NG-DPSM: A neural green-distributed point source method for modelling ultrasonic field emission near fluid-solid interface using physics informed neural network

Abstract

Distributed point source method (DPSM) is a collocation point-based semi-analytical method to model the scattered ultrasonic fields in isotropic and anisotropic materials. It requires the evaluation of Green's function solutions and its rigorous differentiation for complex geometry problems having a large set of distributed point sources. DPSM is much faster than the finite element method (FEM) however, it is analytically demanding as it requires differentiation of the Green's function. The intricacy associated with differentiation operation hinders the potential application of DPSM in large-scale automation and real-time structural health monitoring. The current paper introduces machine-learning-based strategies within DPSM and yields the proposed Neural Green-DPSM (NG-DPSM) framework. A physics-informed neural network (PINN) is incorporated in the DPSM framework for evaluating the Green's function and its gradients. To train the PINN, displacement Green's function solutions of wave propagation in isotropic solid is used as the governing physics. Once the PINN is trained for displacement Green's function solutions, the NG-DPSM framework leverages the trained network and its automatic differentiation capability to predict displacement and stress fields annihilating the rigorous differentiation of Green's functions. The accuracy and efficacy of NG-DPSM are demonstrated using two numerical experiments. First, the ultrasonic fields are evaluated for the problem geometry of a plate immersed in fluid excited at different angles of incidence. Further, the efficacy of the proposed approach is demonstrated for wave scattering through a circular hole in the plate. The results show a strong agreement between the ultrasonic fields computed using both NG-DPSM and conventional DPSM.