Solving boundary value problems of mathematical physics using radial basis function networks

DOI10.1134/S0965542517010079zbMath1368.65240MaRDI QIDQ2357125

Vladimir Ivanovich Gorbachenko, Maxim Valerievich Zhukov

Publication date: 19 June 2017

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

neural networkstrust region methodradial basis function networkscoefficient inverse problemslearning of neural networksboundary value problems of mathematical physics

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Neural networks for/in biological studies, artificial life and related topics (92B20)

Related Items (6)

ON THE CONVERGENCE RATE OF THE SUBGRADIENT METHOD WITH METRIC VARIATION AND ITS APPLICATIONS IN NEURAL NETWORK APPROXIMATION SCHEMES ⋮ Efficient solving of boundary value problems using radial basis function networks learned by trust region method ⋮ Random vibration of hysteretic systems under Poisson white noise excitations ⋮ A collocation method with space-time radial polynomials for inverse heat conduction problems ⋮ Learning radial basis function networks with the trust region method for boundary problems ⋮ Training RBF neural networks for the solution of elliptic boundary value problems

Uses Software

• Mfree2D

Cites Work

• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Solution and control of PDE via global optimization methods
• Solving differential equations with radial basis functions: Multilevel methods and smoothing
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• An introduction to neural network methods for differential equations
• Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
• Numerical methods for solving inverse problems of mathematical physics.
• Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks
• Least-square-based radial basis collocation method for solving inverse problems of Laplace equation from noisy data
• Radial basis collocation method and quasi-Newton iteration for nonlinear elliptic problems
• The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
• Scattered Data Interpolation: Tests of Some Method
• Trust Region Methods
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