A.V. Pankratov - Post-graduate Student, Department of Computer Engineering, Vladimir State University named af-ter A.&N. Stoletovs. E-mail: Aleksey112358@gmail.com V.N. Lantsov - Dr. Sc. (Eng.), Professor, Head of Department of Computer Engineering, Vladimir State University named after A.&N. Stoletovs. E-mail: lantsov@vlsu.ru

In recent years the neural networks approaches have been recognized as a powerful tool for modeling and design of circuits. Neural networks have the ability to model multidimensional and nonlinear relationships. The evaluation from input to output of a trained neural network model is also very fast. These features make neural networks a useful alternative for device modeling where a mathematical model is not available or repetitive simulation is required. A neural network trained to model original circuits can be called the forward model where the model inputs are physical or geometrical parameters and outputs are electrical parameters. For design purposes, the information is often processed in the reverse direction in order to find the geometrical/physical parameters for given values of electrical parameters, which is called the inverse problem. There are two methods to solve the inverse problem, i.e., the optimization method and direct inverse modeling method. In the optimization method, the simulator or the forward model is evaluated repetitively in order to find the optimal solutions of the physical parameters that can lead to a good match between modeled and specified electrical parameters. This method is also known as the synthesis method. In this paper the neural network modeling techniques are presented for modeling and design using the concept of inverse modeling where the inputs to the inverse model are electrical parameters and outputs are physical/geometrical parameters. Training the neural network inverse model directly may become difficult due to the nonuniqueness of the input-output relationship in the inverse model. We propose the two approaches to solve such a problem. The first approach uses the detecting multivalued solutions in training data. The data containing multivalued solutions are divided into groups according to derivative information using a neural network forward model such that individual groups do not have the problem of multivalued solutions. Multiple inverse models are built based on divided data groups, and are then combined to form a complete model. The second approach uses the mixture density network.

 

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