SEARCH · Engineering Papers

Results for “shielding effectiveness”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

423 records · Page 24

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Super Resolving Unrolled Neural Networks for Remote Sensing

In remote sensing systems, the capabilities of the system are constrained by the complex interactions between size, weight, and power (SWAP) of potential designs. In electro-optical (EO) systems, examples of these critical parameters include the system’s sensitivity and resolution. Those parameters can be increased by ever larger optical apertures and focal planes but at the cost of more SWAP. Multi-image super resolution (MISR) techniques allow resolution to be enhanced via computation rather than more sophisticated optical hardware. These algorithms combine multiple images together into a single, higher resolution image, trading temporal resolution and computation for spatial resolution. Fielded MISR techniques, such as Drizzle, can require several hundred images to create a single super resolved image, implying reduced temporal resolution, increased data acquisition load, and limiting mission applications. Iterative techniques, such as model-based image reconstruction and compressive sensing, have been shown to create super resolved images using fewer images than Drizzle. They do this by posing an optimization problem that balances accuracy between a highly accurate physical model and an image model. In the case of super resolution, the physical model is defined by the relation between low resolution input images and the desired high resolution output image. The image model encodes some assumptions about the super resolved image. These assumptions are meant to suppress reconstruction artifacts that arise due to deterministic physical model error, stochastic measurement noise, and potential undersampling. In practice, the performance of iterative methods are limited by imaging models compatible with optimization. Deep learning-based methods can effectively learn image models of arbitrary complexity, but lack the theoretical explainability and robustness of iterative techniques. Consensus equilibrium (CE) generalizes the iterative techniques beyond optimization, enabling blackbox algorithms such as traditional and neural image denoisers to be used as the image model. CE-based approaches retain much of the explainability and robustness of iterative techniques while allowing the expressiveness of machine learning image models to be used. Additionally, by unrolling iterations of CE with an embedded image denoiser, the image denoiser can be further trained and specialized to the specific application with potentially higher quality reconstructions. Under this project, we demonstrated the feasibility of training an unrolled neural network based upon CE. While we didn’t train one, we showed that the CE process is differentiable and its gradient can be tractably computed. We also explored the usage of a variants of CE akin to generative neural works. Most importantly, we applied the CE framework to a number of problems including non-blind deconvolution, upsampling, single-image super resolution, MISR, event-based sensing, and saturated deconvolution. Our MISR prototype creates high quality reconstructions with an order of magnitude fewer images than previous approaches and, critically, produces these reconstructions fast enough for practical usage.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Batch Extraction Studies to Evaluate Trace Element Behavior in PUREX Conditions

The multilab Intentional Forensics Venture is working to identify which stable elements (i.e., taggants) at trace concentrations relative to U would persist throughout the nuclear fuel cycle in a voluntary fuel tagging scheme. A taggant would provide the nuclear forensics community with a “barcode” to help identify nuclear materials found outside of regulatory control. A portion of this project was focused on reprocessing effects and determining which, if any, elements would coextract with U(VI) in standard Pu–U reduction extraction (PUREX) conditions. Elements with a propensity to coextract could, in theory, be used as taggants from a PUREX perspective. Although retention is not a performance requirement, the taggant signature would need to partition predictably from the U stream after the PUREX process to maintain forensic utility. This report documents results from several batch extraction studies with numerous trace elements from HNO 3 (1.5–5 M), with and without U(VI), into 30% tri-n-butyl phosphate (TBP) in kerosene. Extraction and back-extraction tests were used to evaluate nearly 60 elements in surrogate conditions for PUREX, and distribution coefficients (i.e., D-values) for most species were <0.1, indicating few species are likely to co-extract with U through PUREX. Additional studies are needed to optimize sample volumes and dilutions to dial in these low D-values. The D-values (D) were determined for several of the more promising elements, including Re and Se. Ultimately, we conclude that only a limited number of the ~ 60 elements investigated are extractable in the U stream of PUREX, based on measured D values, meaning most candidate elemental taggants would likely be lost at this stage of the nuclear fuel cycle, even when considering a range of acid concentrations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2022

Active learning with multifidelity modeling for efficient rare event simulation

Here, while multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies (including some high-dimensional problems) and two finite element model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

42 ENGINEERING↗

DOE OSTI2021

Combined Mesonet and Tracker

Title: Combined Mesonet and Trackers (UNL Mobile Mesonets) Authors University of Nebraska PI: Adam Houston, UNL Professor (ahouston2@unl.edu) Mailing Address: 126 Bessey Hall P.O. Box 880340 Lincoln, NE 68588-0340 CoMeT Overview The University of Nebraska-Lincoln operates three Combined Mesonet and Tracker (CoMeTs). CoMeTs are Ford Explorers (model years 2015, 2017, and 2019) with forward-mounted suites of meteorological sensors and dual moonroofs, combining the capability of a mobile mesonet to collect near-surface observations with the capability of an unmanned aircraft systems (UAS) tracker vehicle, which enables an observer in the second row of seats to see the aircraft and maintain compliance with Federal Aviation Administration policies on UAS operation. The CoMeTs collect observations of slow temperature and humidity at ~2 m above ground level (AGL) using a Vaisala HMP155A, fast temperature at ~2 m AGL using a Campbell Scientific 109SS-L thermistor, pressure at ~2.5 m AGL using a Vaisala PTB210, wind speed and direction at ~3.25 m AGL using an R.M. Young 05103 propeller anemometer, and vehicle heading using a KVH Industries C-100 fluxgate compass (Barbieri et al. 2019). The HMP155A and 109SS-L thermistor are shielded and aspirated within a U-tube (Waugh and Frederickson 2010; Houston et al. 2016). This list of sensors is also included in the CoMeT data file metadata. Manufacturer specifications for these instruments are given in Table 1 of Hanft and Houston (2018). The reported measured quantities are summarized below.CoMeT-3 was funded through an equipment allocation included in the NSF TORUS award (AGS-1824649). Instrument Description The specific sensors included on each CoMeT are summarized in the table at the end of this section. In general each CoMeT collects observations of slow temperature and humidity at ~2 m above ground level (AGL) using a Vaisala HMP155, fast temperature at ~2 m AGL using a Campbell Scientific 109SS-L thermistor, pressure at ~2.5 m AGL using a Vaisala PTB210 barometer with a Gill pressure port, wind speed and direction at ~3.25 m AGL using an R.M. Young 05103 propeller anemometer, position using a Garmin 19x HVS receiver, and vehicle heading using a KVH Industries C-100 fluxgate compass. The HMP155 and 109SS are shielded and aspirated within a U-tube (Waugh and Frederickson 2010; Houston et al. 2016). Fast temperature and corrected RH measurements (using sensors housed within the U-tube) have a time constant of 10-12 s based on data collected across a temperature and RH shock during the CLOUD-MAP 2017 calibration/validation tests on June 26, 2017. Vehicle speed was < 10 kts for this test. CoMeT-1 CoMeT-2 CoMeT-3 Slow Temperature Slow RH Vaisala HMP155A-L20-PT Part #: 22280-7 Vaisala HMP155E Part #: E1AA11A0B1A1A0A Vaisala HMP155E Part #: E1AA11A0B1A1A0A Fast temperature Campbell Scientific 109SS-L20-PT Part #: 21448-3 Campbell Scientific 109SS-L12-PW Part #: 21448-109 Campbell Scientific 109SS-L12-PW Part #: 21448-150 Pressure Vaisala PTB-210 Part #: A1A1B Gill Pressure Port Part #: 61002 Vaisala PTB-210 Part #: A1A1B Gill Pressure Port Part #: 61002 Vaisala PTB-210 Part #: A1A1B Gill Pressure Port Part #: 61002 Wind RM Young 05103-L20-PT Part #: 18435-310 RM Young 05103-L20-PW Part #: 18435-244 RM Young 05103-L20-PW Part #: 18435-244 GPS Garmin GPS 19x HVS (NMEA 0183) Part #: 010-01010-00 Garmin GPS 19x HVS (NMEA 0183) Part #: 010-01010-00 Garmin GPS 19x HVS (NMEA 0183) Part #: 010-01010-00 Compass KVH C-100 Part #: 01-0177-15 KVH C-100 Part #: 01-0177-15 KVH C-100 Part #: 01-0177-15 Logger Campbell Scientific CR6-NA-XT-SW Part #: 28385-9 Campbell Scientific CR6-WIFI-XT-SW Part #: 28385-6 Campbell Scientific CR6-WIFI-XT-SW Part #: 28385-6 Data Collection and Real-Time Processing The reported measured quantities are summarized in the table below. Quantity Units Source Epoch time Seconds GPS Latitude and longitude Degrees GPS Altitude m GPS Pressure hPa PTB210 Temperature (fast) deg C 109SS-L Temperature (slow) deg C HMP155 RH (slow) % HMP155 Vehicle speed m/s GPS Vehicle heading deg C-100 and GPS In addition to the measured variables, several derived variables are calculated. Corrected/fast relative humidity (%) Relative humidity is adjusted to the fast temperature following Richardson et al. (1998) and Houston et al. (2016). Water vapor mixing ratio (g/kg) Dew point temperature (°C) Potential temperature (Kelvin) Virtual potential temperature (Kelvin) Equivalent potential temperature (Kelvin) Regular intercomparisons between all three CoMeTs were performed during TORUS 2019. Comparisons were also conducted between CoMeT-1 and CoMeT-2 during LAPSE-RATE (2018) on 14 July. In these intercomparisons, the vehicles were parked adjacent to each other aligned perpendicular to (and facing into) the wind. To minimize engine heating effects, intercomparisons were only conducted when the wind speed was >10 kts. Data Format Original data files for each deployment are saved as text files and then converted to NetCDF. NetCDF versions have units that are CF compliant and may not match the original units in the txt files. The naming convention for the NetCDF files is as follows: UNL.CoMeT3.{deployment date YYYYMMDD}.{start time of observation collection in UTC HHMM}.L2.{post-processing codes}.cdf example: UNL.CoMeT3.20190627.1931.L2.g1.f1.cdf Post-processing codes are included to track modifications to the raw data. These codes are closely connected to error flags associated with each record. Each letter corresponds to a particular instrument: g: GPS p: Barometer tf: Fast temperature ts: Slow temperature rh: Relative humidity f: Compass w: Wind monitor a: All instruments Each number corresponds to a particular post-processing action described more below. Measured and derived variables are included in the following table. Variable Heading Standard Name Units time Time seconds since 00:00:00, 01-01-1970 Alt Altitude meters lat Latitude degrees north lon Longitude degrees east fast_temp Air Temperature kelvin slow_temp Air Temperature kelvin pressure Air Pressure pascals logger_RH Relative Humidity percent calc_corr_RH Relative Humidity percent wind_speed Wind Speed meters per second wind_dir Wind From Direction degrees vehicle_dir Vehicle Direction degrees dewpoint Dew Point Temperature kelvin mixing_ratio Humidity Mixing Ratio g/g theta Air Potential Temperature kelvin theta_v Virtual Potential Temperature kelvin theta_e Equivalent Potential Temperature Kelvin error_flag The error_flag variable is a string that matches the post-processing codes listed above. All instruments will have an associated code, but will have a “0” if the datum is unchanged from the initial processed value. Error Codes The following table summarizes the error codes for data collected before 2020: Error Code Relevant CoMeT Description g1 1,2,3 Exact correction. GPS position and time reprocessed from raw data g2 1 As far as we can tell this is an exact correction to an error in the GPS time. During the correct time periods the time suddenly went backwards ~250s and stayed at this offset for 750s when it corrected itself. The offset was applied to the “time warp” period. p1 2 Approximate correction. Hole in the pressure tube connecting the pressure port to the barometer. Resulted in erroneously low air pressure measurements when the vehicle was in motion. Derived variables recalculated (dew point temperature [e depends on qv and p], water vapor mixing ratio, potential temperature, virtual potential temperature, equivalent potential temperature) a1 3 Exact correction. Missing data reprocessed from raw data a2 1 Bug fix to bias correction for ts1, ts2, and rh1: water vapor mixing ratio was off by a factor of 10 and virtual potential temperature was wrong because of this. f1 3 No correction, missing data. Fluxgate compass inoperable. Wind speed and direction calculated using GPS-derived vehicle heading instead. rh1 1 Approximate correction. Constant bias of +1.7% removed from relative humidity. Derived variables recalculated (corrected/fast relative humidity, dew point temperature, water vapor mixing ratio, virtual potential temperature, equivalent potential temperature) ts1 1 Approximate correction. Constant bias of +0.6 K removed from slow temperature. Derived variables recalculated (corrected/fast relative humidity, dew point temperature, water vapor mixing ratio, virtual potential temperature, equivalent potential temperature) ts2 1 Approximate correction. Constant bias of +1.0 K removed. Derived variables recalculated (corrected/fast relative humidity, dew point temperature, water vapor mixing ratio, virtual potential temperature, equivalent potential temperature) References Bolton, D., 1980: The Computation of Equivalent Potential Temperature. Mon. Wea. Rev., 108, 1046–1053, https://doi.org/10.1175/1520-0493(1980)108<1046:TCOEPT>2.0.CO;2. Hanft, W., and A. L. Houston, 2018: An Observational and Modeling Study of Mesoscale Air Masses with High Theta-E. Mon. Wea. Rev., 146, 2503–2524, https://doi.org/10.1175/MWR-D-17-0389.1.Wexler Houston, A. L., R. J. Laurence III, T. W. Nichols, S. Waugh, B. Argrow, and C. L. Ziegler, 2016: Intercomparison of unmanned aircraft-borne and mobile mesonet atmospheric sensors. Journal of Atmospheric and Oceanic Technology. 33, 1569-1582, doi: 10.1175/JTECH-D-15-0178.1. Lowe, P. R., 1977: An Approximating Polynomial for the Computation of Saturation Vapor Pressure. J. Applied Meteorology, 16, 100–103. Richardson, S. J., S. E. Frederickson, F. V. Brock, and J. A. Brotzge, 1998: Combination temperature and relative humidity probes: Avoiding large air temperature errors and associated relative humidity errors. Preprints, 10th Symp. On Meteorological Observations and Instrumentation, Phoenix, AZ, Amer. Meteor. Soc., 278–283. Waugh, S., and S. E. Frederickson, 2010: An improved aspirated temperature system for mobile meteorological observations, especially in severe weather. 25th Conf. on Severe Local Storms, Denver, CO, Amer. Meteor. Soc., P5.2. [Available online at https://ams.confex.com/ams/25SLS/techprogram/paper_176205.htm.]

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Dose Rate Analysis of the WCS Consolidated Interim Storage Facility

This report describes a confirmatory calculation for a proposed consolidated interim storage facility (CISF) to support the US Nuclear Regulatory Commission’s review of the license application submitted by the Interim Storage Partners. The scope of this report is limited to an assessment of the annual dose from direct radiation associated with Phase 1 of the Waste Control Specialists (WCS) CISF and the determination of the minimum controlled area boundary based on the 10 CFR 72.104 limit of 25 mrem annual dose to the whole body. The confirmatory dose rate calculations used the source term and shielding calculation capabilities of the SCALE 6.2.3 computer code system. The calculation method employed in the confirmatory calculations uses a detailed Monte Carlo radiation transport simulation from source to dose rate. This method differs from the two-step method used in the safety analysis report (SAR), which requires determination of the photon and neutron energy and angular distributions on the cask external surface and then the use of this surface source in a new radiation transport calculation to determine dose rate as a function of distance from the storage facility. A simulation was made using the complete site geometry (all casks present) but with only one cask containing source, and a total of 467 independent calculations were performed to obtain the dose rate maps produced by each storage cask. Basic input data and assumptions used in the SAR (e.g., cask design parameters and design basis assembly characteristics) were used in this confirmatory calculation for consistency with the SAR. Local atmospheric conditions for skyshine calculations were simulated using US standard atmosphere data, which describe average air temperature, pressure, and density as a function of altitude. The determined minimum required distances from the WCS Phase 1 CISF to a contour defined by the 25 mrem annual dose limit were approximately 623 m (0.387 miles) in the N-NE direction, 594 m (0.369 miles) in the SSW direction, and 533 m (0.331 miles) in the E-SE direction and the W-NW direction. The annual dose results of the confirmatory calculation are in relatively good agreement with the annual dose values presented in the WCS SAR. The annual dose produced by the Phase 1 CISF at the nearest site boundary, 0.75 miles away from the CISF, was estimated by this study to be approximately 6.02E-02 ± 2.0E-04 mrem, which is significantly smaller than the 25 mrem annual dose limit provided in 10 CFR 72.104. The SAR annual dose rate value for the nearest site boundary was 7.52E-2 mrem, which included 7.73E-03 mrem due to postulated leakage of the FO-, FC-, and FF-canisters. A comparison with the dose rate values reported in the SAR for 16 detector locations, D1 through D16, on the protected area boundary is also included in this report. This comparison shows that the SAR determined higher annual dose values for detectors D1 through D14 by 12% to 45% and lower annual dose values for detectors D15 and D16 by 18% and 8%, respectively, as compared with this ORNL confirmatory calculation. Sensitivity studies have been performed to support a comprehensive review of the application. In these studies, the effects on dose rate of the modeled air volume, density, and humidity were analyzed. The sensitivity calculations showed that the air volume used in the Monte Carlo simulations was adequate and that a larger air volume would not further increase the dose rate due to skyshine contributions. The sensitivity analysis showed that simulation of local atmospheric conditions is important for the accuracy of dose rate estimates at large distances from the facility. Air humidity was demonstrated to have negligible effects on dose rate values for the simulated local atmospheric conditions.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2025

Neutron irradiation & thermomechanical experiment (NITE) - design

For the reliable long-term operation of fusion power plants, it is crucial to understand and predict the lifetime of materials in use. These materials include all structural and functional materials utilized at the first wall, blanket, magnets, and shielding. The key challenge is, that the harsh environment including high heat fluxes, high thermal stress and stress cycling, neutron irradiation, and sputtering on such materials should not be viewed separately. Currently, the synergistic loads cannot be evaluated experimentally because of the lack of adequate facilities. The purpose of that work is to design a synergetic Neutron Irradiation and Thermomechanical Experiment (NITE) for fusion materials. This design will leverage the existing Advanced-Test-Reactor (ATR), a fission reactor at the Idaho National Laboratory. We also acknowledge that with existing fission reactors the exact fusion condition cannot be created, and the limitations are critically discussed. The combination of neutron irradiation with a high heat flux is the focus. This is realized with an irradiation capsule design that includes a TRISO fueled region inside the capsule to enable a steady-state heat flux on one side of the specimen. In conclusion, the experimental design modeling showed that steady-state heat fluxes of 2.4 MW/m 2 with a thermal gradient of above 250°C can be achieved in a 5 mm thick specimen.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

A Supply Chain Road Map for Offshore Wind Energy in the United States

"A Supply Chain Road Map for Offshore Wind Energy in the United States" identifies pathways to developing a domestic offshore wind supply chain that can manufacture and deploy the major components needed to set the United States on a pathway to installing 30 GW of offshore wind by 2030 and 110 GW by 2050. The report estimates that this supply chain could require an investment of at least $\$$22.7 billion this decade to meet an annual demand for components, ports, and vessels in 2030. Although this is a considerable investment, it could allow the industry to install around $\$$100 billion worth of offshore wind this decade by reducing risk of delays due to global supply chain bottlenecks and creating a robust network of assets that will continue to be effective well beyond 2030. The United States would need at least 34 manufacturing facilities employing 10,000 workers, 39,000 jobs in the supporting supply chain, 10 marshaling ports, 4-6 dedicated wind turbine installation vessels, 4-6 dedicated heavy-lift vessels, and 4-8 U.S.-flagged specialized feeder barges to come online this decade to support an average annual deployment of 4-6 gigawatts offshore wind capacity per year. This supply chain could be developed in 6-9 years, but would require near-term decision making and efficient permitting and planning to strategically develop these resources by 2030. Additional investment and expansion would be required in the 2030s as the sector expands into new regions (such as the Gulf of Mexico) and new technologies (such as larger wind turbines and floating wind energy projects). Furthermore, the planning process needs to meaningfully engage with communities that will be impacted by supply chain expansion to achieve just outcomes and maximize benefits to these stakeholders, which will result in a more equitable and sustainable supply chain. While U.S. offshore wind has made significant progress in recent years, remaining supply chain challenges include uncertainty surrounding deployment and procurement timelines; a lack of port and vessel infrastructure; and limitations in the available workforce, supporting supplier networks, and energy justice best practices. However, many of these problems can be addressed through improved communication between key stakeholder groups, support from federal and state governments, and forward-thinking designs of supply chain assets to accommodate future technology changes for fixed-bottom and floating offshore wind. Although it is a significant task, developing these domestic capabilities represents a once-in-a-generation opportunity to contribute to a decarbonized energy future and also create massive economic benefits that are distributed throughout the country.

17 WIND ENERGY↗

DOE OSTI2023

The Impacts of Developing a Port Network for Floating Offshore Wind Energy on the West Coast of the United States

Floating offshore wind is a pre-commercial industry with the potential for significant market growth on the U.S. West Coast in the near future; however, significant investment in port infrastructure will be required to enable the industry to progress from demonstration projects to efficient and cost effective commercial deployment. Developing a system of ports that can enable commercial-scale floating wind development on the West Coast of the United States will require significant levels of funding and coordination between governments, industry, ports, and local communities. A critical first step to strategically planning these resources is understanding the number of ports (and associated investment) that would be required to support different phases of offshore wind projects, including manufacturing, installation, and operation. But simply tallying up these costs is not sufficient to understand how a robust network of ports could impact local communities, the environment, workforce development, the offshore wind industry, and the West Coast region as a whole. In this report, the authors present analyses and perspectives related to port development in California, Oregon, and Washington. We describe the requirements for floating offshore wind ports that conduct manufacturing, installation, and/or service activities, and estimate the investment and time frames required to construct these ports at suitable locations in West Coast states. We develop indicators for the vulnerability and workforce accessibility of coastal communities and consider the potential risks and benefits associated with port development in these locations. We model how the proximity of an offshore wind project to installation and operations ports can impact the levelized cost of energy of the project, and then consider how these costs could be affected by local or foreign supply chains. We build upon these analyses to develop scenarios with increasing levels of offshore wind deployment and port assets on the West Coast and show how these ports could enable deployment goals to be achieved. Finally, we draw upon outreach with key floating wind stakeholders to summarize five key challenges that will need to be overcome to develop a comprehensive port network, and present potential approaches that could help to address these obstacles.

17 WIND ENERGY↗

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↗