NASA's new Surface Biology and Geology (SBG) mission will launch in late 2026 and carry a hyperspectral imager to observe Earth's surface at high resolution (~30 meter) in the visible and thermal regions of the electromagnetic spectrum. Daily data volume is expected to be 2.5 to 5 petabytes. The mission's science objectives include understanding active surface changes, snow and ice accumulation, hazard risks, changing land use, plant physiology, and terrestrial and aquatic ecosystems. To meet these objectives, geophysical properties of Earth's surface must be inferred from observed spectra. Spectra are related to surface states via physical forward models embedded within inference algorithms. These forward models are computationally demanding, and will require emulation in order to keep up with data flow. In this talk we introduce a forward model emulator for SBG using a new method for fitting covariance parameters of Gaussian Processes, called Kernel Flows (KF; Owhadi and Yoo, 2019). KF uses mini-batch stochastic gradient descent and cross-validation to achieve robust estimates in a computationally efficient manner. KF has deep connections to neural networks when viewed through the lens of decision theory. The innovation of this work is in the computational implementation of the algorithm, and its application in the remote sensing context.