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Regular physics-informed neural networks (PINNs) predict the solution ofpartial differential equations using sparse labeled data but only over a singledomain. On the other hand, fully supervised learning models are first trainedusually over a few thousand domains with known solutions (i.e., labeled data)and then predict the solution over a few hundred unseen domains.Physics-informed PointNet (PIPN) is primarily designed to fill this gap betweenPINNs (as weakly supervised learning models) and fully supervised learningmodels. In this article, we demonstrate that PIPN predicts the solution ofdesired partial differential equations over a few hundred domainssimultaneously, while it only uses sparse labeled data. This framework benefitsfast geometric designs in the industry when only sparse labeled data areavailable. Particularly, we show that PIPN predicts the solution of a planestress problem over more than 500 domains with different geometries,simultaneously. Moreover, we pioneer implementing the concept of remarkablebatch size (i.e., the number of geometries fed into PIPN at each sub-epoch)into PIPN. Specifically, we try batch sizes of 7, 14, 19, 38, 76, and 133.Additionally, the effect of the PIPN size, symmetric function in the PIPNarchitecture, and static and dynamic weights for the component of the sparselabeled data in the loss function are investigated.

Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity