@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{clarkdileoni_etal_2023bb,

title = {Reconstructing turbulent velocity and pressure fields from under-resolved noisy particle tracks using physics-informed neural networks},

author = {Patricio Clark Di Leoni and Karuna Agarwal and Tamer A. Zaki and Charles Meneveau and Joseph Katz},

url = {https://doi.org/10.1007/s00348-023-03629-4},

doi = {10.1007/s00348-023-03629-4},

isbn = {1432-1114},

year  = {2023},

date = {2023-01-01},

journal = {Experiments in Fluids},

volume = {64},

number = {5},

pages = {95},

abstract = {Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from under-resolved and noisy particle tracks obtained experimentally remains a significant challenge. We adopt and characterize a method based on Physics-Informed Neural Networks (PINNs). In this approach, the network is regularized by the Navier–Stokes equations to interpolate the velocity data and simultaneously determine the pressure field. We compare this approach to the state-of-the-art Constrained Cost Minimization method Agarwal et al. (2021). Using data from direct numerical simulations and various types of synthetically generated particle tracks, we show that PINNs are able to accurately reconstruct both velocity and pressure even in regions with low particle density and small accelerations. We analyze both the root-mean-square error of the reconstructions as well their energy spectra. PINNs are also robust against increasing the distance between particles and the noise in the measurements, when studied under synthetic and experimental conditions. Both the synthetic and experimental datasets used correspond to moderate Reynolds number flows.},

keywords = {Data assimilation, Machine Learning, PINN},

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{Du_pre2021,

title = {Evolutional deep neural network},

author = {Yifan Du and Tamer A. Zaki},

url = {https://link.aps.org/doi/10.1103/PhysRevE.104.045303},

doi = {10.1103/PhysRevE.104.045303},

year  = {2021},

date = {2021-10-01},

journal = {Phys. Rev. E},

volume = {104},

issue = {4},

pages = {045303},

publisher = {American Physical Society},

keywords = {Deep learning, Machine Learning, Neural Networks},

pubstate = {published},

tppubtype = {article}

}

@article{Wu3461,

title = {High-Reynolds-number fractal signature of nascent turbulence during transition},

author = {Zhao Wu and Tamer A Zaki and Charles Meneveau},

url = {https://www.pnas.org/content/117/7/3461},

doi = {10.1073/pnas.1916636117},

issn = {0027-8424},

year  = {2020},

date = {2020-01-01},

journal = {Proceedings of the National Academy of Sciences},

volume = {117},

number = {7},

pages = {3461--3468},

publisher = {National Academy of Sciences},

keywords = {Bypass, Conditional Sampling, Freestream Turbulence, Machine Learning, Spots, T/NT interface, Transition, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{wu_prf2019,

title = {Application of a self-organizing map to identify the turbulent-boundary-layer interface in a transitional flow},

author = {Zhao Wu and Jin Lee and Charles Meneveau and Tamer Zaki},

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.4.023902},

doi = {10.1103/PhysRevFluids.4.023902},

year  = {2019},

date = {2019-01-01},

journal = {Phys. Rev. Fluids},

volume = {4},

pages = {023902},

publisher = {American Physical Society},

keywords = {Bypass, Machine Learning, Spots, T/NT interface, Transition, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{hack_jfm2016,

title = {Data-enabled prediction of streak breakdown in pressure-gradient boundary layers.},

author = {Mario J P Hack and Tamer A Zaki},

url = {https://engineering.jhu.edu/zaki/wp-content/uploads/2018/12/Hack_JFM2016.pdf},

year  = {2016},

date = {2016-01-01},

journal = {Journal of Fluid Mechanics},

volume = {801},

pages = {43-64},

keywords = {Bypass, Inner, Instability, Klebanoff, Machine Learning, Neural Networks, Outer, Streaks, Transition},

pubstate = {published},

tppubtype = {article}

}