Abstract <p>The application of the equivalence set method for solving inverse multicriteria problems for distributed systems with many input parameters is described. The direct problem, considered as an example, is described by a four-dimensional system of second-order partial differential equations with partial derivatives. This hydrodynamic model has several independent adjustable parameters, the values of which are not always determined from theory or observational data when studying the corresponding processes. Therefore, it is necessary to solve the inverse problem of determining the optimal sets of values of the model parameters by several criteria. To solve this problem, the equivalence set method is used, developed for solving multicriteria problems of discrete optimization and inverse problems of mathematical physics and other sciences. An algorithm for its application is described using this problem as an example, and the results of computer calculations are given.</p>