Edriss Titi | Texas A&M University (original) (raw)

Edriss Titi

Uploads

Papers by Edriss Titi

arXiv (Cornell University), Apr 6, 2016

arXiv (Cornell University), Dec 21, 2022

Computational Geosciences, Dec 5, 2022

Journal of nonlinear science, May 27, 2024

arXiv (Cornell University), May 14, 2023

Journal of Nonlinear Science, May 20, 2022

Quarterly Journal of the Royal Meteorological Society, Aug 1, 2019

Journal of Nonlinear Science, Jun 6, 2023

arXiv (Cornell University), Aug 16, 2016

arXiv (Cornell University), Oct 25, 2010

Journal of Advances in Modeling Earth Systems, Dec 1, 2022

Generating high‐resolution flow fields is of paramount importance for various applications in eng... more Generating high‐resolution flow fields is of paramount importance for various applications in engineering and climate sciences. This is typically achieved by solving the governing dynamical equations on high‐resolution meshes, suitably nudged toward available coarse‐scale data. To alleviate the computational cost of such downscaling process, we develop a physics‐informed deep neural network (PI‐DNN) that mimics the mapping of coarse‐scale information into their fine‐scale counterparts of continuous data assimilation (CDA). Specifically, the PI‐DNN is trained within the theoretical framework described by Foias et al. (2014, https://doi.org/10.1070/rm2014v069n02abeh004891) to generate a surrogate of the theorized determining form map from the coarse‐resolution data to the fine‐resolution solution. We demonstrate the PI‐DNN methodology through application to 2D Rayleigh‐Bénard convection, and assess its performance by contrasting its predictions against those obtained by dynamical downscaling using CDA. The analysis suggests that the surrogate is constrained by similar conditions, in terms of spatio‐temporal resolution of the input, as the ones required by the theoretical determining form map. The numerical results also suggest that the surrogate's downscaled fields are of comparable accuracy to those obtained by dynamically downscaling using CDA. Consistent with the analysis of Farhat, Jolly, and Titi (2015, https://doi.org/10.48550/arxiv.1410.176), temperature observations are not needed for the PI‐DNN to predict the fine‐scale velocity, pressure and temperature fields.