Title: Learning Dynamical Characteristics with Neural Operators for Data Assimilation. Abstract: Data assimilation refers to a group of algorithms that combines numerical models with observations to obtain an optimal estimation of the system's states. In areas like earth science, numerical models are usually formulated by differential equations, also known as the prior dynamics. It is a great challenge for neural networks to properly exploit the dynamical characteristics for data assimilation, because first, it is difficult to represent complicated dynamical characteristics in neural networks, and second, the dynamics are likely to be biased. The state-of-the-art neural networks borrow from the traditional method to introduce dynamical characteristics by optimizing the 4D-Var objective function in which the dynamics are inherently quantified, but the iterative optimization process leads to high computational cost. In this paper, we develop a novel deep learning framework with neural operators for data assimilation. The key novelty of our proposed approach is that we design a so-called flow operator through self-supervised learning to explicitly learn dynamical characteristics for reconstructed states. Numerical experiments on the Lorenz-63 and Lorenz-96 systems, which are the standard benchmarks for data assimilation performance evaluation, show that the proposed method is at least three times faster than state-of-the-art neural networks, and reduces the dynamic loss by two orders of magnitude. It is also demonstrated that our method is well-adapted to biases in the prior dynamics. 