Controlling the longitudinal laser pulse shape in photoinjectors of Free-Electron Lasers is a powerful lever for optimizing electron beam quality, but systematic exploration of the vast design space is limited by the cost of brute-force pulse propagation simulations. We present a generative modeling framework based on Wasserstein Autoencoders to learn a differentiable latent interface between pulse shaping and downstream beam dynamics. Our empirical findings show that the learned latent space is continuous and interpretable while maintaining high-fidelity reconstructions. Pulse families such as higher-order Gaussians trace coherent trajectories, while standardizing the temporal pulse lengths shows a latent organization correlated with pulse energy. Analysis via principal components and Gaussian Mixture Models reveals a well behaved latent geometry, enabling smooth transitions between distinct pulse types via linear interpolation. The model generalizes from simulated data to real experimental pulse measurements, accurately reconstructing pulses and embedding them consistently into the learned manifold. Overall, the approach reduces reliance on expensive pulse-propagation simulations and facilitates downstream beam dynamics simulation and analysis.

翻译：控制自由电子激光器中光注入器的纵向激光脉冲形状是优化电子束质量的有力手段，但通过暴力脉冲传播仿真系统探索广阔设计空间的成本限制了其应用。我们提出了一种基于Wasserstein自编码器的生成建模框架，用于学习脉冲整形与下游束流动力学之间的可微分潜在界面。我们的实证结果表明，学习到的潜在空间具有连续性和可解释性，同时保持了高保真度的重构。高阶高斯函数等脉冲族呈现出连贯的轨迹，而标准化时间脉冲长度则显示出与脉冲能量相关的潜在组织结构。通过主成分分析和高斯混合模型的分析揭示了表现良好的潜在几何结构，使得通过线性插值在不同脉冲类型之间实现平滑过渡成为可能。该模型能够从仿真数据泛化到真实实验脉冲测量，精确重构脉冲并将其一致地嵌入到学习到的流形中。总体而言，该方法减少了对昂贵脉冲传播仿真的依赖，并促进了下游束流动力学的仿真与分析。