Active emulation of computer codes with Gaussian processes -- Application to remote sensing

Signal Processing, Universidad Rey Juan Carlos (URJC), Camino del Molino 5, 28943 Fuenlabrada, Spain Abstract Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and exhaustive simulations. V ery often such codes incorporate heuristics that ironically make them less tractable and transparent. This paper introduces an active learning methodology for adaptively constructing surrogate models, i.e. emulators, of such costly computer codes in a multi-output setting. The proposed technique is sequential and adaptive, and is based on the optimization of a suitable acquisition function. It aims to achieve accurate approximations, model tractability, as well as compact and expressive simulated datasets. In order to achieve this, the proposed Active Multi-Output Gaussian Process Emulator (AMOGAPE) combines the predictive capacity of Gaussian Processes (GPs) with the design of an acquisition function that favors sampling in low density and fluctuating regions of the approximation functions. Comparing different acquisition functions, we illustrate the promising performance of the method for the construction of emulators with toy examples, as well as for a widely used remote sensing transfer code. Keywords: Active learning, Gaussian process, emulation, design of experiments, computer code, remote sensing, radiative transfer model 1 Introduction In many areas of science and engineering, systems are analyzed by running computer code simulations which act as convenient approximations of reality. They allow us to simulate many different systems of interest and characterize the involved processes, such as turbulence or energy transfer, and their interactions and relevance. Depending on the body of literature, they are known as physics-based or mechanistic models, or simply simulators [30, 39]. Two important limitation are associated with simulators. The first, and perhaps the most important problem of these computer codes, is their often high computational cost, which hampers reliable and exhaustive simulations.