However, the success of conventional machine learning tools in data science is primarily attributed to the unprecedented large amount of labeled data-sets (big data), which can be either obtained by experiments or first-principle simulations. A similar methodology is also developed for the Timoshenko beam.Abstract: The recent explosion of machine learning (ML) and artificial intelligence (AI) shows great potential in the breakthrough of metal additive manufacturing (AM) process modeling, which is an indispensable step to derive the process-structure-property relationship. The frequency/wave number relationship of the continuum case can be closely simulated by using the reproducing kernel particle methods. The analysis of the wave equation shows the effectiveness of this approach. An adaptivity similar to hp-finite element method is obtained through the choice of an optimal dilation parameter. A variation in the size of the window implies a geometrical refinement and allows the filtering of the desired frequency range. The interpolation functions consist of spline functions with a built-in window which permits translation as well as dilation. In this study, a wavelet particle method based on the multiresolution analysis encountered in signal processing has been developed. The Reproducing Kernel Particle Methods (RKPM) are emerging as an effective alternative due to the absence of a mesh and the ability to analyze a specific frequency range. In order to capture the important physical phenomena, p-finite elements and/or hp-finite elements are employed. As a powerful tool, the finite element method has been widely used in the study of complex systems. In the analysis of complex phenomena of acoustic systems, the computational modeling requires special attention in order to give a realistic representation of the physics.
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