Vector-Cloud Neural Network Operator

X.H. Zhou*, J. Han, H. Xiao. Frame-independent vector-cloud neural network for nonlocal constitutive modelling on arbitrary grids. Computer Methods in Applied Mechanics and Engineering. 388, 114211, 2022.

Vector-cloud neural network can be used to emulate nonlocal mapping implied by PDE operators.

Conditioning of Data-Driven Models

Reynolds averaged Navier-Stokes equations with explicit data-driven Reynolds stress closure can be ill-Conditioned

Journal of Fluid Mechanics 869, 553-586, 2019 J.-L. Wu, H. Xiao, R. Sun, and Q. Wang

A small error in Reynolds stress can lead to large errors in the mean velocity when solving the RANS equations because of poor model conditioning. We derive a local condition number as an indicator of conditioning and demonstrate that this number explains the error propagation from Reynolds stress to mean velocity with examples.