  Carbon dioxide Capture and Storage (CCS) is an important strategy in
mitigating anthropogenic CO$_2$ emissions. In order for CCS to be successful,
large quantities of CO$_2$ must be stored and the storage site conformance must
be monitored. Here we present a deep learning method to reconstruct pressure
fields and classify the flux out of the storage formation based on the pressure
data from Above Zone Monitoring Interval (AZMI) wells. The deep learning method
is a version of a semi conditional variational auto-encoder tailored to solve
two tasks: reconstruction of an incremental pressure field and leakage rate
classification. The method, predictions and associated uncertainty estimates
are illustrated on the synthetic data from a high-fidelity heterogeneous 2D
numerical reservoir model, which was used to simulate subsurface CO$_2$
movement and pressure changes in the AZMI due to a CO$_2$ leakage.
