Fourier Neural Operator (FNO) is a popular operator learning method, which
has demonstrated state-of-the-art performance across many tasks. However, FNO
is mainly used in forward prediction, yet a large family of applications rely
on solving inverse problems. In this paper, we propose an invertible Fourier
Neural Operator (iFNO) that tackles both the forward and inverse problems. We
designed a series of invertible Fourier blocks in the latent channel space to
share the model parameters, efficiently 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 overcome challenges of
illposedness, data shortage, noises, etc. We developed a three-step process for
pre-training and fine tuning for efficient training. The evaluations on five
benchmark problems have demonstrated the effectiveness of our approach.

本文提出了一种可逆傅里叶神经算子（iFNO），既能解决正向预测问题，又能解决逆向问题，通过设计一系列可逆傅里叶块在潜在通道空间共享模型参数、高效交换信息并相互正则化学习，结合变分自编码器以捕获输入空间内部结构并进行后验推理，从而克服了不适定性、数据不足、噪声等挑战，并通过对五个基准问题的评估证明了我们方法的有效性。