Аннотация:A multi-criteria inverse problem is reduced to a system of operator equations on compact sets. It is shown that some a posteriori error estimates of solutions of the multi-criteria problem decrease with an increasing number of the criteria used. The approximation neural-network method for solving the multi-criteria inverse problem is presented. An example of a numerical solution of the two-criterion problem of geoelectrics is given, and the a posteriori error estimates are calculated.