Ling Guo, Shanghai Normal University
Room 306, No.5 Science Building
In this talk, we will review some recent developments on using Physics-informed neural networks (PINN) to solve in a uniﬁed framework forward, inverse and mixed stochastic problems based on scattered measurements. In the first part of this talk, we will focus on how to use the stochastic version of Physics-informed neural networks (sPINN) for solving steady and time-dependent stochastic problems. Instead of selecting the sPINN architecture empirically, the Bayesian optimization method is employed to optimize the hyper-parameters of sPINN (meta-learning). Then we move to the physics-informed generative adversarial networks (PI-GANs) where the governing physical laws in the form of stochastic diﬀerential equations (SDEs) were encoded into the architecture of GANs using automatic diﬀerentiation. In particular, Wasserstein GANs with gradient penalty (WGAN-GP) is used for its enhanced stability compared to vanilla GANs. The effectiveness of the proposed sPINN (with meta-learning) and PI-GANs for solving SPDEs is demonstrated via several numerical examples.