Fig 2. Illustration of the parts of input space used for training the PINN.

(a) forward model and (b) inverse model. The collocation ($\Omega \times \mathbb{T}$), boundary and initial points ($\partial {\Omega }_D\times \mathbb{T}$ and Ω at t = 0) are utilized in the forward model. However, only the training points ($\Omega \times \mathbb{T}$) are employed in the inverse model. X represents a set of spatial coordinates (x, y, and z), t is a set of coordinates in the time domain, and S is a set of solution values (u and p) corresponding to X and t.