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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Influence on Structural Loading of a Wave Energy Converter by Controlling Variable-Geometry Components and the Power Take-Off

Oceans are harsh environments and can impose significant loads on deployed structures. The deployment of wave energy converters (WECs) faces a design challenge with apparently contradictory goals. A WEC should be designed to maximize the energy absorbed while ensuring the operating wave condition does not exceed the failure limits of the device itself. Therefore, the loads endured by the support structure are a design constraint for the system. Adaptability to different sea states is, therefore, highly desirable. This work uses a WEC-Sim model of a variable-geometry oscillating wave energy converter (VGOSWEC) mounted on a support structure simulated under different wave scenarios. A VGOSWEC resembles a paddle pitching about a fixed hinge perpendicular to the incoming wave fronts. Therefore, the hinge experiences loads perpendicular to its axis as it maintains its position. The geometry of the VGOSWEC is varied by opening a series of controllable flaps on the pitching paddle when the structure experiences threshold loads. Because opening the flaps lets the waves transmit through the paddle, it is hypothesized that opening the flaps should result in load shedding at the base of the support structure. The load shedding is achieved by reducing the moments about the hinge axis. This work compares the hydrodynamic coefficients, natural periods, and response amplitude operators from completely closed to completely open configurations of the controllable flaps. The comparisons quantify the effects of letting the waves transmit through the VGOSWEC. This work shows that the completely open configuration can reduce the pitch and surge loads on the base of the support structure by as much as 80%. It was observed that at the paddle's resonance frequency, the loads on the structure increased substantially. This increase in loads can be mitigated by a rotational power take-off damping about the hinge axis. Changing the rotational power take-off damping was identified as an additional design parameter that can be used to control the loads experienced by the WEC's support structure.

fixed and floating structures↗
DOE OSTI2021

Structural basis for the specificity of PPM1H phosphatase for Rab GTPases

LRRK2 serine/threonine kinase is associated with inherited Parkinson’s disease. LRRK2 phosphorylates a subset of Rab GTPases within their switch 2 motif to control their interactions with effectors. Recent work has shown that the metal-dependent protein phosphatase PPM1H counteracts LRRK2 by dephosphorylating Rabs. PPM1H is highly selective for LRRK2 phosphorylated Rabs, and closely related PPM1J exhibits no activity towards substrates such as Rab8a phosphorylated at Thr72 (pThr72). Here, we have identified the molecular determinant of PPM1H specificity for Rabs. The crystal structure of PPM1H reveals a structurally conserved phosphatase fold that strikingly has evolved a 110-residue flap domain adjacent to the active site. The flap domain distantly resembles tudor domains that interact with histones in the context of epigenetics. Cellular assays, crosslinking and 3-D modelling suggest that the flap domain encodes the docking motif for phosphorylated Rabs. Consistent with this hypothesis, a PPM1J chimaera with the PPM1H flap domain dephosphorylates pThr72 of Rab8a both in vitro and in cellular assays. Therefore, PPM1H has acquired a Rab-specific interaction domain within a conserved phosphatase fold.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Influence on Structural Loading of a Wave Energy Converter by Controlling Variable-Geometry Components and the Power Take-Off: Preprint

Oceans are a harsh environment and can impose significant loads on deployed structures. Deployment of wave energy converters (WECs) faces a design challenge with apparently contradictory goals. A WEC should be designed to maximize the energy absorbed while ensuring the operating wave condition does not exceed the failure limits of the device itself. Therefore, the loads endured by the support structure are a design constraint for the system. Adaptability to different sea states is, therefore, highly desirable. This work uses a WEC-Sim model of a Variable Geometry Oscillating Wave Energy Converter (VGOSWEC) mounted on a support structure simulated under different wave scenarios. A VGOSWEC resembles a paddle pitching about a fixed hinge perpendicular to the incoming waves-fronts. Therefore, the hinge experiences loads perpendicular to its axis as it maintains its position. The geometry of the VGOSWEC was varied by opening a series of controllable flaps on the pitching paddle when the structure experiences threshold loads. Since opening the flaps lets the waves transmit through the paddle, it is hypothesized that opening the flaps should result in load shedding at the base of the support structure. This load shedding is achieved by reducing the moments about the hinge axis. This work compares the hydrodynamic coefficients, natural periods, and Response Amplitude Operators (RAOs) from completely closed to completely open configurations of the controllable flaps. These comparisons quantify the effects of letting the waves transmit through the VGOSWEC. This work shows that the completely open configuration can reduce the pitch and surge loads on the base of the support structure by as much as 80%. It was observed that at the paddle's resonance frequency, the loads on the structure increased substantially. This increase in loads can be mitigated by a rotational Power Take-off (PTO) damping about the hinge axis. Changing the rotational PTO damping was identified as an additional design parameter that can be used to control the loads experienced by the WEC's support structure.

fixed and floating structures↗
DOE OSTI2021

Design of a 3.4-MW wind turbine with integrated plasma actuator-based load control

Historically, cost reduction in wind energy has been accomplished by increasing hub heights and rotor diameters to capture more energy per turbine. The growth in rotor and turbine costs with increasing turbine sizes is also driven by the additional structure that must be added to withstand unsteady aerodynamic loads caused by turbulence, gusts, wind shear, misaligned yaw, upwind wakes, and the tower shadow. In this paper, we present a holistic design solution to integrate active load control using a controllable Gurney flap based on plasma actuators. We illustrate the design solution for a land-based 3.4-MW wind turbine rotor. Comparisons to a baseline reference 3.4-MW wind turbine show significant load reduction (15–18% DEL reduction for flap-wise blade root moments), rotor mass reduction (5–8%), and LCOE reduction (1.16–3.11%). To achieve these results, a comprehensive sequential-iterative design procedure is introduced to integrate the controllable Gurney flap into the turbine design and to drive the design solution toward the best LCOE reduction solution. Results are presented for mapping fatigue load reductions into cost reductions. In addition, an evaluation of active load control extended from Region-III to also include Region-II showed a further 34% reduction in DEL.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

TEAMER: Water Tunnel Data from Testing the Pterofin Skimmer Concept

Pterofin's Skimmer concept relies on a flapping and pitching hydrofoil to extract hydrokinetic energy from water flows. The concept aims to utilize unsteady fluid dynamics phenomena (added mass, shed vorticity, and unsteady boundary layer development) to achieve higher lift coefficients, enabling increased power density of the hydrokinetic device and a fundamental shift in the rpm/torque scaling of the power take off compared with turbines. The Applied Research Laboratory at Penn State, in collaboration with Pterofin, designed and built a proof-of-concept flapping/pitching mechanism which was subsequently tested in ARL's 12-inch water tunnel facility. The mechanical power supplied to or extracted from the mechanism was measured for a range of hydrofoils provided by Pterofin over operating conditions including reduced frequency, Reynolds number, and the ratio between pitching and flapping amplitudes. The power lost to friction in the mechanism was removed from the net power measurement by means of a bare hub tare, with the resultant hydrodynamic power being used to calculate a mechanism-independent and non-dimensional power coefficient. The product of this effort is a dataset describing the power coefficient of a hydrofoil having simultaneous pitching and flapping motions, both of which are approximately sinusoidal. Power coefficients were collected for a range of primary design variables including: - Reduced frequency: 0.01 to 0.95 - Pitching/flapping peak angle ratio: 1.5 to 3.0 - Chord-based Reynolds number: 60,000 to 560,000 Secondary design variables relating to the hydrofoil geometry were explored including: - Aspect ratio - Planform shape - Section thickness distribution - Hydrofoil position relative to the pitching axis - Hydrofoil sweep angle relative to the pitching axis Measured data are provided in mean and time series formats. MATLAB scripts are provided which can be used to generate figures of time-averaged and phase-averaged hydrodynamic power coefficients calculated from the measured data. A complete description of the experiment and data reduction can be found in the Post Access Report for the Pterofin Skimmer test effort which will be available on the TEAMER website. This work was supported by the Pacific Energy Ocean Trust via a TEAMER award.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Towards an intuitive application of WEC control co-design

A simple co-design example in a reduced parameter space is presented for an oscillating flap device. Initially, the WEC geometry and mass properties are considered along with drivetrain gear ratio, inertia, motor constant and stiffness under both PI and optimal control. This parameter space is reduced to those to which performance is most sensitive for a fixed geometry. The gear ratio, drivetrain stiffness, and flap mass are found to be the most impactful design criteria as they can create orders of magnitude variations in power performance. The performance of the optimized system is compared with several sub-optimal variants in terms of electrical and mechanical power capture, transmission coefficients, and transducer power gain. Notably, though substantial power capture improvements are demonstrated when an optimal controller is employed, this power capture remains sensitive to appropriate selections of drivetrain and flap design parameters, implying that control co-design procedures remain necessary for high-performing WECs. Furthermore, a number of practical caveats and extensions to the presented co-design methodology are suggested, including the characterization of system static friction, especially in the presence of high gear ratios.

Control co-design↗
DOE OSTI2023

Influence on Structural Loading of a Wave Energy Converter by Controlling Variable-Geometry Components and the Power Take-Off

Oceans are harsh environments and can impose significant loads on deployed structures. A wave energy converter (WEC) should be designed to maximize the energy absorbed while ensuring the operating wave condition does not exceed the failure limits of the device itself. Therefore, the loads endured by the support structure are a design constraint for the system. Furthermore, the WEC should be adaptable to different sea states. Herethis work uses a WEC-Sim model of a variable-geometry oscillating wave energy converter (VGOSWEC) mounted on a support structure simulated under different wave scenarios. A VGOSWEC resembles a paddle pitching about a fixed hinge perpendicular to the incoming wave fronts. The geometry of the VGOSWEC is varied by opening a series of controllable flaps on the pitching paddle when the structure experiences threshold loads. It is hypothesized that opening the flaps should result in load shedding at the base of the support structure by reducing the moments about the hinge axis. This work compares the hydrodynamic coefficients, natural periods, and response amplitude operators from completely closed to completely open configurations of the controllable flaps. This work shows that the completely open configuration can reduce the pitch and surge loads on the base of the support structure by as much as 80%. Increased loads at the structure’s natural period can be mitigated by an axial power take-off damping acting as an additional design parameter to control the loads at the WEC’s support structure.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

Hawaii Wave Surge Energy Converter (HAWSEC) OSU O.H. Hinsdale Basin

The following information and metadata applies to both the Phase I (Hydrodynamics) and Phase II (Full System Power Take-Off) zip folders which contain testing data from the OSU (Oregon State University) O.H. Hinsdale Wave Research Laboratory, from both OSU and the University of Hawaii at Manoa (UH). See zip folders provided further below in the downloads section. For experimental data of the full system, including PTO, see Phase II dataset. There are two main directories in each Phases's zip folder: "OSU_data" and "UH_data". The "OSU_data" directory contains data collected from their DAQ (data acquisition system), which includes all wave gauge observations, as well as body motions derived from their Qualisys motion tracking system. The organization of the directory follows OSU's convention. Detailed information on the instrument setup can be found under "OSU_data/docs/setup/instm_locations". The experiments conducted are documented in the "OSU_data/docs/daq_logs", which provides the trial number to the corresponding data located under "OSU_data/data" in several formats (e.g., ".mat" and ".txt"). Inside the trial directory, data is provided for each of the instruments defined in "OSU_data/docs/setup/instm_locations". The "UH_data" directory contains data collected from their DAQ. The data is stored in a ".tdms" file format. There are free plug-ins for Microsoft Excel and MathWorks MATLAB to read the ".tdms" format. Below are a few links providing methods to read in the data, but a Google search should identify alternatives sources if these no longer exist (valid as of January 2024): Excel: http://www.ni.com/example/27944/en/ MATLAB: https://www.mathworks.com/matlabcentral/fileexchange/30023-tdms-reader The Excel plugin is recommend to get a quick overview of the data. The UH data is organized by directory name, in which the sub-directories for each experiment contains a directory whose name defines the wave height and period for the experimental data within. For example, a directory name "H02_T0275" corresponds to an experiment with wave height 0.1m and a period of 2.75s. For random wave data, the gamma value is also included in the directory name. For example, a directory name "H02_T0225_G18" corresponds to an experiment with a significant wave height of 0.2m, a peak period of 2.25s, and a gamma value of 1.8, with each spectra being a TMA spectrum. For the free decay experiments, the directory name is defined by the initial angular displacement. For example, a directory name "ang05_run01" corresponds to an experiment with an initial angular displacement of 5 degrees. There is a dataset in the UH data for each corresponding experiment defined in the OSU DAQ logs. The ".tdms" data is output from the DAQ at fixed intervals. Therefore, if multiple files are contained within the folder, the data will need to be stitched together. Within the UH dataset, there are two input channels from the OSU DAQ providing a random square wave signal for time synchronization ("ENV-WHT-0010") and a high/low signal ("ENV-WHT-0012") to identify when the wave maker is active (+5V). The UH data is logged as a collection of channel outputs. Channels not in use for the OSU testing (either Phase I or Phase II) are marked "nan" below. If the sensor is disconnected, it will record noise throughout the experiment. Below are the channel definitions in terms of what they measure: GPS Time = time CYL-POS-0001 = position between flap and fixed reference CYL-LCA-0001 = force between flap and hydraulic cylinder REC-LPT-0001 = nan REC-HPT-0001 = nan REC-HPT-0002 = nan REC-HPT-0003 = nan HHT-HPT-0001 = pressure at exhaust ("head" only) REC-FQC-0001 = nan REC-FQC-0002 = nan HHT-FQC-0001 = flow at exhaust ("head" only) ENV-WHT-0001 = nan ENV-WHT-0002 = nan ENV-WHT-0003 = nan ENV-WHT-0010 = random signal from OSU DAQ ENV-WHT-0012 = high/low signal from OSU DAQ Also included is a calibration curve to convert the string pot data to flap pi...

16 TIDAL AND WAVE POWER↗
DOE OSTI2020

Human‐Skin‐Inspired Adaptive Smart Textiles Capable of Amplified Latent Heat Transfer for Thermal Comfort

Thermally adaptive textiles (TATs) enable human subjects to attain thermal comfort without energy consumption, which can lead to enormous energy savings on heating, ventilation, and air conditioning (HVAC) in buildings. Herein, TAT structures which respond to the sweat and generate pores by opening an array of flap‐shaped pores patterned on the fabric surface are proposed. A moisture‐driven self‐actuator for flap opening by constructing a bilayer consisting of a hygroscopic layer using polyethylene glycol and cellulose acetate, and a hydrophobic polymer using a polyester type polymer, is used and successfully demonstrated an essentially instant 4 °C apparent temperature cooling performance within one minute of sweat–humidity‐initiated actuation while wearing TAT using a sweating skin simulated device.

Kim, Gunwoo↗
DOE OSTI2020

Mycobacterial DNA polymerase I: activities and crystal structures of the POL domain as apoenzyme and in complex with a DNA primer-template and of the full-length FEN/EXO–POL enzyme

Mycobacterial Pol1 is a bifunctional enzyme composed of an N-terminal DNA flap endonuclease/5' exonuclease domain (FEN/EXO) and a C-terminal DNA polymerase domain (POL). Here we document additional functions of Pol1: FEN activity on the flap RNA strand of an RNA:DNA hybrid and reverse transcriptase activity on a DNA-primed RNA template. We report crystal structures of the POL domain, as apoenzyme and as ternary complex with 3'-dideoxy-terminated DNA primer-template and dNTP. The thumb, palm, and fingers subdomains of POL form an extensive interface with the primer-template and the triphosphate of the incoming dNTP. Progression from an open conformation of the apoenzyme to a nearly closed conformation of the ternary complex entails a disordered-to-ordered transition of several segments of the thumb and fingers modules and an inward motion of the fingers subdomain—especially the O helix—to engage the primer-template and dNTP triphosphate. Distinctive structural features of mycobacterial Pol1 POL include a manganese binding site in the vestigial 3' exonuclease subdomain and a non-catalytic water-bridged magnesium complex at the protein-DNA interface. We report a crystal structure of the bifunctional FEN/EXO–POL apoenzyme that reveals the positions of two active site metals in the FEN/EXO domain.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

TEAMER: FOSWEC Mooring Modeling and Analysis, Post Access Report and Data

Floating oscillating surge wave energy converters (FOSWECs) offer several advantages over bottom-hinged oscillating surge wave energy converters, including large wave potential at deep-water sites with fewer permitting and environmental concerns outside territorial waters. As a team, Stevens Institute of Technology, Virginia Tech and Resolute Marine Energy are designing a 100 kW FOSWEC with DOE support (2020-2021) for the PacWave test site "PacWave". The proposed FOSWEC consists of a floating platform, two pivoting flaps, and an innovative power-take-off (PTO). The distance between the two flaps is around half the typical wavelength, resulting in out-of-phase motion and a reduction in motion of the frame and mooring loads. The overall goal of the project is to design, build, deploy and analyze a 1:2 scale (100-kW annual averaged electrical power output) device with reduced levelized cost of energy (LCOE) and peak-to-average power ratio, through the co-design and control of the PTO, WEC, and floating platform. This submission includes a Post Access Report and data for the project of Mooring Modeling and Analysis for Floating Oscillating Surge Wave Energy Converter that Powers Marine Aquaculture of RFTS2 (request for technical support). The data are used to generate all figures in the Post Access Report. Project was a collaboration between Virginia Tech and the National Renewable Energy Lab, with funding from TEAMER.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Optimal Control of an Oscillating Surge Wave Energy Converter

During this project, we experimentally investigated the hydrodynamics and performance of a laboratory-scale oscillating surge wave energy converter (OSWEC).We looked at how flap buoyancy and driveline losses (primarily in the form of stiction) affected the dynamics and performance of the device. In addition, we assessed the influence of flap profile (rounded vs. square edges) on OSWEC hydrodynamics. Through this, we were able to develop a deeper understanding of OSWEC performance and provide guidance on strategies to counteract artifacts that may be present in laboratory models, but are absent in field-scale devices. To do this, we tested a laboratory-scale OSWEC in the Sea Wave Environmental Lab (SWEL) wave tank at the National Renewable Energy Laboratory (NREL). We ran several types of experiments to investigate the hydrodynamics and performance of the device. Overall, we achieved the overall goal of experimentally investigating the hydrodynamics and performance of this device. We discovered important and unexpected trends in performance, and collected time-resolved data to help us further investigate the underlying hydrodynamics responsible for these trends. In addition, we are currently using the time-resolved data from these experiments to build data-driven models of the dynamics, which can in turn be used to inform data-driven model predictive control of this device and address this objective in the future.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Hypersonic Fluid–Structure Interaction on a Cone–Slice–Ramp Geometry

In this study, fluid–structure interactions were measured between a representative control surface and the hypersonic flow deflected by it. The control surface is simplified as a spanwise finite ramp placed on a longitudinal slice of a cone. The front surface of the ramp contains a thin panel designed to respond to the unsteady fluid loading arising from the shock-wave/boundary-layer interactions. Experiments were conducted at Mach 5 and Mach 8 with ramps of different angles. High-speed schlieren captured the unsteady flow dynamics and accelerometers behind the thin panel measured its structural response. Panel vibrations were dominated by natural modes that were excited by the broadband aerodynamic fluctuations arising in the flowfield. However, increased structural response was observed in two distinct flow regimes: 1) attached or small separation interactions, where the transitional regime induced the strongest panel fluctuations. This was in agreement with the observation of increased convective undulations or bulges in the separation shock generated by the passage of turbulent spots, and 2) large separated interactions, where shear layer flapping in the laminar regime produced strong panel response at the flapping frequency. In addition, panel heating during the experiment caused a downward shift in its natural mode frequencies.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

FOSWEC v2: System identification and control testing at Hinsdale Wave Research Laboratory

This report summarizes the design and execution of a wave tank test of the floating oscillating surge wave energy converter (FOSWEC) in the O.H. Hinsdale Wave Research Laboratory Directional Wave Basin at Oregon State University. This device, which uses two "flaps" that pivot about a central platform when excited by waves, has a natural frequency within the range of the waves by which it is excited. The FOSWEC was originally considered to be a 1:33 scale device, however, for the current tests, no fixed relative scale is used (i.e., the WEC is considered to be scaled for the basin’s wave environment in which it operates). The primary goal of this test was to assess the degree to which previously developed modeling, experimentation, and control design methods could be applied to a broad range of wave energy converter designs. Testing was conducted to identify a dynamic model for the impedance and excitation behavior of the device. Using these models, a series of closed loop tests were conducted using a causal impedance matching controller. This report provides a brief description of the results, as well as a summary of the device and experimental design. The results show that the methods applied to this experimental device perform well and should be broadly applicable. The data collected during testing is compressed into FOSWEC.zip. Please refer to Appendix C (pages 61-63) of the test report for descriptions of each test ID corresponding to the compressed files.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Performance characterization and modeling of an oscillating surge wave energy converter

Abstract Testing wave energy converters in the ocean could be expensive and complex, which necessitates the use of numerical modeling. However, accurately modeling the response of wave energy converters with high-fidelity simulations can be computationally intensive in the design stage where different configurations must be considered. Reduced-order models based on simplified equations of motion can be very useful in the design, optimization, or control of wave energy converters. Given the complex dynamics of wave energy converters, accurate representation, and evaluation of relative contributions by different forces are required. This effort is concerned with a performance characterization of the hydrodynamic response of an oscillating surge wave energy converter that is based on a reduced-order model. A state-space model is used to represent the radiation damping term. Morison’s representation of unsteady forces is used to account for the nonlinear damping. Wave tank tests are performed to validate simulations. A free response simulation is used to determine the coefficients of the state-space model. Torque-forced simulations are used to identify the coefficients of the nonlinear damping term for different amplitudes and wave frequencies. The impact of varying these coefficients on the response is investigated. An assessment of the capability of the model in predicting the hydrodynamic response under irregular forcing is performed. The results show that the maximum error is 3% when compared with high-fidelity simulations. It is determined that the nonlinear damping is proportional to the torque amplitude and its effects are more pronounced as the amplitude of the flap oscillations increases.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Revisiting Wagner’s Criteria to Predict Establishment and Retention of Alumina Scales on Ternary NiCrAl Alloys

Despite the advent of numerical modeling approaches and high-performance computing infrastructure, the design and development of corrosion-resistant high temperature alloys (> 500 °C) continue to be largely empirical and typically involve extensive experimentation. This is mainly due to the lack of a single unified physics-based model that can address the impact of multiple competing factors such as time, environment, alloy composition, microstructure, and geometry. The classical Wagner’s criteria have been foundational to estimate the minimum concentrations required of an oxide-forming element to establish and sustain a protective oxide scale. However, the formulation is primarily limited to lower-order alloy systems (binary alloys) and ignores the time dependence of subsurface compositional changes in the alloy. The lack of key data on the temperature and composition dependence of the solubility and transport of oxidants in multicomponent-multiphase alloys further exacerbates the problem. In the present work, a few of these limitations were addressed using a flux-based approach (FLAP) which tracks the spatiotemporal evolution of the fundamental flux balance between oxygen and the oxide-forming elements to enable the prediction of the formation of an external alumina scale in ternary NiCrAl alloys. In conclusion, the modeling results were validated with the literature findings and additional experimental work conducted in the present work.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A comprehensive and fair comparison of two neural operators (with practical extensions) based on $\mathrm{FAIR}$ data

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet, was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO, was published in 2020, and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. Here we consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions.

42 ENGINEERING↗