While the forward solutions help the product analysis, the inverse problems play a crucial role in identifying cause of products failures.
The need for physics informed learning comes only when models are incomplete & data are scattered noisy. PINN, manages inherent noisy data & gives out meaningful solutions with problems that are not well-posed.
The (forward/inverse) problems, without any initial or boundary conditions or lacking parameters in the PDEs, are not possible to solve with regular methods.
It can also tackle higher dimensionality associated with input space. Deep Operator Network (DeepONets) was demonstrated with operator regression & applications to PDEs.