  This study proposes a supervised learning method that does not rely on
labels. We use variables associated with the label as indirect labels, and
construct an indirect physics-constrained loss based on the physical mechanism
to train the model. In the training process, the model prediction is mapped to
the space of value that conforms to the physical mechanism through the
projection matrix, and then the model is trained based on the indirect labels.
The final prediction result of the model conforms to the physical mechanism
between indirect label and label, and also meets the constraints of the
indirect label. The present study also develops projection matrix normalization
and prediction covariance analysis to ensure that the model can be fully
trained. Finally, the effect of the physics-constrained indirect supervised
learning is verified based on a well log generation problem.
