Toward high-speed effective numerical simulation of multiple filamentation of high-power femtosecond laser radiation in transparent medium

High-power femtosecond laser radiation during the propagation in air (and other transparent media) experiences multiple filamentation. Filamentation is a unique nonlinear optical phenomenon, which is accompanied by a wealth of nonlinear optical effects such as formation of extended plasma channels in the beam wake, generation of higher harmonics and supercontinuum, generation of THz radiation. The manifestations of laser filamentation can be useful for solving atmospheric optics problems related to remote sensing of the environment as well as directed transmission of laser power. The classical numerical methods used for simulating the nonlinear long-range atmospheric propagation of high-power radiation with a sufficiently large laser beam aperture have almost reached their limit regarding the acceleration of calculations. To solve this problem and speed-up the numerical simulations of laser filamentation, we propose an improved numerical technique based on a modified method of phase screens constructed on a sparse spatial grid. Within the framework of this technique, we seek for optimal ansatz (substitution function) to the governing equations using the machine learning technology, which provides for the best correspondence to the numerical solution of the test problem using a denser spatial grid