Applied Math Seminar- A Reinforcement Learning Framework for Shape Optimal Design of Airfoils Based on the Steady Euler Equations

Date and Time: Friday, September 27, 2024 1:30pm-2:30pm

Speaker: Jingfeng Wang,  North Carolina State University 

Title: A Reinforcement Learning Framework for Shape Optimal Design of Airfoils Based on the Steady Euler Equations

Place: Zoom Link: https://gwu-edu.zoom.us/j/4092408949

Abstract: In this talk, we will introduce a reinforcement learning framework tailored to solving the shape optimization of airfoils governed by the steady Euler equations. Key challenges include the design of a robust PDE solver, managing geometric deformations based on unstructured meshes during the optimization process, and ensuring the accuracy of nonlinear target functionals.

We will start with introducing the concept of dual consistency, a critical factor in developing stable error estimations using the Dual Weighted Residual (DWR) method for goal-oriented mesh adaptivity. To further improve efficiency in dual solution computation, we have developed an automated hybrid solver that integrates Dual Convolutional Neural Networks (Dual-CNNs), enhancing mesh adaptivity while preserving dual consistency. This advanced solver enables the development of a mechanism-driven reinforcement learning framework, specifically designed for airfoil shape optimization. Within the reinforcement learning framework, a generalized approach to solving various target functional optimization problems can be obtained, but making the optimization process more efficient presents new challenges. Besides, we will also explore how DWR-based mesh adaptation can be extended to a multi-mesh framework, enabling the handling of generalized target functionals.