Extension of Physics-informed Neural Networks to Solving Parameterized PDEs

In this paper, we address PINNs’ problem of repetitive and time-consuming training by proposing a novel extension, parameterized physics-informed neural networks (P$^2$INNs). P2INNs enable modeling the solutions of parameterized PDEs via explicitly encoding a latent representation of PDE parameters. With the extensive empirical evaluation, we demonstrate that P$^2$INNs outperform the baselines both in accuracy and parameter efficiency on benchmark 1D and 2D parameterized PDEs and are also effective in overcoming the known “failure modes”.