of introducing experimental based accurate line positions, a new PES (X01d) was refined with respect to >800 selected CDSD2019 [Tashkun et al. JQSRT (2019) 228, 124] energy levels in the range of 0 – 24,000 cm -1 , with σ rms = 0.5 – 0.7 cm -1 . Most differences between the X01d PES based levels and CDSD2019 energies are within ± 2 cm -1 . A new DMS is fitted from extrapolated CCSD(T)/aug-cc-pV(T,Q,5)Z dipole calculations, with σ rms = 5.1 × 10 -6 au for 11,155 geometries up to 40,000 cm -1 , denoted Ames-2021–40K. Compared to the best available Ames-2021 DMS and room temperature IR line list [Huang et al J. Phys. Chem. A (2022) 126, 5940], the relative intensity differences are expected to be ∼ 1 ‰. The line position accuracy of ''X01d + Ames-2021–40K'' IR line list is significantly improved by adopting CDSD2019 energy levels up to 24,000 cm -1 (J ≤ 150). The Einstein A21 coefficients for E' < 15,000 cm -1 transitions are replaced by more accurate values from the Ames-2021 296K IR line list. In short, the AI-3000K is the X01d PES and Ames-2021–40K DMS based line list enhanced with the A 21 of Ames-2021 296K line list and CDSD energy levels. It provides continuous coverage from 0 to 20,000 cm -1 for the four most abundant isotopologues: 12 C 16 O 2 (626), 13 C 16 O 2 (636), 16 O 12 C 18 O (628), and 16 O 12 C 17 O (627). The impacts of isotopologue and E'/E'' cutoffs have been examined. Intensity convergence (not accuracy) of AI-3000K line list is quantitatively estimated in 1 cm -1 bins. It is better than 99% in the whole range of 0 – 20,000 (or 10,000) cm -1 at 1000 K (or 2000 K), or better than 90% in the whole range of 0 – 15,000 (or 9000) cm -1 at 2000 K (or 3000 K), respectively. Convergence beyond 3000 K will require a new PES and DMS for E' > 40,000 cm -1 . The AI-3000K and HITEMP based IR simulations are compared to high resolution shock tube experiments for CO 2 -Ar mixture up to 2000 K. With line position accuracy comparable to that of HITEMP, AI-3000K IR line list yields better agreements at more frequencies. Potential sources of discrepancies with experiment are discussed.

AI-3000K↗
DOE OSTI2024

Enhancing Fluid Flow Pressure and Saturation Prediction Accuracy and Reducing Uncertainty with Committee Machine – Illinois Basin Decatur Project (IBDP) as a Case Study

This is the conference paper accompanying an oral presentation at the 17th International Conference on Greenhouse Gas Control Technologies GHGT-17 held in Calgary, Canada, October 20-24, 2024. Carbon capture and storage (CCS) is a way to play a critical role in the global transition to a low-emission economy. Current progress is hampered by a number of factors, among which the lack of risk-informed design tools and decision support frameworks is seen as a major roadblock. Significant interest exists in using artificial intelligence to accelerate CCS site feasibility studies, as well as to facilitate the permit application process. Existing works commonly train a single deep learning model. This work investigates the feasibility of using a conventional ensemble learning (committee machine) technique to further improve prediction accuracy. Ensemble-based algorithms generally improve over individual base learners in terms of robustness and accuracy. Deep ensembles, however, are time-consuming to create and train. A pragmatic question is whether small-sized ensembles may lead to prediction improvement. Here we evaluated the efficacy of an ensemble learning technique using the latent spectral model (LSM), an efficient deep neural operator algorithm, as base learners. Preliminary results, obtained using the Illinois Basin-Decatur Project (IBDP) carbon sequestration data/model, show that small-sized ensembles can improve prediction over the base learners, achieving prediction accuracy of ~1.6 psi root mean square error (RMSE) on pressure (relative the average reservoir pressure of 3150 psi), and less than 1.3% for saturation.

Sun, Alexander↗
NASA NTRS1990

A determination of the radio-planetary frame tie and the DSN tracking station locations

The orientation of the reference frame of radio source catalogs relative to that of planetary ephemerides is uncertain by 30 mas (150 nrad). At this level of uncertainty this orientation offset, or 'frame tie', can be a major systematic error source for interplanetary spacecraft orbit determination. This work presents a method of determining the radio-planetary frame tie from a comparison of Very Long Baseline Interferometry (VLBI) and Lunar Laser Ranging (LLR) station coordinate and earth orientation parameter estimates. Preliminary results are presented which indicate that accuracies of 5 mas or better may be achieved with this method. An important by-product of this method of frame tie determination is a set of Deep Space Network (DSN) station locations with 10 cm per component accuracy. This station set is in a geocentric coordinate system with known orientation relative to the radio and planetary frames.

Finger, Mark H.↗
NASA NTRS1991

Use of non-spherical gravity harmonics for relative motion GN/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).

Henderson, David M.↗
NASA NTRS1984

Radiometric Accuracy Assessment of LANDSAT-4 Multispectral Scanner (MSS) Data

The LANDSAT-4 mission has unique characteristics relative to previous LANDSAT missions. The spacecraft is new; the orbit is lower with a more frequent repeat cycle; and the ground processing facility consists of new hardware with different algorithms being applied. How some of these changes affect the character of the radiometric data quality is explored. Banding effects; radiometric differences between LANDSAT 3 and 4; and the woodgrain pattern observed visually in the images are considered.

Alford, W. L.↗
DOE OSTI2022

Protein–Ligand Binding Free-Energy Calculations with ARROW–A Purely First-Principles Parameterized Polarizable Force Field

Protein–ligand binding free-energy calculations using molecular dynamics (MD) simulations have emerged as a powerful tool for in silico drug design. Here, we present results obtained with the ARROW force field (FF)–a multipolar polarizable and physics-based model with all parameters fitted entirely to high-level ab initio quantum mechanical (QM) calculations. ARROW has already proven its ability to determine solvation free energy of arbitrary neutral compounds with unprecedented accuracy. The ARROW FF parameterization is now extended to include coverage of all amino acids including charged groups, allowing molecular simulations of a series of protein–ligand systems and prediction of their relative binding free energies. We ensure adequate sampling by applying a novel technique that is based on coupling the Hamiltonian Replica exchange (HREX) with a conformation reservoir generated via potential softening and nonequilibrium MD. ARROW provides predictions with near chemical accuracy (mean absolute error of ~0.5 kcal/mol) for two of the three protein systems studied here (MCL1 and Thrombin). The third protein system (CDK2) reveals the difficulty in accurately describing dimer interaction energies involving polar and charged species. Overall, for all of the three protein systems studied here, ARROW FF predicts relative binding free energies of ligands with a similar accuracy level as leading nonpolarizable force fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1998

The Effect of Set Size on the Relation Between Saccadic and Perceptual Decisions During Search

We have shown that when searching for a disk in noise at one of 10 locations, the accuracy of the I st saccade is similar to that of the perceptual decision at the time of saccadic programming. The present study has two goals: 1) to test whether this linden - extends to a contrast-discrimination task without noise, and 2) to measure the effect of set size on the relation between saccadic and perceptual decisions. Methods: Three observers searched over a grey background (34.5 cd/sq m) for a bright disk (63.2 cd/sq m) among dim disks (54.1 cd/sq m) along the circumference of a circle (r = 5.9 deg.) centered on a fixation cress. Four set sizes (2, 4, 6, 12) were used. In the 1st condition, stimuli were presented for 1 sec. and observers used natural eye movements. We then measured the accuracy of the first saccade (% correct using a shortest-distance criterion). In the 2nd condition, observers fixated a central cross at all times and the stimulus duration was approx. 70 as less than the median latency of the first saccade in the 1st condition (saccadic programming time). We then recorded perceptual performance and discarded trials in which observers broke fixation. Results: For set sizes of 2, 4, 8, and 12, the mean d' across observers for the perceptual decision was 2.03, 1.96, 1.94, 1.71, respectively, while the mean d' of the first saccade was only 0.73, 1.40, 1.23, 1.17. Conclusions: Unlike detection of a disk in noise, for all observers and set-sizes, the perceptual accuracy at the time of saccadic programming is better than that of the lst saccade. For set-sizes of 4, 6, and 12, the amount of information available to the perceptual system relative to that available to the saccadic system is approximately constant (fixed do ratio). For these higher set sizes, the constancy in do across set size for both perception and saccadic decisions is consistent with a simple signal detection theory (SDT) model that processes noisy signals in parallel. However, for 2 observers, at a set-size of 2, saccadic targeting appears to be worse than the SDT model prediction, perhaps due to speed-accuracy trade-off.

Eckstein, M. P.↗
NASA NTRSDate not supplied

Towards Robust and Accurate Implicit Gradient Methods for Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Discretizations on Tetrahedral Grids

In this paper, we introduce implicit gradient methods as alternatives to conventional least-squares gradient methods for second- and third-order nodal-gradient cell-centered finite-volume discretizations, where solutions are stored at cells but gradients are stored at nodes. Because of the unique configuration of solutions and gradients, implicit gradient systems developed for the node-centered edge-based discretization method can be directly applied once the numerical solutions are interpolated from cells to nodes with sufficient accuracy. The resulting defect-correction solver can be loosely coupled with a flow-equation solver, and at convergence, solutions and gradients that satisfy the corresponding residual equations are obtained. Each iteration is relatively cheap compared with least-squares methods involving hundreds of neighbors. Numerical results are presented for accuracy verification studies and some simple but realistic flow problems.

Computational Fluid Dynamics↗
NASA NTRS1995

On the Utility of the Molecular Oxygen Dayglow Emissions as Proxies for Middle Atmospheric Ozone

Molecular oxygen dayglow emissions arise in part from processes related to the Hartley band photolysis of ozone. It is therefore possible to derive daytime ozone concentrations from measurements of the volume emission rate of either dayglow. The accuracy to which the ozone concentration can be inferred depends on the accuracy to which numerous kinetic and spectroscopic rate constants are known, including rates which describe the excitation of molecular oxygen by processes that are not related to the ozone concentration. We find that several key rate constants must be known to better than 7 percent accuracy in order to achieve an inferred ozone concentration accurate to 15 percent from measurements of either dayglow. Currently, accuracies for various parameters typically range from 5 to 100 percent.

Mlynczak, Martin G.↗
NASA NTRS2003

Accuracy and Precision in the Southern Hemisphere Additional Ozonesondes (SHADOZ) Dataset 1998-2000 in Light of the JOSIE-2000 Results

A network of 12 southern hemisphere tropical and subtropical stations in the Southern Hemisphere ADditional OZonesondes (SHADOZ) project has provided over 2000 profiles of stratospheric and tropospheric ozone since 1998. Balloon-borne electrochemical concentration cell (ECC) ozonesondes are used with standard radiosondes for pressure, temperature and relative humidity measurements. The archived data are available at:http: //croc.gsfc.nasa.gov/shadoz. In Thompson et al., accuracies and imprecisions in the SHADOZ 1998- 2000 dataset were examined using ground-based instruments and the TOMS total ozone measurement (version 7) as references. Small variations in ozonesonde technique introduced possible biases from station-to-station. SHADOZ total ozone column amounts are now compared to version 8 TOMS; discrepancies between the two datasets are reduced 2\% on average. An evaluation of ozone variations among the stations is made using the results of a series of chamber simulations of ozone launches (JOSIE-2000, Juelich Ozonesonde Intercomparison Experiment) in which a standard reference ozone instrument was employed with the various sonde techniques used in SHADOZ. A number of variations in SHADOZ ozone data are explained when differences in solution strength, data processing and instrument type (manufacturer) are taken into account.

Witte, J. C.↗
NASA NTRS1961

Analytical and Preliminary Simulation Study of a Pilot's Ability to Control the Terminal Phase of a Rendezvous with Simple Optical Devices and a Timer

One method of controlling the terminal phase of a space rendezvous between two vehicles is first to correct the flight path of the controlled vehicle so that a constant line of sight is established between the vehicles. This correction is accomplished by thrusting normal to the sight line in a direction to arrest the angular motion of this line. Once this collision course has been established, the second step is to control the closure rate for a safe approach along the line of sight. Adequate control of this maneuver requires range and closure-rate information. A combined analytical and preliminary simulation study was conducted to determine the ability of a human pilot to control the rendezvous by this method using visual sightings made during the initial collision-course control to obtain the range and closure rate. The analytical phase of the study reviewed the geometric relations between the vehicles and formed the basis for techniques to transform the angular sightings into range and closure rate. A preliminary simulation was then made to investigate the accuracy of these techniques. The simulation consisted of an analog computer, an oscilloscope to represent the view a pilot would have-with a stabilized sight, and a timer. Results indicate that pilots, using an optical sight and a timer, can successfully arrest the angular motion of the line of sight between two rendezvous vehicles and obtain relative range and closure rate with sufficient accuracy to perform the final braking maneuver successfully.

Lineberry, Edgar C., Jr.↗
NASA NTRS2011

CALIPSO Lidar Ratio Retrieval Over the Ocean

We are demonstrating on a few cases the capability of CALIPSO to retrieve the 532 nm lidar ratio over the ocean when CloudSat surface scattering cross section is used as a constraint. We are presenting the algorithm used and comparisons with the column lidar ratio retrieved by the NASA airborne high spectral resolution lidar. For the three cases presented here, the agreement is fairly good. The average CALIPSO 532 nm column lidar ratio bias is 13.7% relative to HSRL, and the relative standard deviation is 13.6%. Considering the natural variability of aerosol microphysical properties, this level of accuracy is significant since the lidar ratio is a good indicator of aerosol types. We are discussing dependencies of the accuracy of retrieved aerosol lidar ratio on atmospheric aerosol homogeneity, lidar signal to noise ratio, and errors in the optical depth retrievals. We are obtaining the best result (bias 7% and standard deviation around 6%) for a nighttime case with a relatively constant lidar ratio (in the vertical) indicative of homogeneous aerosol type

Josset, Damien B.↗
DOE OSTI2024

Demonstration of the rodeo algorithm on a quantum computer

The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of 0.08% using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann-Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann-Feynman calculations, we find a relative error of 0.7%. Here, we conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.

algorithm↗
DOE OSTI2021

Broadband Stability of the Habitable Zone Planet Finder Fabry–Pérot Etalon Calibration System: Evidence for Chromatic Variation

The comblike spectrum of a white light–illuminated Fabry–Pérot etalon can serve as a cost-effective and stable reference for precise Doppler measurements. Understanding the stability of these devices across their broad (hundreds of nanometers) spectral bandwidths is essential to realizing their full potential as Doppler calibrators. However, published descriptions remain limited to small bandwidths or short time spans. We present an ∼6 month broadband stability monitoring campaign of the Fabry–Pérot etalon system deployed with the near-infrared Habitable Zone Planet Finder (HPF) spectrograph. We monitor the wavelengths of each of ∼3500 resonant modes measured in HPF spectra of this Fabry–Pérot etalon (free spectral range = 30 GHz, bandwidth = 820–1280 nm), leveraging the accuracy and precision of an electro-optic frequency comb reference. These results reveal chromatic structure in the Fabry–Pérot mode locations and their evolution with time. We measure an average drift on the order of 2 cm s{sup –1} day{sup −1}, with local departures up to ±5 cm s{sup –1} day{sup −1}. We discuss these behaviors in the context of the Fabry–Pérot etalon mirror dispersion and other optical properties of the system and the implications for the use of similar systems for precise Doppler measurements. Our results show that this system supports the wavelength calibration of HPF at the ≲10 cm s{sup −1} level over a night and the ≲30 cm s{sup −1} level over ∼10 days. Our results also highlight the need for long-term and spectrally resolved study of similar systems that will be deployed to support Doppler measurement precision approaching ∼10 cm s{sup −1}.

42 ENGINEERING↗
DOE OSTI2019

Validation of RELAP-7 for Forced Convective and Natural Circulation Reactor Flows

New reactor designs such as small modular reactors and newly proposed passive safety systems rely on natural circulation two-phase flow cooling of the reactor core under accident conditions. Without a pump to drive the flow, the circulation rate is a strong function of void fraction. Under these conditions where the flow rate, pressure drop, and heat transfer are all closely coupled through the mixture density, the accurate prediction of void fraction is pivotal. Furthermore, while these passive systems boast a more reliable cooling option, the sensitivity of the system to two-phase flow instabilities is more likely than in forced convective cooling and can result in dangerous density wave or flow excursion conditions. Improvement of one-dimensional system codes and further development of three-dimensional code capability are all important efforts in addressing these issues. The proposed work is a critical step towards providing confidence through validation of the capability of thermal-hydraulic tools to meet the emerging challenges in reactor simulation. Historically, system analysis codes develop a stiffness over time due to fine-tuning of adjustable code parameters that result in a reluctance or inability to adopt improved models. Therefore, a rigorous effort should be invested in preparation for RELAP-7 to identify required modeling improvements of constitutive relations and validation of the code applicability to the wide range of possible reactor flow conditions. Part of this validation involves the uncertainty quantification which is a critical step in the Code Scaling, Applicability, and Uncertainty (CSAU) methodology and Best-Estimate Plus Uncertainty (BEPU) licensing method. BEPU allows recovery of safety margins and potentially optimizing plant performance, resulting in economic benefit for the reactor operators. Beginning with the collection of past experimental data covering prototypic LWR conditions, this document reviews three critical datasets available for the validation of system codes. The experimental methods, procedures, facilities, instrumentation, and supplementary information are consolidated to aid the validation efforts of this work and future projects. These three datasets (824 conditions) are chosen due to their wide acceptance and demonstrated application for code validation. Two experimental datasets from the Nuclear Power Engineering Corporation (NUPEC) span prototypic conditions of Boiling Water Reactors (BWR) and Pressurized Water Reactors (PWR). These datasets are labeled as the BFBT (BWR Full-size Fine-mesh Bundle Test) and the PSBT (PWR Subchannel and Bundle Test) datasets respectively. The third dataset is taken in an internally heated annulus that is scaled based on a BWR subassembly and includes two-phase flows important to post-blowdown analysis. Together, the datasets consider the full range of pressure and mass flux expected in LWR forced convective flows from steady-state to long term cooling conditions. Recognizing the deficiency of available data under low-pressure, low-flow, a new natural circulation dataset consisting of 107 conditions is obtained. With system pressures ranging between 145 and 950 kPa, natural circulation is driven by a heat flux up to 275 kW/m2 in a 3 m long heated region of the annulus test section which is followed by a 2 m long unheated region before entering a condenser. Stable natural circulation flow rates in this facility were measured to be between 182 and 590 kg/m2-s. Pressure and temperature are measured at ten locations in the facility. In addition, measurements of void fraction, interfacial area concentration, and gas velocity are obtained at five axial locations in the annulus test section. The RELAP5-3D code demonstrates good accuracy for void fraction predictions in BFBT and PSBT benchmarks, but shows relatively large discrepancy in the annulus experiments at lower pressures. In two-phase natural circulation, large oscillations are observed in many system parameters during the simulation of 19 experiment cases which were conducted at low pressures, and the model shows good predictive performance with the remaining 88 experiment cases. However, some discrepancies in void fraction and temperature predictions are found which may require improved constitutive modeling under these low-pressure, low-flow condition. The quantified uncertainty in void fraction predictions in three forced convection benchmarks due to uncertainties in boundary conditions and geometries are relatively small, except for a few cases in the annulus experiment. The output uncertainty of the natural circulation model is quantified by considering the measurement error in boundary conditions, and it is shown that the output uncertainty ranges are relatively small for the range of conditions considered. Through this work, a clear pathway is provided for validation of RELAP7 once the code is available.

42 ENGINEERING↗
DOE OSTI2023

On the influence of over-parameterization in manifold based surrogates and deep neural operators

Constructing accurate and generalizable approximators (surrogate models) for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. The main question is what type of surrogate models we should construct and should these models be under-parameterized or over-parameterized. In this work, we propose new developments and perform comparisons for two promising approaches: manifold-based polynomial chaos expansion (m-PCE) and the deep neural operator (DeepONet), and we examine the effect of over-parameterization on generalization. While m-PCE enables the construction of a mapping by first identifying low-dimensional embeddings of the input functions, parameters, and quantities of interest (QoIs), a neural operator learns the nonlinear mapping via the use of deep neural networks. Here, we demonstrate the performance of these methods in terms of generalization accuracy by solving the 2D time-dependent Brusselator reaction-diffusion system with uncertainty sources, modeling an autocatalytic chemical reaction between two species. We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of the input functions and the output QoIs. To further enhance the accuracy of the DeepONet, we introduce weight self-adaptivity in the loss function. We demonstrate that the performance of m-PCE and DeepONet is comparable for cases of relatively smooth input-output mappings. However, when highly non-smooth dynamics is considered, DeepONet shows higher approximation accuracy. We also find that for m-PCE, modest over-parameterization leads to better generalization, both within and outside of distribution, whereas aggressive over-parameterization leads to over-fitting. In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics. Furthermore, we compare the performance of the above models with another recently proposed operator learning model, the Fourier Neural Operator, and show that its over-parameterization also leads to better generalization. Taken together, our studies show that m-PCE can provide very good accuracy at very low training cost, whereas a highly over-parameterized DeepONet can provide better accuracy and robustness to noise but at higher training cost. In both methods, the inference cost is negligible.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Computation of Transonic Flows Using Potential Methods

The proposed paper will describe the state of the art associated with numerical solution of the full or exact velocity potential equation for solving transonic, external-aerodynamic flows. The presentation will begin with a review of the literature emphasizing research activities of the past decade. Next, the various forms of the full or exact velocity potential equation, the equation's corresponding mathematical characteristics, and the derivation assumptions will be presented and described in detail. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, will be presented and discussed relative to the more complete Euler or Navier-Stokes formulations. The technical presentation will continue with a description of recently developed full potential numerical approach characteristics. This description will include governing equation nondimensionalization, physical-to-computational-domain mapping procedures, a limited description of grid generation requirements, the spatial discretization scheme, numerical implementation of boundary conditions, and the iteration scheme. The next portion of the presentation will present and discuss numerical results for several two- and three-dimensional aerodynamic applications. Included in the results section will be a discussion and demonstration of a typical grid refinement analysis for determining spatial convergence of the numerical solution and level of solution accuracy. Computer timings for a variety of full potential applications will be compared and contrasted with similar results for the Euler equation formulation. Finally. the presentation will end with concluding remarks and recommendations for future work.

Hoist, Terry L.↗