Gaussian Process Regression and Nested Sampling for Planetary Parameter Prediction

In this project, we implemented a Gaussian Process (GP) regression framework using MATLAB to model two planetary (Earth) parameters, the surface temperature and albedo, as functions of planetary rotation rate and insolation (the amount of sunlight impinging on the planet). We used simulation data from the NASA ROCKE-3D general circulation model developed by the NASA Goddard Institute for Space Studies (GISS). The GP model generates a joint multivariate Gaussian distribution that is entirely captured by a covariance matrix and the output of a training data set. The covariance matrix is determined by the input data and the three hyperparameters a GP requires: lengthscale, noise variance, and signal variance. We optimized this set of hyperparameters by using standard kernel functions to generate the covariance matrix and then calculating the log-likelihood of the outputs given the model and the inputs. The kernel functions we used included the squared exponential kernel and the Matern family of kernels. The Nested Sampling and Markov Chain Monte Carlo algorithms were used to efficiently explore the high-dimensional parameter space using log-likelihood. We also locate the areas of highest uncertainty to inform future data generation and collection (Bayesian Adaptive Exploration). We visualize the predictions through surface plots that display the predicted mean and uncertainty of the planet’s surface temperature and albedo as a function of the values of rotation rate and insolation.