seminar

Deep learning algorithms have emerged recently for solving partial differential equations (PDEs), especially in conjunction with sparse data. In particular, the recently developed physics-informed neural networks (PINNs) have shown their effectiveness in solving both forward and inverse PDE problems. Different from the classical numerical methods in which the differential operators are approximated by the data on certain discrete lattices (meshes), PINNs compute all the differential operators of a PDE using the automatic differentiation technique involved in the backward propagation. Consequently, no mesh (structured mesh or unstructured mesh used in the classical numerical methods) is required for the PINN to solve PDEs, which saves a lot of effort in grid generation. Another attractive feature is that PINNs are capable of solving the inverse PDE problems effectively and with the same code that is used for forward problems. In this talk, I will introduce several newly developed PINNs for solving forward and inverse PDE problems as well as their applications: (1) reconstructions of multiscale flow fields via PINNs; (2) multi-fidelity PINNs for inverse PDE problems with multi-fidelity data; and (3) uncertainty quantification in PINNs.