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.

翻译：本文提出了一种快速、可微分、GPU加速的优化方法，用于在包含平面反射体和直衍射边的环境中进行光线路径追踪。基于费马原理，我们的方法将路径寻找问题重新表述为总路径长度的最小化问题，从而能够在现代GPU架构上实现高效的并行执行。与现有方法需要为反射和衍射分别设计算法不同，我们的统一表述在所有交互序列中保持问题维度的一致性，使其特别适合向量化计算。通过隐式微分，我们实现了无需对求解器迭代过程进行微分的高效梯度计算，显著优于传统的自动微分方法。数值模拟结果表明，该方法的收敛速度可与专门的牛顿法相媲美，同时为大规模应用提供了更优的可扩展性。该方法可与JAX和DrJIT等可微分编程库无缝集成，为无线传播建模中的逆向设计与优化开辟了新的可能性。源代码已在https://github.com/jeertmans/fpt-jax公开提供。