Neural Network Technique in Some Inverse Problems of Mathematical Physics

A Two-layer Semi Empirical Model of Nonlinear Bending of the Cantilevered Beam

“…A simpler case leads to refinement of model parameters, which is mathematically expressed in coefficients of inverse problems. To solve such problems, there are a number of approaches, one of which is the use of neural networks [4,7]. A variant (to which the problem considered in this article belongs) is also possible, when no choice of parameters allows us to reflect experimental data with reasonable accuracy.…”

“…Previously, we solved such problems using our methodology for constructing the neural network model of the object by differential equations and additional data [1][2][3][4][5][6][7][8]. However, the training of neural networks requires a fairly large computational cost.…”

“…The developed methods can be applied for long-term forecasting of the behavior of building beams, various structural elements of load-lifting machines and mechanisms, taking into account the real picture of wear, aging and corrosion of metal. In [10] the necessity of an estimation of influence of deterioration of the 4 Author to whom any correspondence should be addressed building equipment and the hand tool on working conditions of workers of building industry as the most traumatic kind of activity is revealed and justified. From this point of view, solving inverse problems in modeling the state of loaded elements will increase the reliability of forecasting results.…”

Unified approach to constructing the neural network models of real objects. Part 1

“…In other works, cellular neural networks were used to solve partial differential equations. They combine the features of cellular automata and neural networks.…”

“…In the monograph, the possibilities of using neurocomputers in solving boundary value problems of field theory were studied. In the work of Gorbachenko and Moskvitin, the neural network approach is used in ill‐posed problems, ie, for solving the inverse problem of mathematical physics, in which the coefficients of the equation (or functions entering the initial‐boundary conditions) are recovered from the set of solution values at certain points of the domain. In the works of Gorbachenko and Yanichkina, following the work of the authors of the article, radial‐basis networks were used to solve partial differential equations.…”