  This paper introduces the Neural Network for Nonlinear Hawkes processes
(NNNH), a non-parametric method based on neural networks to fit nonlinear
Hawkes processes. Our method is suitable for analyzing large datasets in which
events exhibit both mutually-exciting and inhibitive patterns. The NNNH
approach models the individual kernels and the base intensity of the nonlinear
Hawkes process using feed forward neural networks and jointly calibrates the
parameters of the networks by maximizing the log-likelihood function. We
utilize Stochastic Gradient Descent to search for the optimal parameters and
propose an unbiased estimator for the gradient, as well as an efficient
computation method. We demonstrate the flexibility and accuracy of our method
through numerical experiments on both simulated and real-world data, and
compare it with state-of-the-art methods. Our results highlight the
effectiveness of the NNNH method in accurately capturing the complexities of
nonlinear Hawkes processes.
