Physics-informed neural network simulation of thermal cavity flow.

Area of Science:

• Computational Fluid Dynamics
• Machine Learning
• Applied Physics

Background:

• Physics-informed neural networks (PINNs) offer an alternative to traditional simulation methods.
• PINNs can be integrated with existing simulation techniques.
• This study explores PINNs for forward simulations without relying on pre-existing data.

Purpose of the Study:

• To evaluate the efficacy of PINNs in performing forward simulations of a 2D natural convection-driven cavity.
• To investigate the capability of PINNs to handle higher-dimensional parameter spaces (3D simulations across x, z, and Rayleigh number domains).
• To validate PINN results against established solutions for natural convection.

Main Methods:

• Utilized PINNs for simulations based on the vorticity-stream function formulation of the Navier-Stokes equations.
• Conducted 2D simulations across spatial (x, z) domains at constant Rayleigh numbers (Ra).
• Performed 3D simulations across spatial (x, z) and parameter (Ra) domains to assess higher-dimensional learning.

Main Results:

• Both 2D and 3D PINN simulations accurately reproduced published results for Ra values ranging from 10^3 to 10^6.
• Higher Ra values in 2D simulations required more training iterations, indicating stronger nonlinear fluid-thermal coupling.
• The 3D simulation converged but demanded more training than 2D cases due to the curse of dimensionality.

Conclusions:

• PINNs are validated as a viable tool for standard fluid dynamics simulations.
• PINNs demonstrate feasibility for exploring higher-order parameter spaces beyond conventional methods.
• Increased dimensionality in PINN simulations leads to a higher computational burden.