Upcoming Event: CSEM Student Forum

Derivative-Informed Fourier Neural Operator with Applications to PED-Constrained Optimization

John Yao, CSEM Student

Abstract

In this talk, we will discuss efficient methods for constructing neural operator approximations of parametric PDE solutions. By exploiting low-dimensional sensitivity information within a high-dimensional map (when such features exist), we generate and learn high-dimensional Jacobian with computational costs that are independent of discretization dimensions. We use the sensitivity information to construct a derivative-informed neural operator (DINO) that serves as a powerful surrogate for various applications, notably high-dimensional design and inverse problems involving PDE-constrained optimization. We show that DINO results in significantly improved surrogate accuracy at the same training data generation cost as conventional operator learning methods, leading to high quality solutions in design and inverse problems. Our numerical results cover a range of applications, including fluid flow and nonlinear elasticity.