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We report the utilization of radial basis function neural networks (RBFNN) with multi-quadric (MQ) and inverse multi-quadric (IMQ) basis functions for numerical simulation of velocity-field reconstruction in fluid-structure interaction (FSI) problem with the presence of a very step velocity jump at the fluid-solid interface. The NN models were developed and utilized as approaches of investigation to fully reconstruct the velocity-field at the fluid-solid interface. One-dimensional compressible fluid coupled with elastic solid under strong impact, which belongs to an Eulerian-Lagrangian Riemann problem, was simulated. When the resolution in the vicinity of the interface was further investigated and analyzed, the RBFNN-IMQ models have shown better performance than the RBFNN-MQ and the RBFNN with Gaussian basis function, in which the RBFNN with Gaussian basis function has been previously shown to produce better accuracy compared to the MLP model for the problem considered. Meanwhile, the RBFNN with Gaussian basis function models were better than the RBFNN-MQ models for the problem considered. The NN model accuracies were validated to the problem analytical solution and the simulation results were further presented and discussed.