A novel physics-informed framework based on radial basis functions for solving forward and inverse elastostatic problems

Abstract

This paper presents a novel physics-informed framework based on radial basis functions (RBFs) for solving forward and inverse elastostatic problems in two dimensions. The proposed framework integrates RBFs into physics-informed neural networks (PINNs), employing a fully connected neural network with the angle of source point as input, and the source point location and shape parameter as outputs, to approximate the solutions across the computational domain. By leveraging the established RBF formula and automatic differentiation technique, we construct a loss function based on the governing equations and boundary conditions. The neural network is then trained using the back-propagation of loss function and the gradient descent method, with the aim of optimizing the source point distribution and shape parameter. Numerical experiments demonstrate the effectiveness and accuracy of the proposed framework for dealing with elastostatic and inverse Cauchy problems even in complex geometries and thin-walled structures. Compared to traditional methods, including PINNs and RBF collocation methods, the proposed framework provides improved accuracy and robustness, resulting in more reliable numerical results.