Lisa Kusch (TU Eindhoven)
Meta-Optimization of Physics-Informed Neural Networks for Freeform Reflector and Lens Design
Wednesday, 17 December 2025, 11:00–12:00 in HG03.085
Abstract
In optical design for illumination purposes, the objective is to determine a freeform optical surface that produces a desired light distribution at a target, given an input distribution from a light source. For specific configurations of the optical system, this inverse problem can be formulated as a partial differential equation (PDE) of Monge-Ampère type with a transport boundary condition. The focus of the present work is on parallel-to-far-field systems with a single convex reflector or freeform lens surface.
Numerically, a least-squares finite difference solver can be used to solve this type of PDE. In recent studies, a neural network-based approach has demonstrated potential as a viable alternative, often outperforming the least-squares approach [1]. These models rely on a loss function comprising three components: one for the residual in the interior of the domain, one for the boundary condition, and one to penalize non-convexity.
In this talk, the derivation of the underlying equations and the results of using a physics-informed neural network approach are presented. Further results on the optimization strategy for finding the neural network parameters will be discussed. This includes a meta-optimization strategy to explore the meta-parameters of the presented method. Finally, future projects and challenges in the context of freeform optical design are presented.
[1] R. Hacking, L. Kusch, K. Mitra, M. Anthonissen, W. IJzerman, A neural network approach for solving the Monge–Ampère equation with transport boundary condition, Journal of Computational Mathematics and Data Science, 15:100119, 2025.