Physics-informed Deep Learning for Flow Modelling and Aerodynamic Optimization

PDE-constrained optimization is an exceedingly difficult task due to the curse of dimensionality. This is particularly true in aerodynamics optimization as remeshing or deformation of existing meshes is often required. In this paper, we aim to overcome this challenge by proposing a simulation-based optimization framework that can handle various optimization problems efficiently. The proposed approach is able to simultaneous make predictions and perform optimizations. Specifically, the framework consists of a surrogate model to generate high-fidelity solutions and a gradient-based algorithm to address high-dimensional optimization problems. The starting point is to use physics-informed neural network (PINN) to construct surrogate models that output flow fields for airfoils of varied configurations. In this sense, PINN is computationally cheap as no labelled training data from a separate high-fidelity simulation is required. Thus, a trained surrogate model can efficiently generate flow fields for any intermediate optimization scenarios. More importantly, we design the architecture of surrogate models and include design variables as inputs to PINN. This mechanism enables neural network to extract geometric features of various input computational domains. A trained surrogate model can represent solutions on unseen design cases from both seen and unseen categories. In the optimization process, a quasi-Newton algorithm is used and further accelerated by automatic differentiation, a popular algorithm designed to efficiently compute the gradients of objective functions with respect to design parameters. An optimization examples aiming to achieve the maximal lift-to-drag ratio has been presented. The example is a single parameter optimization problem focusing on finding the optimal angle of attack. The proposed method is straightforward to implement and computationally efficient, providing a promising alternative for computationally intensive optimization problems.