***Major revision to the paper(DCNO_old and DCNO_new)*** 

    - Add the (testing) error dynamics for high-frequency ($> 10\pi$) and low- frequency ($\leq 10\pi$) components in Figure 1.1 ( c ) ( d )
    - Add a paragraph in Section 2.1(Numerical Methods for Multiscale PDEs) introducing the connection of dilated convolution with local bases in mulitscale numerical methods and the global-local decompostion of multiscale solutions. 
    - Update Table 1. We now train all the models with both the $L^2$ and the weighted loss ($L^T$), and evalute the results with relative $L^2$ and $L^T$ error.
    - Add a figure (Figure 4.3) to visulize the results of Navier-Stokes equation.
    - Add a figure (Figure 4.4) to visualize inverse coefficient identification. 


***Navier-Stokes videos***

    Vorticity:  NS_1e-3_T50.avi, NS_1e-4_T25.avi,  NS_1e-5_T20.avi,  NS_1e-6_T15.avi

    Predictions: NS_1e-3_T50_pred.avi, NS_1e-4_T25_pred.avi,  NS_1e-5_T20_pred.avi,  NS_1e-6_T15_pred.avi

    Videos are generated by the pictures in the corresponding files (NS_1e-3_T50, NS_1e-4_T25, NS_1e-5_T20, NS_1e-6_T15)