## 1 Introduction
The displacement field resulting from the application of optical flow has a subpixel resolution, usually with values less than 1 pixel. [PERSON] and [PERSON] [17] used the optical flow technique and image correlation to measure the deformation of a birdlike airfoil. The results show higher spatial resolution compared to the image correlation technique. The DIC-based method can measure accurate displacement, but it is expensive and time-consuming. By integrating a digital camera into a laser head to film the moment of crack formation during laser beam welding for austenitic stainless steels and based on the optical flow technique, [PERSON] et al. [18; 19] developed a 2-dimensional (2D) measurement technique that provides, for the first time, a local analysis of the strain field in the immediate vicinity of the solidification front. Convolutional neural networks (CNN) [20] are one of the famous deep learning algorithms. They have achieved great success in per-pixel prediction problems due to their learning ability and high efficiency, supported by semantic segmentation, depth estimation, optical flow estimation, etc. Strain prediction can be regarded as a similar problem, especially when aiming at optical flow estimation, which learns correspondences between images. A milestone network FlowNet [21] first achieved the optical flow estimation based on deep learning. It adopts a generic U-Net architecture. The accuracy of FlowNet is still lower than traditional variational methods, so following FlowNet, many extensions have been developed to reduce the number of parameters and improve accuracy. In 2016, FlowNet2 [22] was proposed by stacking multiple subnetworks. The accuracy could be significantly improved at the cost of increased number of parameters and longer run time. SPyNet [23] incorporates the coarse-to-fine idea of the variational methods; it up-samples the learned flow and warps it on the second image to refine the flow. The model size is reduced, but the accuracy cannot compete with FlowNet2. The small and efficient network PWC-Net [24] is 17 times smaller than Flownet2 while maintaining high accuracy on several standard datasets; it leverages some simple but well-established principles from classical approaches, such as pyramidal processing, warping, and cost volume. Anotherconcurrent work, LiteFlowNet [25], also adopts feature warping and proposes a novel flow regularization module. Subsequently, an increasing number of ideas emerged in optical flow estimation; IRR [26] adopts iterative optimization flow and weight sharing. \(HD^{3}\)[27] introduces matching density estimation. VCN [28] improves the cost volume to 4D tensor. MaskFlownet [29] solves the occlusion problem. In 2020, a completely different network RAFT [30] was proposed. It removes the spatial pyramid structure and consists of three main components: a feature encoder, a correlation layer, and a recurrent update operator. This model has become a new milestone and is followed by many works [31; 32; 33; 34]. Due to the success of deep learning in optical flow estimation, some CNN based methods can now retrieve displacement and strain fields as traditional DIC. They overcome its disadvantages, such as long computation time. Ref. [35] compares two image crack segmentation methods: the first applies a threshold on the strain map derived from the DIC, and the other uses a deep convolutional neural network. [PERSON] et al. [36] develops a network named StrainNet by modifying the number of down-samplings of FlowNet. It can obtain the full-resolution displacement and strain fields from reference and deformed speckle images. [PERSON] et al. [37] proposed a deep learning method, Deep DIC, which includes two models, DisplacementNet and StrainNet, for displacement and strain prediction. The two models are slightly different in depth and up-sampling operation. The prediction results are highly consistent with commercial DIC software. In [38], a Hermite dataset is created to simulate deformation.