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Title: Computing Residual Diffusivity by Adaptive Basis Learning via Super-Resolution Deep Neural Networks
It is expensive to compute residual diffusivity in chaotic incompressible flows by solving advection-diffusion equation due to the formation of sharp internal layers in the advection dominated regime. Proper orthogonal decomposition (POD) is a classical method to construct a small number of adaptive orthogonal basis vectors for low cost computation based on snapshots of fully resolved solutions at a particular molecular diffusivity D0* . The quality of POD basis deteriorates if it is applied to D0<<  D0* . To improve POD, we adapt a super-resolution generative adversarial deep neural network (SRGAN) to train a nonlinear mapping based on snapshot data at two values of D0* . The mapping models the sharpening effect on internal layers as D0 becomes smaller. We show through numerical experiments that after applying such a mapping to snapshots, the prediction accuracy of residual diffusivity improves considerably that of the standard POD.  more » « less
Award ID(s):
1924548 1632935
PAR ID:
10170782
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
The 6th International Conference on Computer Science, Applied Mathematics and Applications
Volume:
1121
Page Range / eLocation ID:
279-290
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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