Computing Residual Diffusivity by Adaptive Basis Learning via Super-Resolution Deep Neural Networks

2019/09/27 by Jiancheng Lyu, Jack Xin, Lyu, Jiancheng +3
Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1910.00403

openalex publication_date 2019/09/27 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28

Abstract

It is expensive to compute residual diffusivity in chaotic in-compressible 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.

Related

• Diffusion Mechanism in Residual Neural Network: Theory and Applications
• Exploring Physical Latent Spaces for High-Resolution Flow Restoration
• PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction
• A deep neural network approach on solving the linear transport model under diffusive scaling
• Super-resolving sparse observations in partial differential equations: A physics-constrained convolutional neural network approach