通过神经网络参数化直接优化三维有限光源反射器
Direct Optimization of a 3D Finite-Source Reflector via Neural-Network Parameterization
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中文总结 AI 辅助
该研究提出一种用神经网络参数化三维自由形式反射器的直接优化方法，结合可微分光线追踪、H⁻¹型谱权重及带特定更新规则的BFGS算法，可在单GPU上数秒内可靠收敛，实现有限光源到指定远场分布的转换。
中文摘要 AI 辅助
我们提出了一种用于三维自由形式反射器的直接优化方法，该反射器可将有限光瞳（étendue）光源的光线转换为规定的远场角强度分布。反射器轮廓由小型神经网络（多层感知机）表示，该网络通过可微分光线追踪目标进行端到端训练。我们还将发射方向参数化为日晷坐标（gnomonic coordinates），并展示如何利用这一设置确保每条发射光线都与反射器相交。在每次迭代中，网络会转换为双三次样条表示以提高光线追踪效率，该平滑表面的相交问题通过阻尼牛顿法求解，梯度则通过隐函数定理计算。追踪得到的输出分布在“软”直方图上与期望目标进行比较，采用H⁻¹型谱权重以强调通量的长程传输，从而提升收敛性。优化使用带自缩放Broyden更新和高原扰动规则的BFGS方法，以防止停滞。对于所有测试示例，该方法在单个GPU上可在数秒内可靠收敛。
英文摘要
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.
发表机构
- Eindhoven University of Technology（埃因霍温理工大学）
- Signify（昕诺飞）
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