Machine Learning Surrogate Modeling for Meshless Methods: Leveraging Universal Approximation

This paper presents a machine learning (ML) surrogate modeling for fast processing in meshless/meshfree methods. The main idea is to leverage the universal approximation (UA) propriety of supervised ML models (shallow/deep learning and other regression models) to surrogate the heavy shape function construction in meshless methods. The resulting ML metamodel preserves the same accuracy of the meshless interpolation while avoiding costly matrix inversion operations. The total computation time for solving 3D test simulation problems (using more than 20k nodes) is reduced by a factor of 1k in the case of the Gaussian process (GP) metamodel.