Deep Learning for Feynman's Path Integral in Strong-Field Time-Dependent Dynamics

Feynman's path integral approach is to sum over all possible spatiotemporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in the classical view. However, the complete characterization of the quantum wave function with infinite paths is a formidable challenge, which greatly limits the application potential, especially in the strong-field physics and attosecond science. Instead of brute-force tracking every path one by one, here we propose a deep-learning-performed strong-field Feynman's formulation with a preclassification scheme that can predict directly the final results only with data of initial conditions, so as to attack unsurmountable tasks by existing strong-field methods and explore new physics. Our results build a bridge between deep learning and strong-field physics through Feynman's path integral, which would boost applications of deep learning to study the ultrafast time-dependent dynamics in strong-field physics and attosecond science and shed new light on the quantum-classical correspondence.