Application of Reduced Order Surrogate Models for Solving Inverse Problems by the Optimization Method with Apriori Information Accumulation.

Abstract

The paper suggests a method of creating combined reduced order surrogate models for solving multi-parameter inverse problems by the optimization method. The peculiarity of the method is the combination of the known advantages of these models with the introduction of additional apriori information about the objects under study. This information is obtained by modeling following the generated design of a homogeneous computer experiment at the stage preceding the application of the model. The design of experiment includes the main mandatory factors, as well as several additional factors ensure higher accuracy of the solution problem by taking into account the increased amount of information about the object when varying the effects of physical actions on it, as well as interference. The method requires the mandatory creation of surrogate models based on deep fully connected neural networks. This is due to the use of the unique generalizing properties of artificial neural networks, which allows us to implicitly determine the patterns of the object's response to physical disturbances hidden in the data. In addition, the use of deep neural networks increases the accuracy of approximation of response hypersurfaces when building surrogate models. The dimensionality of the search space is reduced by applying nonlinear transformations under the Kernel PCA method, which allows for its significant reduction, providing a considerably simplified structure of the neural network surrogate model and facilitated conditions for the implementation of optimization algorithms for finding extremes. Since inverse problems, due to their incorrect formulation, are characterized by complex topographies of response hypersurfaces when solved by the optimization method, the method provides for the use of algorithms for finding global extremes. The effectiveness of the method is demonstrated in model examples, which showed a sufficiently high accuracy on test problems.