Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems
This work addresses the need for operator learning methods that can solve inverse problems, which is crucial for applications in fields like physics and engineering, though it is incremental as it builds on existing FNO frameworks.
The authors tackled the limitation of Fourier Neural Operators (FNO) being used only for forward prediction by proposing an invertible FNO (iFNO) to handle both forward and inverse problems, achieving advantages in evaluations on seven benchmark tasks.
Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving inverse problems. In this paper, we propose an invertible Fourier Neural Operator (iFNO) for jointly tackling the forward and inverse problems. We developed a series of invertible Fourier blocks in the latent channel space to share the model parameters, exchange the information, and mutually regularize the learning for the bi-directional tasks. We integrated a variational auto-encoder to capture the intrinsic structures within the input space and to enable posterior inference so as to mitigate challenges of illposedness, data shortage, noises that are common in inverse problems. We proposed a three-step process to combine the invertible blocks and the VAE component for effective training. The evaluations on seven benchmark forward and inverse tasks have demonstrated the advantages of our approach.