[marcusaurelius]

I am working on a physics-informed neural network (PINN) implementation using DeepXDE for solving a non-dimensional natural convection problem in a square cavity. The problem involves the Navier-Stokes and energy equations with non-dimensional parameters such as Rayleigh number (Ra) and Prandtl number (Pr). The cavity has Dirichlet boundary conditions for velocities and temperature on three walls and a Neumann boundary condition for temperature on the top wall.

The neural network has a 10-layer fully connected structure with 150 neurons per layer and "swish" activation. Training is performed using the Adam optimizer with cosine decay uptp 60000 iterations and fine-tuned using the L-BFGS optimizer.

This setup works perfectly fine to validate at low Rayleigh number up to 10E4. but it fails miserably to validate at higher Ra = 10E5 or above.

I seek advice on improving accuracy and predict accurate natural convection at higher Rayleigh numbers.

[sharonyue]

It is well-known PINN is difficult to deal with high Re flow. You can try to train it with a 10 times bigger viscosity, then decrease the viscosity a bit by load the trained parameters. But it is still chanllenging.

[marcusaurelius]

Thanks, I am trying your to start with higher viscosity. If you have any other suggestions, please let me know.