T. V. Lazovskaya, D. A. Tarkhov and A. N. Vasilyev Pages 10 - 15 ( 6 )
Background: We consider the unified neural network simulation methodology concerning with construction of the robust mathematical models of complex systems in physics and technology based on the differential equation. This methodology allows overcoming the problems of research and simulation in Engineering caused by the complexity of geometry, different scale of processes etc. The analysis of patents with the differential equation solution as the essential part of a technique is carried out.Method: We present all stages of neural network modeling from the functional basis selection and quality functional building to verifying and refining models of objects in their operating. Results: Our approach successful applying to different types of problems with parameters is presented in this article. The stiff differential problem and differential-algebraic task with the different number of solutions are considered. In the catalyst problem, we solve the task in the region that is wider than the region of existence of the solution of the differential equation. Conclusion: The particular algorithms based on our unified neural network approach can be patented. The corresponding algorithms allow the natural parallelism. Moreover, Neurochip structures accelerating the work of the concrete equation solving algorithms can also be patented. Our methods can be used to create a new paradigm of supercomputing.
Artificial neural network (ANN), interval parameter, boundary value problem, heat-and-mass transfer, porous catalyst, point data, thermal diffusivity, stiff differential equation, differential-algebraic system.
Higher Mathematics Department, Institute of Applied Mathematics & Mechanics, Peter the Great Polytechnic University, P.O. Box: 195251, St Petersburg