A controversial issue in the research of mathematics of intelligence h
as been that of the roles of a priori knowledge versus adaptive learni
ng, After discussing mathematical difficulties of combining a priority
with adaptivity encountered in the past, we introduce a concept of a
model-based neural network, whose adaptive learning is based on a prio
ri models. Applications to target detection in SAR images are discusse
d, We briefly overview the SAR principles, derive relatively simple ph
ysics-based models of SAR signals, and describe model-based neural net
works that utilize these models. A number of real-world application ex
amples are presented.