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.