FFEINR: flow feature-enhanced implicit neural representation for spatiotemporal super-resolution

Abstract

Large-scale numerical simulations are capable of generating data up to terabytes or even petabytes. As a promising method of data reduction, super-resolution (SR) has been widely studied in the scientific visualization community. However, most of them are based on deep convolutional neural networks or generative adversarial networks and the scale factor needs to be determined before constructing the network. As a result, a single training session only supports a fixed factor and has poor generalization ability. To address these problems, this paper proposes a flow feature-enhanced implicit neural representation (FFEINR) for spatiotemporal super-resolution of flow field data. It can take full advantage of the implicit neural representation in terms of model structure and sampling resolution. The neural representation is based on a fully connected network with periodic activation functions, which enables us to obtain lightweight models. The learned continuous representation can decode the low-resolution flow field input data to arbitrary spatial and temporal resolutions, allowing for flexible upsampling. The training process of FFEINR is facilitated by introducing feature enhancements for the input layer, which complements the contextual information of the flow field. To demonstrate the effectiveness of the proposed method, a series of experiments are conducted on different datasets by setting different hyperparameters. The results show that FFEINR achieves significantly better results than the trilinear interpolation method.

Graphical abstract

A. Supplementary experiments

1.1 A.1. Performance on different time steps

As shown in Fig. 7, we compare the visualization results of PipeCylinder dataset at different time steps. FFEINR achieves better results than the baseline method in the region of the flow field around obstacles or in the interior of vortices across different time steps.

Fig. 7

Qualitative comparison at different time steps. Top to bottom: $t=1070, 1366, 1430$. FFEINR outperforms Trilinear in predicting data at different time steps. Specifically, FFEINR achieves more accurate results than interpolation methods in the region of the flow field around obstacles or in the interior of vortices across time steps

1.2 A.2. Performance with different fixed scale factors

In order to illustrate the impact of fixed scale factors on network performance, we conduct supplementary experiments on the Cylinder dataset. As shown in Table 6, the scale factor can affect training time and model performance. The larger the scale factor in the temporal dimension during training, the longer the training time. In the experiments with the factor of $(S\times 4, T\times 4)$ and $(S\times 4, T\times 8)$, the model performance decreases significantly compared to the factor $(S\times 4, T\times 2)$, but the effects of extended resolution inference are roughly the same, which means that the out-of-distribution performance of the model is relatively stable. However, in our experiment, if the scale factor in the spatial dimension during training is too small $(S\times 2)$ or too large $(S\times 8)$, the model performs poorly in extended resolution tasks. The reason may be that the factor of $S\times 4$ achieves a balance between the degree of low-resolution data loss and the interpolation performance of the model.

Table 6 Quantitative comparison of the extended resolution with different training scale factors. Except for $(S\times 2, T\times 2)$, FFEINR outperforms Trilinear in most indicators. Considering the trade-off between training time and effectiveness, setting the scaling factor of $(S\times 4, T\times 2)$ during training can achieve the optimal results