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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Multilevel techniques for compression and reduction of scientific data—the univariate case

We present a multilevel technique for the compression and reduction of univariate data and give an optimal complexity algorithm for its implementation. A hierarchical scheme offers the flexibility to produce multiple levels of partial decompression of the data so that each user can work with a reduced representation that requires minimal storage whilst achieving the required level of tolerance. The algorithm is applied to the case of turbulence modelling in which the datasets are traditionally not only extremely large but inherently non-smooth and, as such, rather resistant to compression. Here, we decompress the data for a range of relative errors, carry out the usual analysis procedures for turbulent data, and compare the results of the analysis on the reduced datasets to the results that would be obtained on the full dataset. The results obtained demonstrate the promise of multilevel compression techniques for the reduction of data arising from large scale simulations of complex phenomena such as turbulence modelling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A co-kurtosis PCA based dimensionality reduction with nonlinear reconstruction using neural networks

For turbulent reacting flow systems, identification of low-dimensional representations of the thermo-chemical state space is vitally important, primarily to significantly reduce the computational cost of device-scale simulations. Principal component analysis (PCA), and its variants, are a widely employed class of methods. Recently, an alternative technique that focuses on higher-order statistical interactions, co-kurtosis PCA (CoK-PCA), has been shown to effectively provide a low-dimensional representation by capturing the stiff chemical dynamics associated with spatiotemporally localized reaction zones. While its effectiveness has only been demonstrated based on a priori analyses with linear reconstruction, in this work, we employ nonlinear techniques to reconstruct the full thermo-chemical state and evaluate the efficacy of CoK-PCA compared to PCA. Specifically, we combine a CoK-PCA-/PCA-based dimensionality reduction (encoding) with an artificial neural network (ANN) based reconstruction (decoding) and examine, a priori, the reconstruction errors of the thermo-chemical state. In addition, we evaluate the errors in species production rates and heat release rates, which are nonlinear functions of the reconstructed state, as a measure of the overall accuracy of the dimensionality reduction technique. We employ four datasets to assess CoK-PCA/PCA coupled with ANN-based reconstruction: zero-dimensional (homogeneous) reactor for autoignition of an ethylene/air mixture that has conventional single-stage ignition kinetics, a dimethyl ether (DME)/air mixture which has two-stage (low and high temperature) ignition kinetics, a one-dimensional freely propagating premixed ethylene/air laminar flame, and a two-dimensional dataset representing turbulent autoignition of ethanol in a homogeneous charge compression ignition (HCCI) engine. Finally, results from the analyses demonstrate the robustness of the CoK-PCA based low-dimensional manifold with ANN reconstruction in accurately capturing the data, specifically from the reaction zones.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Application of an equation‐oriented framework to formulate and estimate parameters of chemical looping reaction models

Abstract Accurate, predictive reaction models are critical for the design and optimization of chemical looping combustion (CLC) reactors. The formulation and estimation of kinetic parameters for these reaction models using a first‐principles equation‐oriented (EO) approach is particularly beneficial as large amounts of experimental data spanning process‐relevant conditions can be used to estimate parameters in a computationally tractable way. This work demonstrates the application of a novel EO framework to develop reduction reaction kinetic models of an iron‐based CLC oxygen carrier (OC). An optimization problem is formulated to estimate kinetic parameters that provide the best fit to the experimental data. The model predicts the state of the OC with mean square error values of 2.5%–4.4% across the full range of validation data, including multiple reduction cycles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Inverse bremsstrahlung absorption rate for super-Gaussian electron distribution functions including plasma screening

Here we provide analytic expressions for the effective Coulomb logarithm for inverse bremsstrahlung absorption which predict significant corrections to the Langdon effect and overall absorption rate compared to previous estimates. The calculation of the collisional absorption rate of laser energy in a plasma by the inverse bremsstrahlung mechanism usually makes the approximation of a constant Coulomb logarithm. We dispense with this approximation and instead take into account the velocity dependence of the Coulomb logarithm, leading to a more accurate expression for the absorption rate valid in both classical and quantum conditions. In contrast to previous work, the laser intensity enters into the Coulomb logarithm. In most laser-plasma interactions the electron distribution function is super-Gaussian [Langdon, Phys. Rev. Lett. 44, 575 (1980)], and we find the absorption rate under these conditions is increased by as much as ≈ 30% compared to previous estimates at low density. In many cases of interest the correction to Langdon's predicted reduction in absorption is large; for example at Z = 6 and Te = 400 eV the Langdon prediction for the absorption is in error by a factor of ≈ 2. However, we also account for the additional effect of plasma screening, which predicts a reduction in absorption by a similar amount (up to ≈ 30%). These two effects compete to determine the overall absorption, which may be increased or decreased, depending on the conditions. The corrections can be incorporated into radiation-hydrodynamics simulation codes by replacing the familiar Coulomb logarithm with an analytic expression which depends on the super-Gaussian order “M” and the screening length.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Stellar chemical abundances: in pursuit of the highest achievable precision

The achievable level of precision on photospheric abundances of stars is a major limiting factor on investigations of exoplanet host star characteristics, the chemical histories of star clusters, and the evolution of the Milky Way and other galaxies. While model-induced errors can be minimized through the differential analysis of spectrally similar stars, the maximum achievable precision of this technique has been debated. As a test, we derive differential abundances of 19 elements from high-quality asteroid-reflected solar spectra taken using a variety of instruments and conditions. We treat the solar spectra as being from unknown stars and use the resulting differential abundances, which are expected to be zero, as a diagnostic of the error in our measurements. Our results indicate that the relative resolution of the target and reference spectra is a major consideration, with use of different instruments to obtain the two spectra leading to errors up to 0.04 dex. Use of the same instrument at different epochs for the two spectra has a much smaller effect (∼0.007 dex). The asteroid used to obtain the solar standard also has a negligible effect (∼0.006 dex). Assuming that systematic errors from the stellar model atmospheres have been minimized, as in the case of solar twins, we confirm that differential chemical abundances can be obtained at sub-0.01 dex precision with due care in the observations, data reduction, and abundance analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Development of beam emission spectroscopy for turbulence transport study in Heliotron J

This paper describes the development study of the beam emission spectroscopy (BES) for the turbulent transport study in Heliotron J. Modification of the sightlines (10 × 4 for edge and 10 × 2 for edge) enables us to obtain 2-dimensional BES imaging. The cooling effect on the reduction in the electrical noise of avalanche photodiode (APD) assembly has been investigated using a refrigerant cooling system. When the temperature of the APD element has set to be −20 °C, the electrical noise can be reduced more than 50%. The measurement error of the phase difference in the case of low signal level has been tested by two light-emitting diode lamps. The APD cooling has an effect to improve the measurement error at the low signal level of APD.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRSDate not supplied

Validation of Remotely Sensed and Modeled Soil Moisture at Forested and Unforested Sites

Soil moisture is an important driver for forest ecosystems, influencing fire occurrence and extent, insect and pathogen impacts, and tree growth, which creates a need for regular, globally extensive soil moisture information that only satellite-based sensors or models can achieve. However, the reliability of soil moisture measurements in forests is not well understood due to a lack of suitable validation sites (especially relative to unforested ecosystems) and interference caused by high vegetation water content on remotely sensed measurements; although recent studies have started to address this gap [1], [2], [3], [4]. Here we validate the performance of multiyear remotely sensed (SMAP/Sentinel), remotely sensed data assimilation modelled (SMAP-L4), and modelled (NLDAS) surface and root zone (0-1 m) soil moisture datasets with data from in-situ sensors at 39 National Ecological Observatory Network (NEON) sites throughout the contiguous US. Due to differences in spatial resolution, NEON soil moisture (~0.2 km measurement zone) correlations were expected to be stronger with the SMAP/Sentinel product (3 km resolution) than with coarser resolution SMAP-L4 (9 km resolution) or NLDAS products (13 km resolution). However, given the sensitivity of satellite measurements to vegetation water content we expected a deterioration in the correlations based on remotely sensed measurements (SMAP/Sentinel and SMAP-L4) as aboveground biomass increased, whereas the model-based data (NLDAS) was expected to be largely insensitive to vegetation type. We recognize that the SMAP/Sentinel product was developed for unforested regions, therefore our application is outside its primary use case. Soil moisture is measured at up to 8 depths in five soil plots spaced up to 40 m apart at each NEON terrestrial site. Correlation parameters were calculated for the three remotely sensed and modelled data products relative to in-situ measurement following Entekhabi et al. [5]. The datasets comprised 94 (SMAP-L4), 28 (SMAP/Sentinel), and 106 (NLDAS) sites-years for surface soils and 13 (SMAP-L4) and 14 (NLDAS) site-years for the root zone. At unforested sites, the performance of the three remotely sensed and modelled data products was similar for surface soils (Table 1). For example, unbiased RMSD (ubRMSD), which SMAP uses as its primary performance metric [6], ranged from 0.05 to 0.06 m3 m-3 (Table 1), indicating the ability of all three products to track changes in soil moisture over time. The performance of the three products deteriorated at forested sites, however, while the difference in performance was modest for SMAP-L4 and NLDAS, the deterioration in SMAP/Sentinel performance was substantial. For instance, SMAP/Sentinel ubRMSD increased from 0.06 to 0.11 m3 m-3 and absolute mean difference (Abs MD; which includes measurement bias and spatial representativeness errors) increased from 0.06 to 0.16 m3 m-3, indicating both a reduction in ability to track temporal changes and absolute amounts of soil moisture in forest ecosystems. SMAP-L4 and NLDAS had lower unbiased RMSD for root zone (0-1 m) than surface soils at both forested and unforested sites (Tables 1 and 2; SMAP/Sentinel does not produce a root zone measurement). However, in most cases the correlation coefficient (r) was lower for the root zone than surface soils, suggesting the lower unbiased RMSD may be attributed to greater temporal stability of soil moisture in the root zone rather than improved data product performance. Mean difference and absolute mean difference, which encompass measurement bias and spatial representativeness errors, were greater for root zone than surface soils at unforested sites for both data products, but the opposite was generally true at forested sites. As with surface soils, there was relatively little change in the performance of SMAP-L4 and NLDAS between the unforested and forested sites. In summary, all three data products were able to adequately represent soil moisture at unforested sites, at least when aggregating across sites. However, while the performance of all three products deteriorated at forested sites, SMAP-L4 and NLDAS maintained sufficient performance to remain suitable for some use cases (ubRMSD <0.06 m3 m-3 and RMSD <0.13 m3 m-3). In contrast, the relatively poorer performance of the SMAP/Sentinel product at forested sites seems insufficient for most use cases (ubRMSD >0.1 m3 m-3 and RMSD >0.2 m3 m-3). We attribute the large reduction in the performance of the SMAP/Sentinel product in forests to its use of C-band wavelengths, which are particularly sensitive to vegetation interference, and apparently outweighed any gains provided by its higher spatial resolution. A combined SMAP/NISAR soil moisture product may provide improved performance relative to SMAP/Sentinel due to NISAR’s use of L-band wavelengths, which are less sensitive to vegetation (NISAR is scheduled for launch in early 2024).

Edward Ayres↗
DOE OSTI2014

Fundamental limitations of high contrast imaging set by small sample statistics

In this paper, we review the impact of small sample statistics on detection thresholds and corresponding confidence levels (CLs) in high-contrast imaging at small angles. When looking close to the star, the number of resolution elements decreases rapidly toward small angles. This reduction of the number of degrees of freedom dramatically affects CLs and false alarm probabilities. Naively using the same ideal hypothesis and methods as for larger separations, which are well understood and commonly assume Gaussian noise, can yield up to one order of magnitude error in contrast estimations at fixed CL. The statistical penalty exponentially increases toward very small inner working angles. Even at 5-10 resolution elements from the star, false alarm probabilities can be significantly higher than expected. Here we present a rigorous statistical analysis that ensures robustness of the CL, but also imposes a substantial limitation on corresponding achievable detection limits (thus contrast) at small angles. This unavoidable fundamental statistical effect has a significant impact on current coronagraphic and future high-contrast imagers. Finally, the paper concludes with practical recommendations to account for small number statistics when computing the sensitivity to companions at small angles and when exploiting the results of direct imaging planet surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1991

Model order reduction applied to a hot-bench simulation of an aeroelastic wind-tunnel model

Simulations of an aeroelastically scaled wind-tunnel model were developed for hot-bench testing of a digital controller. The digital controller provided active flutter-suppression, rolling-maneuver-load alleviation, and plant estimation. To achieve an acceptable time scale for the hot-bench application, the mathematical model of the wind-tunnel model was reduced from 220 states to approximately 130 states while assuring that the required accuracy was preserved for all combinations of 10 inputs and 56 outputs. The reduction was achieved by focussing on a linear, aeroelastic submodel of the full mathematical model and by applying a method based on the internally balanced realization of a dynamic system. The error-bound properties of the internally balanced realization significantly contribute to its utility in the model reduction process. The reduction method and the results achieved are described.

Buttrill, Carey S.↗
NASA NTRSDate not supplied

Mitigating the Impacts of Measurement Error in the Quesst Mission Community Noise Study

Beginning in 2025, the NASA Quesst mission will conduct a series of community response tests involving flyovers of the X-59 aircraft at select localities across the United States. Several waves of a longitudinal survey will be administered over approximately one month of testing in order to capture perceptual responses to low-amplitude sonic booms, or “sonic thumps”. Simultaneously, noise exposure levels will be estimated by fusing model-based predictions with measurements taken from a sparse network of monitors in the region. As one of the aims of the study is to produce a dose-response curve, a regression model relating perceptual response to noise exposure levels, it is important to acknowledge the potential attenuation bias that results from measurement error in the estimated noise exposure levels. In this presentation we review and compare several methods for dealing with measurement error in generalized linear mixed models. The methods are demonstrated on simulated data and real data collected during past NASA risk reduction studies.

measurement error↗
NASA NTRS1989

An adaptive data-smoothing routine

An adaptive noise reduction algorithm that can be implemented on a microcomputer is developed. Smoothing polynomials are used where the polynomial coefficients are chosen such that the mean-square-error between the noisy and smoothed data is minimized. This approach is equivalent to the implementation of a low-pass finite impulse response filter. The noise reduction depends on the order of the smoothing polynomial. A whiteness test on the error sequence is incorporated to search for the optimal smoothing. Expansion coefficients may be computed via the fast Fourier transform, and the resulting smoothing process is the equivalent of the implementation of an adaptive ideal low-pass filter. Results are obtained for an analytical signal with added white Gaussian noise. The routine may be applied to any smooth signal with additive random noise.

Taylor, Clayborne D.↗
NASA NTRS1991

Estimation of geopotential differences over intercontinental locations using satellite and terrestrial measurements

An error analysis study was conducted in order to assess the current accuracies and the future anticipated improvements in the estimation of geopotential differences over intercontinental locations. An observation/estimation scheme was proposed and studied, whereby gravity disturbance measurements on the Earth's surface, in caps surrounding the estimation points, are combined with corresponding data in caps directly over these points at the altitude of a low orbiting satellite, for the estimation of the geopotential difference between the terrestrial stations. The mathematical modeling required to relate the primary observables to the parameters to be estimated, was studied for the terrestrial data and the data at altitude. Emphasis was placed on the examination of systematic effects and on the corresponding reductions that need to be applied to the measurements to avoid systematic errors. The error estimation for the geopotential differences was performed using both truncation theory and least squares collocation with ring averages, in case observations on the Earth's surface only are used. The error analysis indicated that with the currently available global geopotential model OSU89B and with gravity disturbance data in 2 deg caps surrounding the estimation points, the error of the geopotential difference arising from errors in the reference model and the cap data is about 23 kgal cm, for 30 deg station separation.

Pavlis, Nikolaos K.↗
DOE OSTI2018

Effects of exposure estimation errors on estimated exposure-response relations for PM2.5

Highlights: • Recent literature has identified associations between concentrations of fine particulate matter (PM2.5) in ambient air and adverse health effects at estimated exposure concentrations below current air ambient quality standards. • The models and analyses used do not usually quantify uncertainty about exposure estimates. • Realistic errors in exposure estimates can be estimated from available air quality monitoring stations by predicting concentrations at each station from concentrations at neighboring stations. • Exposure estimation errors are large enough to obscure low-dose nonlinearities or thresholds in the true concentration-response (C-R) function, artificially making them appear to be linear at low doses. • Better estimates of C-R functions will require modeling exposure distributions and estimation errors, rather than just estimating average exposure concentrations. Associations between fine particulate matter (PM2.5) exposure concentrations and a wide variety of undesirable outcomes, from autism and auto theft to elderly mortality, suicide, and violent crime, have been widely reported. Influential articles have argued that reducing National Ambient Air Quality Standards for PM2.5 is desirable to reduce these outcomes. Yet, other studies have found that reducing black smoke and other particulate matter by as much as 70% and dozens of micrograms per cubic meter has not detectably affected all-cause mortality rates even after decades, despite strong, statistically significant positive exposure concentration-response (C-R) associations between them. This paper examines whether this disconnect between association and causation might be explained in part by ignored estimation errors in estimated exposure concentrations. We use EPA air quality monitor data from the Los Angeles area of California to examine the shapes of estimated C-R functions for PM2.5 when the true C-R functions are assumed to be step functions with well-defined response thresholds. The estimated C-R functions mistakenly show risk as smoothly increasing with concentrations even well below the response thresholds, thus incorrectly predicting substantial risk reductions from reductions in concentrations that do not affect health risks. We conclude that ignored estimation errors obscure the shapes of true C-R functions, including possible thresholds, possibly leading to unrealistic predictions of the changes in risk caused by changing exposures. Instead of estimating improvements in public health per unit reduction (e.g., per 10 µg/m{sup 3} decrease) in average PM2.5 concentrations, it may be essential to consider how interventions change the distributions of exposure concentrations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Hybridizing pseudo-Hamiltonians and non-local pseudopotentials in diffusion Monte Carlo

An accurate treatment of effective core potentials (ECPs) requires care in continuum quantum Monte Carlo (QMC) methods. While most QMC studies have settled on the use of familiar non-local (NL) pseudopotentials with additional localization approximations, these approaches have been shown to result in moderate residual errors for some classes of molecular and solid state applications. Here, we revisit an idea proposed early in the history of QMC ECPs that does not require localization approximations, namely, a differential class of potentials referred to as pseudo-Hamiltonians. We propose to hybridize NL potentials and pseudo-Hamiltonians to reduce residual non-locality of existing potentials. We derive an approach to recast pseudopotentials for 3d elements as hybrid pseudo-Hamiltonians with optimally reduced NL energy. We demonstrate the fidelity of the hybrid potentials by studying atomic ionization potentials of Ti and Fe and the binding properties of TiO and FeO molecules with diffusion Monte Carlo (DMC). We show that localization errors have been reduced relative to potentials with the same NL channels for Sc–Zn by considering the DMC energy change with respect to the choice of approximate localization. While localization error decreases proportionate to the reduced NL energy without a Jastrow, with a Jastrow, the degree of reduction decreases at higher filling of the d-shell. Our results suggest that a subset of existing ECPs may be recast in this hybrid form to reduce the DMC localization error. They also point to the prospect of further reducing this error by generating ECPs within this hybrid form from the start.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Robust Tensor Hypercontraction of the Particle–Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory

One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of coupled-cluster methods by representation of a four-dimensional tensor of electron-repulsion integrals in terms of five two-dimensional matrices. Pierce et al. have already shown that the application of a robust form of THC to the particle–particle ladder (PPL) term reduces the cost of this term in couple-cluster singles and doubles (CCSD) from O(N 6 ) to O(N 5 ) with negligible errors in energy with respect to the density-fitted variant. In this work, we have implemented the least-squares variant of THC (LS-THC) which does not require a nonlinear tensor factorization, including the robust form (R-LS-THC), for the calculation of the excitation and electron attachment energies using equation-of-motion coupled cluster methods EOMEE-CCSD and EOMEA-CCSD, respectively. We have benchmarked the effect of the R-LS-THC-PPL approximation on excitation energies using the comprehensive QUEST database and the accuracy of electron attachment energies using the NAB22 database. Here, we find that errors on the order of 1 meV are achievable with a reduction in total calculation time of approximately 5x.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

A SURVEY OF ALKALI LINE ABSORPTION IN EXOPLANETARY ATMOSPHERES

We obtained over 90 hr of spectroscopic observations of four exoplanetary systems with the Hobby-Eberly Telescope. Observations were taken in transit and out of transit, and we analyzed the differenced spectra-i.e., the transmission spectra-to inspect it for absorption at the wavelengths of the neutral sodium (Na I) doublet at {lambda}{lambda}5889, 5895 and neutral potassium (K I) at {lambda}7698. We used the transmission spectrum at Ca I {lambda}6122-which shows strong stellar absorption but is not an alkali metal resonance line that we expect to show significant absorption in these atmospheres-as a control line to examine our measurements for systematic errors. We use an empirical Monte Carlo method to quantify these systematic errors. In a reanalysis of the same data set using a reduction and analysis pipeline that was derived independently, we confirm the previously seen Na I absorption in HD 189733b at a level of (- 5.26 {+-} 1.69) Multiplication-Sign 10{sup -4} (the average value over a 12 A integration band to be consistent with previous authors). Additionally, we tentatively confirm the Na I absorption seen in HD 209458b (independently by multiple authors) at a level of (- 2.63 {+-} 0.81) Multiplication-Sign 10{sup -4}, though the interpretation is less clear. Furthermore, we find Na I absorption of (- 3.16 {+-} 2.06) Multiplication-Sign 10{sup -4} at <3{sigma} in HD 149026b; features apparent in the transmission spectrum are consistent with real absorption and indicate this may be a good target for future observations to confirm. No other results (Na I in HD 147506b and Ca I and K I in all four targets) are significant to {>=}3{sigma}, although we observe some features that we argue are primarily artifacts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

IMPROVED V II log(gf) VALUES, HYPERFINE STRUCTURE CONSTANTS, AND ABUNDANCE DETERMINATIONS IN THE PHOTOSPHERES OF THE SUN AND METAL-POOR STAR HD 84937

New experimental absolute atomic transition probabilities are reported for 203 lines of V II. Branching fractions are measured from spectra recorded using a Fourier transform spectrometer and an echelle spectrometer. The branching fractions are normalized with radiative lifetime measurements to determine the new transition probabilities. Generally good agreement is found between this work and previously reported V II transition probabilities. Two spectrometers, independent radiometric calibration methods, and independent data analysis routines enable a reduction in systematic uncertainties, in particular those due to optical depth errors. In addition, new hyperfine structure constants are measured for selected levels by least squares fitting line profiles in the FTS spectra. The new V II data are applied to high resolution visible and UV spectra of the Sun and metal-poor star HD 84937 to determine new, more accurate V abundances. Lines covering a range of wavelength and excitation potential are used to search for non-LTE effects. Very good agreement is found between our new solar photospheric V abundance, log ε(V) = 3.95 from 15 V II lines, and the solar-system meteoritic value. In HD 84937, we derive [V/H] = –2.08 from 68 lines, leading to a value of [V/Fe] = 0.24.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗