Numerical solving of hydrodynamic problems using machine learning methods
DOI:
https://doi.org/10.18372/2310-5461.38.12823Keywords:
hydrodynamic problem, search for a solution, numerical method, machine learning, neural network, reinforcement learningAbstract
The use of the neural network approach in the process of finding a solution of a hydrodynamic problem by numerical methods is proposed. The two areas of possible application of the technology of neural networks are considered – the choice of initial approximation to the solution and the search for the next approximation. To select the initial approximation, it is proposed to solve the combined task of classification and regression based on the existing base of distributions samples and on the existing base of patterns of space transformations. An architecture of the combined neural network which solves this problem is proposed.
For finding the transformation of the problem space, the use of radial-basis neural network is proposed. The mathematical apparatus for tuning the network with arbitrary number of neurons of the output layer is proposed. It is proposed to take the number of hidden layer neurons less than the number of educational transformation samples and find an approximate solution. The task of finding the optimal weight values in this case can be considered as a task of minimization of the target function, which describes the network outputt error.
It is proposed to construct a neural network for finding the next approximation of a solution of a hydrodynamic problem based on a generalization of the principle previously proposed for solving solutions of one-dimensional differential equations.
Finding the next approximation in the case of solving a task on a multiprocessor system is presented as a game with multiple players, each of which must find a compromise between local and global search purposes. It is proposed to replace one common neural network with a set of neural networks that interact with each other. The proposed approaches can reduce the amount of computation needed to find a solution.
References
Глазок О.М., Квач М.М. Розв’язання гідродинамічної задачі за методом багатоточкового пошуку у розподіленому обчислювальному середовищі/ О.М.Глазок, М.М.Квач. //Проблеми інформатизації та управління: зб. наук. праць. – К.: НАУ. – 2015. – Вип. 4(52). – С. 9-16.
S.Raschka, V.Mirjalili. Python Machine Learning: Machine Learning and Deep Learning with Python, scikit-learn, and TensorFlow, 2nd ed. – Packt Publishing, 2017. – 622 p.
Combining machine learning with computational hydrodynamics for prediction of tidal surge inundation at estuarine ports. /Jon French, Robert Mawdsley, Taku Fujiyama, Kamal Achuthanb. //UITАМ Symposium on Storm Surge Modelling and Forecasting Procedia: IUTAM No.25 (2017). – Pp 28-35. doi:10.1016/j.piutam.2017.09.005
Weymouth G.D., Dick K.P. Physics-Based Learning Models for Ship Hydrodynamics. //Journal of Ship Research, Vol. 57, no. 1 (March 1, 2013). – 1–12.
A. Alibakshi. Strategies to develop robust neural network models: prediction of flash point as a case study //Analytica Chimica Acta, 2018. – 34 p. doi:10.1016/j.aca.2018.05.015.
Advantages of Radial Basis Function Networks for Dynamic System Design / Hao Yu; T. Xie, S. Paszczynski; B.M. Wilamowski. // IEEE Transactions on Industrial Electronics. Vol. 58, Issue 12, Dec. 2011 . – P. 5438-5450. doi:10.1109/TIE.2011.2164773.
Lagaris I.E., Likas A. and Fotiadis D.I.. Artificial neural networks for solving ordinary and partial differential equations // IEEE Transactions on Neural Networks, Sep. 1998. – Vol. 9, No. 5. – Pp. 987-1000.
Яничкина Е.В., Горбаченко В.И. Решение эллиптических дифференциальных уравнений в частных производных с использованием радиально-базисных нейронных сетей. //Научная сессия МИФИ-2006. Нейроинформатика. Часть 3. Теория нейронных сетей. Применение нейронных сетей. Нейронные сети и когнитивные системы. – С. 15-21.
Mahmoud S., Miles S., Luck M.. Cooperation emergence under resource-constrained peer punishment. //Proc. of the 2016 Int. Conf. on Autonomous Agents & Multiagent Systems. P. 900-908.
Vidhate D.A., Kulkarni P.. Enhanced Cooperative Multiagent Learning Algorithms (ECMLA) using Reinforcement Learning. //Int. Conference on Computing, Analytics and Security Trends (CAST). IEEE Xplorer, 2017. – Pp. 556-561.
