Regarding the spatial and temporal encoding in NS.py

[Vishwanath1999]

@paraklas @sifanw094
I want to understand the spatio-temporal encoding involved in NS.py which is the following.

def input_encoding(t, x, y):
       k_t = np.power(10.0, np.arange(0, M_t + 1))
       out = np.hstack([1, k_t * t,
                        np.cos(k_x * w_x * x), np.cos(k_y * w_y * y),
                        np.sin(k_x * w_x * x), np.sin(k_y * w_y * y),
                        np.cos(k_xx * w_x * x) * np.cos(k_yy * w_y * y),
                        np.cos(k_xx * w_x * x) * np.sin(k_yy * w_y * y),
                        np.sin(k_xx * w_x * x) * np.cos(k_yy * w_y * y),
                        np.sin(k_xx * w_x * x) * np.sin(k_yy * w_y * y)])
       return out

why is there an exponential encoding of time? and also the k_xx and k_yy meshgrid based encoding is not very intuitive. Can anyone pls help me understand this?
In the main training loop there is reinitialization of PINN in every time marching step. Can't we just init a single PINN model for all time steps and train it for all steps which is what intuitively makes sense to me. Pls correct if I am wrong.

[9NM0]

这个编码好像是为了让网络直接满足周期性边界条件

[sifanexisted]

Thank you for the active discussion. Yes, I confirm that this embedding is designed to enforce the exact periodic boundary conditions.