We employ two machine learning techniques, i.e., neural networks and genetic-programming-based symbolic regression, to examine the dynamics of the electron-positron pair creation process with full space–time resolution inside the interaction zone of a supercritical electric field pulse. Both algorithms receive multiple sequences of partially dressed electronic and positronic spatial probability densities as training data and exploit their features as a function of the dressing strength in order to predict each particle’s spatial distribution inside the electric field. A linear combination of both predicted densities is then compared with the unambiguous total charge density, which also contains contributions associated with the independent vacuum polarization process. After its subtraction, the good match confirms the validity of the machine learning approach and lends some credibility to the validity of the predicted single-particle densities.

中文翻译：

---

正负电子对生成过程中的机器学习技术

我们采用两种机器学习技术，即神经网络和基于遗传编程的符号回归，以在超临界电场脉冲的相互作用区域内以全时空分辨率检查正负电子对产生过程的动力学。这两种算法都接收多个部分修饰的电子和正电子空间概率密度序列作为训练数据，并利用它们的特征作为修饰强度的函数来预测每个粒子在电场内的空间分布。然后将两个预测密度的线性组合与明确的总电荷密度进行比较，后者还包含与独立真空极化过程相关的贡献。减去之后，