Abstract
In this paper, we test the methods and algorithms for constructing neural network models from equations and data using the example of the problem on the restoration of the Laplace equation solutions according to the measurements in a unit square. We estimate the quality of approximate solutions constructed with the help of neural networks for different sets of system parameters (the number of points in which the operator is calculated, the number of test points on one side of the square). During the experiment, all test points inside the square are regenerated. Selection of the solution is carried out by optimization of the error functional. Optimization is carried out using the algorithm of training neural networks Resilient Propagation (RProp). The algorithms considered can be applied to a wide range of practically interesting problems, since they practically do not depend on the form of the differential equation, its linearity, the geometry of the region, etc.
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Acknowledgment
This paper is based on research carried out with the financial support of the grant of the Russian Scientific Foundation (Project No. 18-19-00474).
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Tarkhov, D.A., Migovan, M.A., Ivanenko, K.A., Smirnov, S.A., Kobicheva, A.M. (2019). The Problem of Solution Restoration by Measurements for the Laplace Equation. In: Antipova, T., Rocha, A. (eds) Digital Science. DSIC18 2018. Advances in Intelligent Systems and Computing, vol 850. Springer, Cham. https://doi.org/10.1007/978-3-030-02351-5_51
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DOI: https://doi.org/10.1007/978-3-030-02351-5_51
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