aiqbench analysis
This research applies neural network parameterization to directly optimize 3D freeform reflectors, enabling efficient end-to-end training via differentiable ray tracing. By representing the reflector profile with a multilayer perceptron and solving intersections using implicit function theorem gradients, the method achieves reliable convergence in seconds on a single GPU. The approach represents a significant advancement in applying machine learning to complex optical design problems involving finite étendue sources.
Direct Optimization of a 3D Finite-Source Reflector via Neural-Network Parameterization
arXiv:2609.00899v1 Announce Type: cross Abstract: We present a direct optimization method for three-dimensional freeform reflectors that transform the light of a finite-\'etendue source into a prescribed far-field angular intensity distribution. The reflector profile is represented by a small neural network (a multilayer perceptron), which is trained end-to-end through a differentiable ray-tracing objective. We furthermore parameterize the emission directions in gnomonic coordinates, and show how we use this to ensure that every emitted ray intersects the reflector. At each iteration, the network is converted to a bicubic spline representation for ray-tracing efficiency, and intersections with this smooth surface are solved by a damped Newton solve, with gradients computed via the implicit function theorem. The traced output distribution is compared with the desired target on a 'soft' histogram, under an $H^{-1}$-type spectral weighting that emphasizes long-range transport of flux to improve convergence. Optimization is performed using a BFGS method with self-scaled Broyden updates and a plateau-perturbation rule to prevent stalling. The method converges reliably within seconds on a single GPU for all examples tested.
Abstract:We present a direct optimization method for three-dimensional freeform reflectors that transform the light of a finite-étendue source into a prescribed far-field angular intensity distribution. The reflector profile is represented by a small neural network (a multilayer perceptron), which is trained end-to-end through a differentiable ray-tracing objective. We furthermore parameterize the emission directions in gnomonic coordinates, and show how we use this to ensure that every emitted ray intersects the reflector. At each iteration, the network is converted to a bicubic spline representation for ray-tracing efficiency, and intersections with this smooth surface are solved by a damped Newton solve, with gradients computed via the implicit function theorem. The traced output distribution is compared with the desired target on a 'soft' histogram, under an $H^{-1}$-type spectral weighting that emphasizes long-range transport of flux to improve convergence. Optimization is performed using a BFGS method with self-scaled Broyden updates and a plateau-perturbation rule to prevent stalling. The method converges reliably within seconds on a single GPU for all examples tested.
16 pages, 4 figures, 2 tables. Submitted to Journal of the Optical Society of America A
Optics (physics.optics); Machine Learning (cs.LG)
arXiv:2609.00899 [physics.optics]
(or arXiv:2609.00899v1 [physics.optics] for this version)
https://doi.org/10.48550/arXiv.2609.00899 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 279 words
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