  Many time series are effectively generated by a combination of deterministic
continuous flows along with discrete jumps sparked by stochastic events.
However, we usually do not have the equation of motion describing the flows, or
how they are affected by jumps. To this end, we introduce Neural Jump
Stochastic Differential Equations that provide a data-driven approach to learn
continuous and discrete dynamic behavior, i.e., hybrid systems that both flow
and jump. Our approach extends the framework of Neural Ordinary Differential
Equations with a stochastic process term that models discrete events. We then
model temporal point processes with a piecewise-continuous latent trajectory,
where the discontinuities are caused by stochastic events whose conditional
intensity depends on the latent state. We demonstrate the predictive
capabilities of our model on a range of synthetic and real-world marked point
process datasets, including classical point processes (such as Hawkes
processes), awards on Stack Overflow, medical records, and earthquake
monitoring.
