Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems

• URL: http://arxiv.org/abs/2402.11722v1
• Date: Sun, 18 Feb 2024 22:16:43 GMT
• Title: Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems
• Authors: Da Long and Shandian Zhe
• Abstract summary: We propose an invertible Fourier Neural Operator (iFNO) that tackles both the forward and inverse problems. We integrated a variational auto-encoder to capture the intrinsic structures within the input space and to enable posterior inference. The evaluations on five benchmark problems have demonstrated the effectiveness of our approach.
• Score: 18.48295539583625
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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