Multivariate GPs

[XiankangTang]

I am currently working on the simulation of multivariate Gaussian processes. I am using Gaussian regression to reconstruct a greyscale map, that is a greyscale map where the intensity values are considered as a function of the coordinates. Because my structure is periodic, I chose to use the product of the RBF kernel function and the periodic kernel function as my kernel function. Here is my model.

`class GPModel(gpytorch.models.ExactGP):
def init(self, train_x, train_y, likelihood):
super(GPModel, self).init(train_x, train_y, likelihood)
self.mean_module = gpytorch.means.ConstantMean()
# self.base_kernel_1 = gpytorch.kernels.MaternKernel(nu=1.5, ard_num_dims=2)
self.base_kernel_1 = gpytorch.kernels.RBFKernel(ard_num_dims=2)
self.base_kernel_2 = gpytorch.kernels.PeriodicKernel(ard_num_dims=2)
self.base_kernel_3 = gpytorch.kernels.RBFKernel(ard_num_dims=2)
self.base_kernel_4 = gpytorch.kernels.PeriodicKernel(ard_num_dims=2)
self.base_kernel_5 = gpytorch.kernels.RBFKernel(ard_num_dims=2)
self.base_kernel_6 = gpytorch.kernels.PeriodicKernel(ard_num_dims=2)
self.base_kernel_7 = gpytorch.kernels.RBFKernel(ard_num_dims=2)
self.base_kernel_8 = gpytorch.kernels.PeriodicKernel(ard_num_dims=2)
self.covar_module = gpytorch.kernels.ScaleKernel(self.base_kernel_1 * self.base_kernel_2
+self.base_kernel_3 * self.base_kernel_4
+self.base_kernel_5 * self.base_kernel_6
+self.base_kernel_7 * self.base_kernel_8)

def forward(self, x):
    mean_x = self.mean_module(x)
    covar_x = self.covar_module(x)
    return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)`

My question is why the final simulation results have nothing to do with the fact that I'm using several sets of RBFs and the product of periodic kernel functions.

This is the absolute difference between the simulation results and the original picture, do they look different, I think the difference is too small.