Integration of Geodesics in The Gravitational Field of a Rotating Black Hole Using A Nonlinear Neural Operator

The construction of model images of black hole shadows requires numerical integration of the equations of motion of photons in curved space-time, which is an example of an unstable system of nonlinear differential equations, the solution of which by classical iterative methods such as Runge - Kutta is a rather resource-intensive problem. A promising approach to solve this problem is the use of neural networks to approximate the nonlinear operators of the solution of ODEs. In this paper, the problem of finding geodesics is solved using a neural network DeepONet. Accuracy sufficient for image construction has been achieved at a higher speed of operation.