Решение дифференциальных уравнений с помощью исскусственных нейронных сетей
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Date
2013
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faculty of engineering and natural sciences
Abstract
We should note the special role of differential equations in the solution of many problems in mathematics, physics and engineering, as it is not always possible to establish a functional relationship between the data and the variables, but it is often possible to derive a differential equation that allows you to accurately predict the course of a particular process under certain conditions. Differential equations have great practical importance, being a powerful tool for exploring the many problems of science and technology: they are widely used in mechanics, astronomy, physics, in many problems of chemistry and biology. This is because very often the laws that govern certain processes are recorded in the form of differential equations, and the equations themselves act as a mean of quantitative interpretation of thus laws. To solve thus equations we take the most well suited networks belonging to a class of Hopfield neural networks. These networks have a way of transmitting output signals to the inputs, and the response of such networks is dynamic, i.e. after receive a new input the output is calculated and transmitting by feedback network modifies the input. Then the output is recalculated, and the process is repeated again. For the network, which can be considered as stable, the sequence of iterations lead to smaller changes in outputs, and at the end the output does not become permanent. There is also an unstable network, for which the process of selection of the output may never end. That's the essence of the network settings for gaining the desired result. Of course, there is also a classical numerical methods. But there are situations where these methods may not lead to a solution, or it can be obtained for a very large number of iterations. The neural network is much more flexible in this respect, and generally, an algorithm based on them is more efficient.
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Keywords
модель лотки - вольтерры, равновесная цена в модели вальраса, уравнение фолкнер
Citation
Газизов Т / Решение дифференциальных уравнений с помощью исскусственных нейронных сетей / 6M070400 — «Вычислительная техника и программное обеспениe» / 2013