Benjamin Liu ’24


Computer Science

Project Title

Beyond Roughness: Statistical Characterization of Two-dimensional Fields Under Random Sampling

I explored machine learning methods to estimate and analyze different types of environmental data. Environmental data come as geographically distributed sets of measured or modeled variables, for example rainfall or vegetation type, that we may treat as samples of a spatial random field and its temporal evolution. Random fields are characterized by hyperparameters that define the statistical relationship between their values at different points in space and time. The isotropic Matérn random field is a general class with three continuous parameters that define its spectral structure: variance (σ2), mean-squared differentiability (ν) and correlation length (ρ). Working with Frederik Simons, I developed machine-learning methods to estimate the parameters of random fields. I employed MATLAB and Python programs to generate large sets of training data and developed a convolutional neural network to estimate their parameters. I gained significant experience working with neural networks and non-classification forms of machine learning methods. The project has given me more insight into the research process in the field of machine learning and artificial intelligence as a whole and how to apply these technologies to environmental data.

Internship Year


Project Category

Climate and Environmental Science


Simons Research Group, Department of Geosciences, Princeton University - Princeton, New Jersey


Frederik Simons, Professor of Geosciences