  Multi-physical inversion plays a critical role in geophysics. It has been
widely used to infer various physical properties~(such as velocity and
conductivity). Among those inversion problems, some are explicitly governed by
partial differential equations~(PDEs), while others are not. Without explicit
governing equations, conventional multi-physical inversion techniques will not
be feasible and data-driven inversion requires expensive full labels. To
overcome this issue, we develop a new data-driven multi-physics inversion
technique with extremely weak supervision. Our key finding is that the pseudo
labels can be constructed by learning the local relationship among geophysical
properties at very sparse well-logging locations. We explore a multi-physics
inversion problem from two distinct measurements~(seismic and EM data) to three
geophysical properties~(velocity, conductivity, and CO$_2$ saturation). Our
results show that we are able to invert for properties without explicit
governing equations. Moreover, the label data on three geophysical properties
can be significantly reduced by 50 times~(from 100 down to only 2 locations).
