Higher-Order error estimates for physics-informed neural networks approximating the primitive equations

Understand

Large-scale dynamics of the oceans and the atmosphere are governed by primitive equations (PEs).

• Due to the nonlinearity and nonlocality, the numerical study of the PEs is generally challenging.
• Neural networks have been shown to be a promising machine learning tool to tackle this challenge.
• In this work, we employ physics-informed neural networks (PINNs) to approximate the solutions to the PEs and study the error estimates.