  We propose a novel approach to marked Hawkes kernel inference which we name
the moment-based neural Hawkes estimation method. Hawkes processes are fully
characterized by their first and second order statistics through a Fredholm
integral equation of the second kind. Using recent advances in solving partial
differential equations with physics-informed neural networks, we provide a
numerical procedure to solve this integral equation in high dimension. Together
with an adapted training pipeline, we give a generic set of hyperparameters
that produces robust results across a wide range of kernel shapes. We conduct
an extensive numerical validation on simulated data. We finally propose two
applications of the method to the analysis of the microstructure of
cryptocurrency markets. In a first application we extract the influence of
volume on the arrival rate of BTC-USD trades and in a second application we
analyze the causality relationships and their directions amongst a universe of
15 cryptocurrency pairs in a centralized exchange.
