Covariance estimation is a fundamental problem in statistics, and Functional Data Analysis is no exception. However, computing the empirical covariance can be computationally expensive for functional observations on multi-dimensional domains. Moreover, for sparsely observed functional data, the necessary pairs of observations for covariance estimation may be missing, making empirical covariance infeasible. We propose estimating the underlying covariance kernel using a neural network architecture. Building on the concept of raw covariance introduced in prior work, our method differs in that it requires training the neural network only once, whereas previous approaches must fit a local smoothing function every time the covariance is estimated.