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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗
DOE OSTI2021

Black-Box Neural System Identification and Differentiable Programming to Improve Earth System Model Predictions February

Focal Area(s): Focal Area 2: AI for predictive modeling, including AI-derived model components, and AI-enabled applications including parameter optimization, data assimilation, and uncertainty quantification. Focal Area 1: AI-assisted data assimilation using numerical Earth system models. Science Challenge: Earth system models have structural biases that lead to uncertain predictions, and their complexity and expense makes it difficult constraining the models with data or improved physical understanding.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

The Potential Benefits of Handling Mixture Statistics via a Bi-Gaussian EnKF: Tests With All-Sky Satellite Infrared Radiances

The meteorological characteristics of cloudy atmospheric columns can be very different from their clear counterparts. Thus, when a forecast ensemble is uncertain about the presence/absence of clouds at a specific atmospheric column (i.e., some members are clear while others are cloudy), that column's ensemble statistics will contain a mixture of clear and cloudy statistics. Such mixtures are inconsistent with the ensemble data assimilation algorithms currently used in numerical weather prediction. Hence, ensemble data assimilation algorithms that can handle such mixtures can potentially outperform currently used algorithms. In this study, we demonstrate the potential benefits of addressing such mixtures through a bi-Gaussian extension of the ensemble Kalman filter (BGEnKF). The BGEnKF is compared against the commonly used ensemble Kalman filter (EnKF) using perfect model observing system simulated experiments (OSSEs) with a realistic weather model (the Weather Research and Forecast model). Synthetic all-sky infrared radiance observations are assimilated in this study. In these OSSEs, the BGEnKF outperforms the EnKF in terms of the horizontal wind components, temperature, specific humidity, and simulated upper tropospheric water vapor channel infrared brightness temperatures. This study is one of the first to demonstrate the potential of a Gaussian mixture model EnKF with a realistic weather model. Our results thus motivate future research toward improving numerical Earth system predictions though explicitly handling mixture statistics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Early season prediction of within-field crop yield variability by assimilating CubeSat data into a crop model

Accurate early season predictions of crop yield at the within-field scale can be used to address a range of crop production, management, and precision agricultural challenges. While the remote sensing of within-field insights has been a research goal for many years, it is only recently that observations with the required spatio-temporal resolutions, together with efficient assimilation methods to integrate these into modeling frameworks, have become available to advance yield prediction efforts. Here we explore a yield prediction approach that combines daily high-resolution CubeSat imagery with the APSIM crop model. The approach employs APSIM to train a linear regression that relates simulated yield to simulated leaf area index (LAI). That relationship is then used to identify the optimal regression date at which the LAI provides the best prediction of yield: in this case, approximately 14 weeks prior to harvest. Instead of applying the regression on satellite imagery that is coincident, or closest to, the regression date, our method implements a particle filter that integrates CubeSat-based LAI into APSIM to provide end-of-season high-resolution (3 m) yield maps weeks before the optimal regression date. The approach is demonstrated on a rainfed maize field located in Nebraska, USA, where suitable collections of both imagery and in-situ data were available for assessment. The procedure does not require in-field data to calibrate the regression model, with results showing that even with a single assimilation step, it is possible to provide yield estimates with good accuracy up to 21 days before the optimal regression date. Yield spatial variability was reproduced reasonably well, with a strong correlation to independently collected measurements (R 2 = 0.73 and rRMSE = 12%). When the field averaged yield was compared, our approach reduced yield prediction error from 1 Mg/ha (control case based on a calibrated APSIM model), to 0.5 Mg/ha (using satellite imagery alone), and then to 0.2 Mg/ha (results with assimilation up to three weeks prior to the optimal regression date). Such a capacity to provide spatially explicit yield predictions early in the season has considerable potential to enhance digital agricultural goals and improve end-of-season yield predictions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Assimilation of Satellite-Derived Soil Moisture for Improved Forecasts of the Great Plains Low-Level Jet

In the context of forecasting societally impactful Great Plains low-level jets (GPLLJs), the potential added value of satellite soil moisture (SM) data assimilation (DA) is high. GPLLJs are both sensitive to regional soil moisture gradients and frequent drivers of severe weather, including mesoscale convective systems. An untested hypothesis is that SM DA is more effective in forecasts of weakly synoptically forced, or uncoupled GPLLJs, than in forecasts of cyclone-induced coupled GPLLJs. Using the NASA Unified Weather Research and Forecasting (NU-WRF) Model, 75 GPLLJs are simulated at 9-km resolution both with and without NASA Soil Moisture Active Passive SM DA. Differences in modeled SM, surface sensible (SH) and latent heat (LH) fluxes, 2-m temperature (T2), 2-m humidity (Q2), PBL height (PBLH), and 850-hPa wind speed (W850) are quantified for individual jets and jet-type event subsets over the south-central Great Plains, as well as separately for each GPLLJ sector (entrance, core, and exit). At the GPLLJ core, DA-related changes of up to 5.4 kg m–2 in SM can result in T2, Q2, LH, SH, PBLH, and W850 differences of 0.68°C, 0.71 g kg –2 , 59.9 W m –2 , 52.4 W m –2 , 240 m, and 4 m s –1 , respectively. W850 differences focus along the jet axis and tend to increase from south to north. Further, jet-type differences are most evident at the GPLLJ exit where DA increases and decreases W850 in uncoupled and coupled GPLLJs, respectively. Data assimilation marginally reduces negative wind speed bias for all jets, but the correction is greater for uncoupled GPLLJs, as hypothesized.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

On the dual advantage of placing observations through forward sensitivity analysis

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Integration of seismic-pressure-petrophysics inversion of continuous active-seismic monitoring data for monitoring and quantifying CO 2 plume (Final Report)

The overall objective of this project is to develop and validate an integrated package of joint seismic-pressure-petrophysics inversion (jSPPI) of continuous active-source seismic monitoring dataset capable of providing real-time monitoring of CO 2 plume during geologic carbon sequestration (GCS). The three specific developments include: (a) the methodologies for fast seismic full waveform inversion of continuous active source seismic monitoring, (CASSM) datasets for simultaneously estimating velocity and attenuation, and with data assimilation; (b) joint Bayesian petrophysical inversion of seismic models and pressure data for providing and updating CO 2 saturation models; (c) the methods using multiple datasets including (Crainfield and Frio-II borehole) synthetic, laboratory, and field CASSM datasets. The outcomes of jSPPI include (a) a workflow for processing CASSM data, (b) Bayesian inversion algorithms using CASSM data and pressure response data, and (c) integration with data assimilation algorithms for continuously updating site-specific models used for prediction and reservoir management. The validation of joint FWI will be conducted using synthetic models based on the Cranfield and Frio experiments as well as field CASSM datasets collected as part of the Frio-II pilot injection. To quantify and map the mass and distribution of CO 2 (saturation), we will jointly invert velocity and attenuation measurements from the FWI with a Bayesian approach using a rock physics model for attenuation (e.g., White’s attenuation model with two selected patch sizes (White, 1976; Dutta and Seriff, 1979)). The Bayesian inversion will be applied to each time step in the CASSM survey in an updating scheme, which integrates with an ensemble of reservoir simulations at each step. A more complete experimental validation dataset will be collected as part of a mesoscale (2-3 m) gas-CO 2 injection experiment utilizing a higher frequency version of the CASSM system developed for laboratory studies; the integrated inversion will be demonstrated using this dataset which will provide both a dense geometry as well as more precise secondary confirmation measurements (e.g. saturation) typically not available in the field. The resulting real-time map of CO 2 saturation is able to provide a deeper scientific understanding of the complex, time-varying dynamics of subsurface fluid flow migration path as well as the rapid detection of CO 2 leakage hazards.

25 ENERGY STORAGE↗
DOE OSTI2025

A 1 km soil moisture dataset over eastern CONUS generated by assimilating SMAP data into the Noah-MP land surface model

An improved fine-scale soil moisture (SM) dataset at 1 km grid spacing, covering much of the eastern continental US, was generated by assimilating 9 km Soil Moisture Active Passive (SMAP) SM data into the v4.0.1 Noah-MP land surface model. With 12 ensemble members, the assimilation was carried out using the ensemble Kalman filter algorithm within NASA's Land Information System. The SM analysis for 2016 was fully validated against in situ observations from four different networks and compared with four other existing datasets. Results indicate that this SM analysis surpasses other datasets in top-layer SM distribution, including a machine-learning-based product, despite all SM estimates being less heterogeneous than observed. The analysis of anomalous errors suggests that large similarity in intrinsic errors is likely due to overlapping data sources among the selected SM datasets. More detailed evaluations were performed over two geographic areas. The observations collected by the Atmospheric Radiation Measurement facility in Oklahoma suggest that soil temperature and surface heat fluxes are concurrently simulated with good accuracy. Investigation into the 2016 southeastern US drought response further indicates drier conditions and higher evapotranspiration estimates compared to GLEAMv4.1. Notably, large errors are associated with grids having clay soil textures, underscoring the need for refined model treatments for specific soil types to further improve SM estimates. The dataset is publicly available on Zenodo at https://doi.org/10.5281/zenodo.14370563 (Tai et al., 2024).

Tai, Sheng-Lun [Pacific Northwest National Laborat↗
DOE OSTI2024

MITgcm-AD v2: Open source tangent linear and adjoint modeling framework for the oceans and atmosphere enabled by the Automatic Differentiation tool Tapenade

The Massachusetts Institute of Technology General Circulation Model (MITgcm) is widely used by the climate science community to simulate planetary atmosphere and ocean circulations. A defining feature of the MITgcm is that it has been developed to be compatible with an algorithmic differentiation (AD) tool, TAF, enabling the generation of tangent-linear and adjoint models. These provide gradient information which enables dynamics-based sensitivity and attribution studies, state and parameter estimation, and rigorous uncertainty quantification. Importantly, gradient information is essential for computing comprehensive sensitivities and performing efficient large-scale data assimilation, ensuring that observations collected from satellites and in-situ measuring instruments can be effectively used to optimize a large uncertain control space. As a result, the MITgcm forms the dynamical core of a key data assimilation product employed by the physical oceanography research community: Estimating the Circulation and Climate of the Ocean (ECCO) state estimate. Although MITgcm and ECCO are used extensively within the research community, the AD tool TAF is proprietary and hence inaccessible to a large proportion of these users. The new version 2 (MITgcm-AD v2) framework introduced here is based on the source-to-source AD tool Tapenade, which has recently been open-sourced. Another feature of Tapenade is that it stores required variables by default (instead of recomputing them) which simplifies the implementation of efficient, AD-compatible code. The framework has been integrated with the MITgcm model’s main branch and is now freely available.

Adjoints↗
DOE OSTI2025

Global teleconnections influencing large-scale drought in the United States using SVDI

Understanding recent large-scale drought patterns and the mechanisms producing extreme drought events is vital for future drought forecasts and understanding future drought risks. Increasingly, vapor pressure deficit (VPD) has been used as an important measure of evaporative demand and proxy for drought detection. In this study, VPD is used to calculate the new Standardized VPD Drought Index (SVDI) with NASA North American Land Data Assimilation System (NLDAS) data. Previous studies have shown that SVDI accurately identifies the timing and magnitude short-term droughts in the United States (U.S). In the present study, SVDI is now used to identify large-scale drought patterns between 1980 and 2021 and drought variability driven by selected global teleconnections originating in the Pacific and Atlantic Oceans. Spatial drought characteristics were extracted from SVDI using empirical orthogonal function (EOF) analysis. Then a k-means clustering algorithm was applied to both EOF principal components and primary teleconnections, including the El Nino-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) to identify drought events driven by the Pacific Ocean. Results show that the SVDI is useful in evaluating large-scale drought variability in the U.S. related to global teleconnections, and that mechanisms influencing summer drought patterns in the Western and Southwestern U.S. are driven by a tropical-extratropical interactions originating in the equatorial Pacific Ocean related to ENSO dynamics with interdecadal variability modulated by PDO. The large-scale droughts in the Central and Southern U.S., like those in 2011 and 2012, on the other hand, are driven by the North Pacific Ocean warm pool during a strong negative PDO, which subsequently influenced variability in the Bermuda-Azores High in the Atlantic Ocean. In summer 2011, the Bermuda-Azores High weakened, reducing the onshore winds and moisture transport along the eastern Gulf of Mexico and contributing to ongoing drought in the region. The Northern Pacific and Atlantic Ocean sea surface temperatures (SSTs) have increased between 1980 and 2021. In conclusion, as SSTs continue to rise in the Northern Pacific Ocean, one consequence of the coupled North Pacific warm pool and atmospheric dynamics, is to increase summer drought variability over a large region in the southern and midwestern U.S. under global warming.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Super Resolution for Renewable Energy Resource Data With Wind From Reanalysis Data (Sup3rWind) and Application to Ukraine [Slides]

In this work we present a novel deep learning-based downscaling method, using generative adversarial networks (GANs), for generating high-resolution wind resource data from ECMWF Reanalysis v5 data (ERA5). We show that by training a GAN model on ERA5, as opposed to coarsened high-resolution data, we achieve results that are competitive with conventional dynamical downscaling. This GAN-based downscaling method additionally reduces computational costs over dynamical downscaling by two orders of magnitude. All GANs are trained on data sampled from CONUS, selected to provide a diverse sampling of terrain conditions, and validated on observational data along with data held out from training. This cross-validation shows low error and high correlations with observations and excellent agreement with hold out data across physical distributions. Our approach is finally used to downscale 30km hourly ERA5 to 2-km 5-minute wind data, for January 2000 through December 2023, at multiple hub heights, over Ukraine, Moldova, and part of Romania. Comparisons against observational data from Meteorological Assimilation Data Ingest System (MADIS) and multiple wind farms show the same level of performance as for CONUS validation. This 24 year data record is the first member of the "super resolution for renewable energy resource data with wind from reanalysis data" dataset (Sup3rWind).

17 WIND ENERGY↗
DOE OSTI2021

Assimilation of Multiscale Data into Multifidelity Biogeochemical Models (Final Report)

Quantitative predictions of subsurface processes rely on computational models that capture, with different degrees of fidelity, complex interactions between hydrologic and biogeochemical processes. Molecular- and pore-scale models provide a high-fidelity representation of these processes but are impractical at the field scale. Reduced complexity (e.g., field-scale or data-driven) models sacrifice some degree of fidelity in favor of computational efficiency. Uncertainty and assimilation of data into model predictions, pose a question of model selection: Given a significant difference in computational cost, can a lower-fidelity model be preferable to its higher-fidelity counterpart? Since a predictive model must be computable in reasonable time it has to operate at the field scale, with molecular- and pore-scale data (obtained either from simulations or measurements) determining both the model's structure and parameters. Availability of such multi-resolution data raises a question hitherto undressed in hydrogeology: Can a coarse model dynamically ``learn'' its own structure (e.g., adjust the reaction pathways in its transport module) as more fine-scale data become available during simulations? Our results in multifidelity simulations, data assimilation, and machine learning led us to hypothesize that the answer to these questions is ``yes''. The overarching goal of this project was to confirm this hypothesis by developing scalable, computationally efficient tools for assimilation of data into multiscale models, in which fine-scale data and simulations dynamically inform and autonomously modify coarse-scale models. Our research led to nine manuscripts, three of which have been published and the other six are currently under review.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2022

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Estimating Ocean Observation Impacts on Coupled Atmosphere‐Ocean Models Using Ensemble Forecast Sensitivity to Observation (EFSO)

Ensemble Forecast Sensitivity to Observation (EFSO) is a technique that can efficiently identify the beneficial/detrimental impacts of every observation in ensemble-based data assimilation (DA). While EFSO has been successfully employed on atmospheric DA, it has never been applied to ocean or coupled DA due to the lack of a suitable error norm for oceanic variables. This study introduces a new density-based error norm incorporating sea temperature and salinity forecast errors, making EFSO applicable to ocean DA for the first time. We implemented the oceanic EFSO on the CFSv2-LETKF and investigated the impact of ocean observations under a weakly coupled DA framework. By removing the detrimental ocean observations detected by EFSO, the CFSv2 forecasts were significantly improved, showing the validation of impact estimation and the great potential of EFSO to be extended as a data selection criterion.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .

Srinivasan, Ashwanth↗
DOE OSTI2022

Inferring and evaluating satellite-based constraints on NO x emissions estimates in air quality simulations

Satellite observations of tropospheric NO 2 columns can provide top-down observational constraints on emissions estimates of nitrogen oxides (NO x ). Mass-balance-based methods are often applied for this purpose but do not isolate near-surface emissions from those aloft, such as lightning emissions. Here, we introduce an inverse modeling framework that couples satellite chemical data assimilation to a chemical transport model. In the framework, satellite-constrained emissions totals are inferred using model simulations with and without data assimilation in the iterative finite-difference mass-balance method. The approach improves the finite-difference mass-balance inversion by isolating the near-surface emissions increment. We apply the framework to separately estimate lightning and anthropogenic NO x emissions over the Northern Hemisphere for 2019. Using overlapping observations from the Ozone Monitoring Instrument (OMI) and the Tropospheric Monitoring Instrument (TROPOMI), we compare separate NO x emissions inferences from these satellite instruments, as well as the impacts of emissions changes on modeled NO 2 and O 3 . OMI inferences of anthropogenic emissions consistently lead to larger emissions than TROPOMI inferences, attributed to a low bias in TROPOMI NO 2 retrievals. Updated lightning NO x emissions from either satellite improve the chemical transport model's low tropospheric O 3 bias. The combined lighting and anthropogenic emissions updates improve the model's ability to reproduce measured ozone by adjusting natural, long-range, and local pollution contributions. Thus, the framework informs and supports the design of domestic and international control strategies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Assimilating partial observation to enhance feedback control of stochastic dynamical systems

Here, in this paper, we present a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage partial observation of the state process, a common occurrence in practical scenarios. Traditional stochastic optimal control methods assume full state observation, which is often not feasible in real-world fluid dynamics control problems. Our approach underscores the significance of utilizing observational data to inform control policy design. Specifically, we introduce a kernel learning backward stochastic differential equation (SDE) filter to enhance data assimilation efficiency and propose a sample-wise stochastic optimization method within the stochastic maximum principle framework. We demonstrate the efficacy and accuracy of our method in the control of advection-diffusion-reaction flow problem and the Dubins airplane maneuvering problem with model uncertainty.

data driven↗
DOE OSTI2022

Neural operator prediction of linear instability waves in high-speed boundary layers

Here, we investigate if neural operators can predict the linear evolution of instability waves in high-speed boundary layers. To this end, we extend the design of the DeepOnet to ensure accurate and robust predictions, and also to perform data assimilation. In particular, we train DeepONet to take as inputs an upstream disturbance and a downstream location of interest, and to provide as output the perturbation field downstream in the boundary layer. DeepONet thus approximates the linearized and parabolized Navier-Stokes operator for this flow. For successful application to the high-speed boundary layer problem, we add sample weighting and Fourier input features to the regular DeepONet formulation. Once trained, the DeepOnet can perform fast and accurate predictions of the downstream disturbances within the range of training frequencies (inside the distribution). In addition, we show that DeepONet can solve the inverse problem, where downstream wall measurements are adopted as input, and a trained network can predict the upstream disturbances that led to these observations. This capability, along with the forward predictions, allows us to perform a full data assimilation cycle efficiently: starting from wall-pressure data, we predict the upstream disturbance using the inverse DeepONet and its evolution using the forward DeepONet. Finally, we introduce three new metrics to benchmark the training, evaluation and break-even cost of neural operators.

42 ENGINEERING↗