[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.