Shape optimization based on physics-informed neural networks

Shape optimization, which involves modelling and optimization of a designed geometry to achieve targeted goals, is a prominent but challenging topic. The complexity and high dimensionality of the search space make some existing methods computationally expensive. In this talk, we propose a physics-informed neural networks (PINN) as a solver for the flow around an object and also a provider of gradient information for shape optimization. In this study a PINN is employed to solve the flow around a cylinder and to optimize the cylinder shape in order to minimize its drag. The point cloud used for training the PINN is adapted using the gradient of the objective functions so that accurate flow fields can be obtained for geometries closer to optimal shape. The proposed model, given adequate training, is capable of efficiently exploring a high dimensional shape space generate optimal shapes without any prior knowledge and in a reasonable cost. We illustrate this for shape optimization to reduce drag around a 2D cylinder at Reynolds number 20.