Supervision: Pierre Vandergheynst,Daniel Probst
Semester project (master)
Coordinate-based neural networks, sometimes called Implicit Neural Representations (INRs), used for instance in NeRFs, learn to represent highly complex functions by treating pairs of coordinates and associated function evaluations as a dataset. These representations turn out to be extremely useful because they are resolution-independent and allow one to easily manipulate the underlying function via manipulations of its latent representation. Most of the applications so far have occurred in the realm of images, videos, or computer graphics. There are, however, situations - in chemistry, biology, and physics - where one would like to represent a (family of) continuous closed surfaces efficiently. In chemistry, for instance, such a function could represent the van der Waals surface of a molecule and be used to model chemical interactions. In this project, we will train INR-type neural architecture to efficiently represent families of surfaces by mapping them first to spherical functions. This common representation will allow us to build useful inductive biases, such as rotation invariance, and provide a unique domain to compare surfaces for classification or regression tasks. We will apply this system to learn representations of small molecules and solve benchmark tasks in chemistry.