Photo-electron spectra obtained with intense pulses generated by free-electron lasers through self-amplified spontaneous emission are intrinsically noisy and vary from shot to shot. We extract the purified spectrum, corresponding to a Fourier-limited pulse, with the help of a deep neural network. It is trained on a huge number of spectra, which was made possible by an extremely efficient propagation of the Schr"odinger equation with synthetic Hamilton matrices and random realizations of fluctuating pulses. \added{We show that the trained network is sufficiently generic such that it can purify atomic or molecular spectra, dominated by resonant two- or three-photon ionization, non-linear processes which are particularly sensitive to pulse fluctuations. This is possible without training on those systems.

中文翻译：

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使用合成汉密尔顿矩阵通过机器学习从噪声脉冲中纯化电子光谱

由自由电子激光器通过自放大自发发射产生的强脉冲获得的光电子光谱本质上是有噪声的，并且每次发射都不同。我们借助深度神经网络提取与傅立叶极限脉冲相对应的纯化光谱。通过大量的光谱对其进行训练，这是通过利用合成汉密尔顿矩阵和波动脉冲的随机实现来实现的Schr“ odinger方程的极高效传播而实现的。\ add {我们证明了训练后的网络足够通用，因此它可以纯化原子或分子光谱，主要由对脉冲波动特别敏感的共振两光子或三光子电离非线性过程控制，而无需在这些系统上进行训练就可以实现。