Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems
<|reference_start|>Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems: 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.<|reference_end|>
@article{long2024invertible,
    title={Invertible Fourier Neural Operators for Tackling Both Forward and
  Inverse Problems},
    author={Da Long and Shandian Zhe},
    journal={arXiv preprint arXiv:2402.11722},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.11722},
    primaryClass={cs.LG}
}