  Spatial L{\'{e}}vy-like flights are introduced as a way in the absorbing
phase transitions to produce non-local interactions. We utilize the
autoencoder, an unsupervised learning method, to predict the critical points
for $(1+1)$-d directed percolation with such spatial long-range interactions.
After making a global coverage of the reaction-diffusion distance and taking a
series of different values for the parameter ${\beta}$ in the distribution
$P(r){\sim}1/r^{\beta}$, the critical points $P_c$ that can be continuously
varied are obtained. And the dynamic decay of the particle density under the
critical points was counted as a way to determine the critical exponent
${\delta}$ of the survival rate. We also investigate the active behavior of the
system's particles under the critical point with increasing time steps, which
allows us to determine the characteristic time $t_f$ of the finite-scale
systems. And the dynamic exponents $z$ are obtained using the scaling relation
$t_f{\sim}L^{z}$. We find that the autoencoder can identify this characteristic
evolutionary behavior of particles. Finally, we discuss the compliance of the
scaling form $1/{\delta}-({\beta}-2)/{\delta}z=2$ in different ${\beta}$
intervals as well as a method to introduce a global scaling mechanism by
generating a random walking step using the L{\'{e}}vy distribution.
