@article{du_etal_2023,

title = {State estimation in minimal turbulent channel flow: A comparative study of 4DVar and PINN},

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

url = {https://www.sciencedirect.com/science/article/pii/S0142727X22001412},

doi = {https://doi.org/10.1016/j.ijheatfluidflow.2022.109073},

issn = {0142-727X},

year  = {2023},

date = {2023-01-01},

journal = {International Journal of Heat and Fluid Flow},

volume = {99},

pages = {109073},

abstract = {The state of turbulent, minimal-channel flow is estimated from spatio-temporal sparse observations of the velocity, using both a physics-informed neural network (PINN) and adjoint-variational data assimilation (4DVar). The performance of PINN is assessed against the benchmark results from 4DVar. The PINN is efficient to implement, takes advantage of automatic differentiation to evaluate the governing equations, and does not require the development of an adjoint model. In addition, the flow evolution is expressed in terms of the network parameters which have a far smaller dimension than the predicted trajectory in state space or even just the initial condition of the flow. Provided adequate observations, network architecture and training, the PINN can yield satisfactory estimates of the flow field, both for the missing velocity data and the entirely unobserved pressure field. However, accuracy depends on the network architecture, and the dependence is not known a priori. In comparison to 4DVar estimation which becomes progressively more accurate over the observation horizon, the PINN predictions are generally less accurate and maintain the same level of errors throughout the assimilation time window. Another notable distinction is the capacity to accurately forecast the flow evolution: while the 4DVar prediction depart from the true flow state gradually and according to the Lyapunov exponent, the PINN is entirely inaccurate immediately beyond the training time horizon unless re-trained. Most importantly, while 4DVar satisfies the discrete form of the governing equations point-wise to machine precision, in PINN the equations are only satisfied in an L2 sense.},

keywords = {4DVar, Adjoint variational method, Data assimilation, Physics informed neural networks, PINN, State estimation, Turbulence},

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{buchta_jfm2022,

title = {Assimilation of wall-pressure measurements in high-speed flow over a cone},

author = {David A. Buchta and Stuart J. Laurence and Tamer A. Zaki},

doi = {10.1017/jfm.2022.668},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {947},

pages = {R2},

publisher = {Cambridge University Press},

keywords = {Boundary layers, Data assimilation, Hypersonic, Stability, Transition},

pubstate = {published},

tppubtype = {article}

}

@article{wang_Stochastic_jfm2022,

title = {Origin of enhanced skin friction at the onset of boundary-layer transition},

author = {Mengze Wang and Gregory L. Eyink and Tamer A. Zaki},

doi = {10.1017/jfm.2022.296},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {941},

pages = {A32},

publisher = {Cambridge University Press},

keywords = {Channel, Data assimilation, Drag, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{wang_Synch_jfm2022,

title = {Synchronization of turbulence in channel flow},

author = {Mengze Wang and Tamer A. Zaki},

doi = {10.1017/jfm.2022.397},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {943},

pages = {A4},

publisher = {Cambridge University Press},

keywords = {Channel, Data assimilation, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{wang_Hesisan_jfm2022,

title = {What is observable from wall data in turbulent channel flow?},

author = {Qi Wang and Mengze Wang and Tamer A. Zaki},

doi = {10.1017/jfm.2022.295},

year  = {2022},

date = {2022-01-01},

journal = {Journal of Fluid Mechanics},

volume = {941},

pages = {A48},

publisher = {Cambridge University Press},

keywords = {Channel, Data assimilation, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{mons_prf2021,

title = {Ensemble-variational assimilation of statistical data in large-eddy simulation},

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

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.6.104607},

doi = {10.1103/PhysRevFluids.6.104607},

year  = {2021},

date = {2021-10-01},

journal = {Phys. Rev. Fluids},

volume = {6},

issue = {10},

pages = {104607},

publisher = {American Physical Society},

keywords = {Channel, Data assimilation, Ensemble Variational Methods, EnVar, LES, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{zaki_prf2021,

title = {From limited observations to the state of turbulence: Fundamental difficulties of flow reconstruction},

author = {Tamer A. Zaki and Mengze Wang},

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.6.100501},

doi = {10.1103/PhysRevFluids.6.100501},

year  = {2021},

date = {2021-10-01},

journal = {Phys. Rev. Fluids},

volume = {6},

issue = {10},

pages = {100501},

publisher = {American Physical Society},

keywords = {Data assimilation, Ensemble Variational Methods, EnVar, Turbulence},

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}

}

@article{buchta_jfm2021,

title = {Observation-infused simulations of high-speed boundary-layer transition},

author = {David A. Buchta and Tamer A. Zaki},

doi = {10.1017/jfm.2021.172},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Fluid Mechanics},

volume = {916},

pages = {A44},

publisher = {Cambridge University Press},

keywords = {Data assimilation, Ensemble Variational Methods, EnVar, Hypersonic},

pubstate = {published},

tppubtype = {article}

}

@article{wang_jfm2021,

title = {State estimation in turbulent channel flow from limited observations},

author = {Mengze Wang and Tamer A. Zaki},

doi = {10.1017/jfm.2021.268},

year  = {2021},

date = {2021-01-01},

journal = {Journal of Fluid Mechanics},

volume = {917},

pages = {A9},

publisher = {Cambridge University Press},

keywords = {Adjoint, Channel, Data assimilation, Turbulence},

pubstate = {published},

tppubtype = {article}

}

@article{wu_prf2020,

title = {Data compression for turbulence databases using spatiotemporal subsampling and local resimulation},

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

url = {https://link.aps.org/doi/10.1103/PhysRevFluids.5.064607},

doi = {10.1103/PhysRevFluids.5.064607},

year  = {2020},

date = {2020-06-01},

journal = {Phys. Rev. Fluids},

volume = {5},

pages = {064607},

publisher = {American Physical Society},

keywords = {Data assimilation},

pubstate = {published},

tppubtype = {article}

}

@article{Wang_jcp2019,

title = {Discrete adjoint of fractional-step incompressible Navier-Stokes solver in curvilinear coordinates and application to data assimilation},

author = {Mengze Wang and Qi Wang and Tamer A Zaki},

url = {http://www.sciencedirect.com/science/article/pii/S0021999119304735},

doi = {https://doi.org/10.1016/j.jcp.2019.06.065},

issn = {0021-9991},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Computational Physics},

volume = {396},

pages = {427 - 450},

abstract = {The discrete adjoint of an incompressible Navier-Stokes algorithm in generalized coordinates is derived and applied to estimate the states of saturated and turbulent circular Couette flows. The forward Navier-Stokes model is based on the fractional-step algorithm in curvilinear coordinates on a structured grid [1], which has been widely adopted in direct numerical simulations of transitional and turbulent flows. The discrete adjoint equations adopt the same stencil and temporal scheme as the forward discretization, and expressions are derived that relate the discrete adjoint variables to their continuous counterpart. The key ingredients of the forward algorithm can be retained in the adjoint, including the computation of the cell geometry, the approximate factorization method, and the parallelization strategy. The accuracy, efficiency, and stability of the adjoint solver are also commensurate with the forward model. In addition, a novel symmetric projector is proposed to guarantee that the outcome of the adjoint algorithm is divergence free. The implementation of the algorithm in double precision satisfies the forward-adjoint relation up to eight significant figures, and further validation is performed using circular Couette flow. The forward and adjoint growth rates of instability modes from linear theory are accurately reproduced. In addition, an adjoint-variational data-assimilation algorithm (4DVar) is adopted to reconstruct the initial condition of circular Couette flows from limited measurements, obtained from an independent simulation. When the flow is comprised of saturated wavy vortices, wall measurements are sufficient to reconstruct an initial condition that latches onto the target state after a short time. For the more challenging turbulent case, coarse-grained velocity data are used to estimate the initial condition.},

keywords = {Data assimilation, Discrete adjoint, Fraction-step algorithm, Generalized coordinates, Navier-Stokes, Taylor-Couette flow},

pubstate = {published},

tppubtype = {article}

}

@article{mons_jcp2019,

title = {Kriging-enhanced ensemble variational data assimilation for scalar-source identification in turbulent environments},

author = {Vincent Mons and Qi Wang and Tamer A Zaki},

url = {http://www.sciencedirect.com/science/article/pii/S0021999119305406},

doi = {https://doi.org/10.1016/j.jcp.2019.07.054},

issn = {0021-9991},

year  = {2019},

date = {2019-01-01},

journal = {Journal of Computational Physics},

volume = {398},

pages = {108856},

abstract = {Various ensemble-based variational (EnVar) data assimilation (DA) techniques are developed to reconstruct the spatial distribution of a scalar source in a turbulent channel flow resolved by direct numerical simulation (DNS). In order to decrease the computational cost of the DA procedure and improve its performance, Kriging-based interpolation is combined with EnVar DA, which enables the consideration of relatively large ensembles with moderate computational resources. The performance of the proposed Kriging-EnVar (KEnVar) DA scheme is assessed and favorably compared to that of standard EnVar and adjoint-based variational DA in various scenarios. Sparse regularization is implemented in the framework of EnVar DA in order to better tackle the case of concentrated scalar emissions. The problem of optimal sensor placement is also addressed, and it is shown that significant improvement in the quality of the reconstructed source can be obtained without supplementary computational cost once the ensemble required by the DA procedure is formed.},

keywords = {Channel, Data assimilation, Optimization, Scalar dispersion, Sensor placement, Source identification, Turbulence},

pubstate = {published},

tppubtype = {article}

}