Talks on Unified DA/ML

Recent talks on ensemble learning of turbulence models

Recently, I gave a few presentations on our work of learning turbulence models with ensemble Kalman methods. The slides and videos are shared here:

Slides for a 20-Minute Presentations at CFC2023, Cannes, France

2023-04-28-CFC-Cannes-final.pdf

Download PDF • 3.51MB

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Slides for a 45-Minute talk in the Seminar Series "Intelligent and Bio-inspired Mechanics", Online

2023-04-11-IBiM-seminar-final.pdf

Download PDF • 6.43MB

You can find the recording of the seminar on YouTube:

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.