Fast, Differentiable, GPU-Accelerated Ray Tracing for Multiple Diffraction and Reflection Paths

2025-10-17

AI Summary

Modeling electromagnetic wave propagation in complex environments containing planar reflectors and straight diffracting edges remains challenging due to the combinatorial explosion of multi-bounce reflection and diffraction paths and the lack of differentiable, scalable path optimization frameworks. Method: This paper proposes a unified, differentiable, and GPU-accelerated ray-path tracing optimization method grounded in Fermat’s principle. It formulates higher-order reflection and diffraction path search as a total optical path length minimization problem, embedding all interactions within a dimensionally consistent implicit differentiable framework—eliminating explicit case-based handling of reflections versus diffractions. Gradients are computed efficiently via implicit differentiation, avoiding costly automatic differentiation in iterative solvers. End-to-end gradient propagation and massive vectorized parallelism are realized using JAX and DrJIT. Results: The method achieves Newton-like convergence speed and significantly improves scalability for path ensembles exceeding 10,000 rays. It is open-sourced and validated on practical inverse wireless propagation design tasks.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Learning & Optimization for CV

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We present a fast, differentiable, GPU-accelerated optimization method for ray path tracing in environments containing planar reflectors and straight diffraction edges. Based on Fermat's principle, our approach reformulates the path-finding problem as the minimization of total path length, enabling efficient parallel execution on modern GPU architectures. Unlike existing methods that require separate algorithms for reflections and diffractions, our unified formulation maintains consistent problem dimensions across all interaction sequences, making it particularly suitable for vectorized computation. Through implicit differentiation, we achieve efficient gradient computation without differentiating through solver iterations, significantly outperforming traditional automatic differentiation approaches. Numerical simulations demonstrate convergence rates comparable to specialized Newton methods while providing superior scalability for large-scale applications. The method integrates seamlessly with differentiable programming libraries such as JAX and DrJIT, enabling new possibilities in inverse design and optimization for wireless propagation modeling. The source code is openly available at https://github.com/jeertmans/fpt-jax.

Problem

• Optimizes ray path tracing for reflections and diffractions
• Unifies reflection and diffraction handling for parallel computation
• Enables efficient gradient computation for inverse design applications

Innovation

• GPU-accelerated ray tracing for multiple diffraction paths
• Unified formulation maintains consistent problem dimensions
• Implicit differentiation enables efficient gradient computation