The proposed framework for adaptive Fourier integration can be extended to handle non-stationary Gaussian processes by incorporating time-varying spectral densities. In the context of Gaussian processes, non-stationarity refers to the covariance function depending on both the spatial distance between points and the specific points themselves. This can be achieved by introducing additional parameters or functions in the spectral density that capture the non-stationarity. For example, one could introduce time-dependent parameters in the spectral density function to model temporal variations in the process. By allowing the spectral density to vary with time or other relevant variables, the framework can adapt to non-stationary processes and provide accurate evaluations of the covariance function at irregular locations.