@article{clarkdileoni_etal_2023,

title = {Neural operator prediction of linear instability waves in high-speed boundary layers},

author = {Patricio Clark Di Leoni and Lu Lu and Charles Meneveau and George Em Karniadakis and Tamer A. Zaki},

url = {https://www.sciencedirect.com/science/article/pii/S0021999122008567},

doi = {https://doi.org/10.1016/j.jcp.2022.111793},

issn = {0021-9991},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Computational Physics},

volume = {474},

pages = {111793},

abstract = {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.},

keywords = {Deep operator networks, DeepONet, High-speed boundary layers, Instability waves, Machine Learning, Neural operators},

pubstate = {published},

tppubtype = {article}

}

@article{hao_etal_2023,

title = {Instability-wave prediction in hypersonic boundary layers with physics-informed neural operators},

author = {Yue Hao and Patricio Clark Di Leoni and Olaf Marxen and Charles Meneveau and George Em Karniadakis and Tamer A. Zaki},

url = {https://www.sciencedirect.com/science/article/pii/S1877750323001801},

doi = {https://doi.org/10.1016/j.jocs.2023.102120},

issn = {1877-7503},

year  = {2023},

date = {2023-01-01},

journal = {Journal of Computational Science},

volume = {73},

pages = {102120},

abstract = {Fast and accurate prediction of the nonlinear evolution of instability waves in high-speed boundary layers requires specialized numerical algorithms, and augmenting limited observation in this extreme flow regime is challenging. The deep operator networks (DeepONet) has been shown to be an effective tool for providing accurate and fast physics-informed predictions. DeepONet is trained to map an incoming perturbation to the associated downstream flow field within the nonlinear flow regime. The training is performed using high-fidelity data from direct numerical simulations of the compressible Navier–Stokes equations, when the gas can be approximated as calorically perfect and when chemical non-equilibrium effects must be computed. The performance and requirements of training the DeepONet in each case are evaluated. In addition, we show that informing the training of the DeepONet with the continuity equation improves the accuracy of the results, especially in absence of sufficient training data. Success of the physics-informed DeepONet to predict missing fields depends on the observables. Specifically, prediction of a unique solution depends on the available measurements. These results are a promising step towards applications of neural operator networks to more complex high-speed flow configurations and to data assimilation.},

keywords = {Deep operator networks, DeepONet, High-speed boundary layers, Hypersonics, Machine Learning, Non-equilibrium chemical reaction},

pubstate = {published},

tppubtype = {article}

}

@article{mao_jcp2021,

title = {DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators},

author = {Zhiping Mao and Lu Lu and Olaf Marxen and Tamer A. Zaki and George Em Karniadakis},

url = {https://www.sciencedirect.com/science/article/pii/S0021999121005933},

doi = {https://doi.org/10.1016/j.jcp.2021.110698},

issn = {0021-9991},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Computational Physics},

volume = {447},

pages = {110698},

keywords = {Chemically reacting flow, Data assimilation, Deep learning, DeepONet, Hypersonic, Operator approximation},

pubstate = {published},

tppubtype = {article}

}

@article{cai_jcp2021,

title = {DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks},

author = {Shengze Cai and Zhicheng Wang and Lu Lu and Tamer A. Zaki and George Em Karniadakis},

url = {https://www.sciencedirect.com/science/article/pii/S0021999121001911},

doi = {https://doi.org/10.1016/j.jcp.2021.110296},

issn = {0021-9991},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Computational Physics},

volume = {436},

pages = {110296},

keywords = {Data assimilation, Deep learning, DeepONet, Multiscale modeling, Mutiphysics, Operator approximation},

pubstate = {published},

tppubtype = {article}

}