A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...

points 1 and 2 lie on a streamline, the fluid has constant density, the flow is steady, and there is no friction. Although these restrictions sound severe, the Bernoulli equation is very useful, ...

and Navier-Stokes equation. The experimental results show that when PIANO learns neural operators from PDE datasets with various physical mechanisms, its accuracy and generalization are better ...