Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization

This article introduces a novel neural operator, the Derivative-Informed Fourier Neural Operator (DIFNO), and explores its capabilities in approximating solutions to partial differential equations (PDEs) and its application to PDE-constrained optimization. The research likely focuses on improving the accuracy and efficiency of solving PDEs using neural networks, potentially by incorporating derivative information to enhance the learning process. The use of Fourier transforms suggests an approach that leverages frequency domain analysis for efficient computation. The mention of universal approximation implies the model's ability to represent a wide range of PDE solutions. The application to PDE-constrained optimization indicates a practical use case, potentially for tasks like optimal control or parameter estimation in systems governed by PDEs.