Abstract:
A neural network method for solving boundary value problems of mathematical physics is developed. In particular, based on the trust region method, a method for learning radial basis function networks is proposed that significantly reduces the time needed for tuning their parameters. A method for solving coefficient inverse problems that does not require the construction and solution of adjoint problems is proposed.
Key words:boundary value problems of mathematical physics, neural networks, radial basis function networks, learning of neural networks, trust region method, coefficient inverse problems.