Ntumba Elie Nsampi after successfully defending his thesis. Photo: MPI-INF/Philipp Zapf-Schramm
On Thursday, 16 July 2026 Ntumba Elie Nsampi defended his thesis with the title: “Aggregation in Neural Fields via Differential Constraints”. Since May 2022 he was PhD student in Computer Science at Saarland University in Saarbrücken and the Max Planck Institute for Informatics under the supervision of Dr. Thomas Leimkühler and Prof. Hans-Peter Seidel, head of Computer Graphics department . The doctoral degree is awarded by Saarland University.
Abstract of the thesis:
Aggregation operators, that is, operators defined through integration over continuous domains such as space, direction, or light paths, are central to visual computing. In prac-tice, aggregation on continuous functions is typically carried out either through discrete approximations or through Monte Carlo sampling. Neural fields have emerged as flexible representations of continuous signals, but despite their appealing properties, it remains unclear how aggregation operators can be realized directly on neural fields without re-verting to conventional approaches.
This thesis addresses this challenge through the observation that certain aggregation ope-rators, although global in nature, can in some cases be reformulated as local differential constraints. This makes it possible to realize aggregation on neural fields without resort-ing to explicit numerical integration. Building on this observation, this thesis contributes two methods that instantiate this prin-ciple in different settings. The first contribution is a method for continuous convolution on functions encoded as neural fields, based on convolution identities and the sparsity in-duced by repeated differentiation of piecewise polynomial kernels. The second contribu-tion is a novel formulation for volumetric inverse rendering under full global illumination, in which both the optical properties of the medium and the transported light field are represented as neural fields, while global illumination is enforced through a differential formulation of the radiative transfer equation together with image-based supervision.