Artificial-Intelligence-Velocimetry-Thermometry (AIVT)

This is the official implementation of the paper:
"AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold Networks".

We propose the Artificial Intelligence Velocimetry-Thermometry (AIVT) method to reconstruct a continuous and differentiable representation of temperature and velocity in turbulent convection from measured 3D velocity data. AIVT is based on physics-informed Kolmogorov-Arnold Networks (cKANs) and is trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations.

We apply AIVT to a unique dataset containing simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained through a combination of Particle Image Thermometry (PIT) and Lagrangian Particle Tracking (LPT). Unlike previous studies, our approach directly compares machine learning results to true volumetric, simultaneous temperature and velocity measurements.

We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data, achieving a high fidelity comparable to numerical simulations. This provides a powerful new avenue for analyzing turbulence at high Reynolds numbers.

Instructions:

1. Download the dataset:
   The dataset is available at http://datadryad.org/share/n5eo80Hghuks7loseWI8ZpVlfjB5Yv4TAuRRT5WVW6U

2. Move the data to the correct directory:

   mv path_to_downloaded_data ../Data/Rayleigh-Benard-Convection/
   

3. Run our models using the provided Jupyter notebooks.
   The repository includes results for the following models:

   • cKAN with 149k parameters
   • MLP with 151k parameters
   • MLP with 282k parameters

   Each notebook contains all the necessary code to replicate the results presented in the paper. The results were generated using JAX.

Note: To run these notebooks, you need the source files located in ../Instant_AIVT. These files should be automatically downloaded when the project is cloned. Ensure that all dependencies are installed before executing the notebooks.