On important information for inverse problems and its visualization

The «important information» is considered as the formalization of the intuitive notions of the information related with «goal», «instruction», «control», «intention». The important information corresponds the knowledge of the movement in the control variables space that is necessary to achieve the goal with the known uncertainty under the present system state. The important information has the vector (goal functional gradient) and the tensor (Fisher’s information matrix) components. For inverse problems vector component transfer for such information is described by adjoint equations. The illustrations are provided that present the generation and transfer of the vector component of important information in inverse computation fluid dynamics problems. We also consider the communication of important information to other existing information theories.