Applications Of Machine Learning On Particle Packing And Mesh Optimization

Local structure identification and mesh optimization are two popular research topics in the fields of particle packing and mesh generation respectively.Conventional methods often rely on manual function construction,such as the order parameter in particle packing and the target function in mesh generation,which greatly reduces the applicability of such methods.With the rise of the machine learning methods,data-driven methods show increasing advantages.Machine Learning methods can autonomously extract statistical laws or hidden patterns from large amounts of data,making data-intensive approach become the fourth paradigm in scientific research.This paper applies machine learning methods to local structure identification and mesh optimization problems,and discuss the development prospects of new methods in these traditional problems.Local structure identification is of great importance in many scientific and engineering fields.In this work,we propose an improved unsupervised learning method,which is descriptor-free,for local structure identification in particle packing.The point cloud is used as the input of the improved method,which directly comes from spatial positions of particles and does not rely on specific descriptors.The improved method constructs an autoencoder based on the point cloud network combined with Gaussian mixture models for dimension reduction and clustering.Numerical examples show that the improved method performs well in local structure identification of quasicrystal disk and sphere packings,achieving comparable accuracy with previous methods.For disordered packings which have been considered nearly having no local structures,the improved method identifies a nontrivial 7-neighbor motif in the maximally dense random packing of disks,and finds acentric structural motifs in the random close packing of spheres,which demonstrate the ability of the new method on identification of new and unknown local structures.Mesh quality significantly influence the accuracy and efficiency of numerical simulations in practical engineering.In this work,we propose a supervised machine learning method,for the improvement and optimization of the mesh quality.The coordinate-based point cloud is also used as the input,without depending on other features.This method constructs the deep learning model with reference to Point Net,predicts the displacement vector of the node,and then optimizes the mesh quality via continuous iterations.Numerical examples show that the method performs well in mesh optimization of randomly disturbed uniform meshes,and achieves better mesh quality and efficiency than existing methods,indicting its feasibility in mesh optimization field.For randomly disturbed non-uniform meshes,more improvement still needs to be done.The method is able to achieve similar results for randomly disturbed meshes with different types,demonstrating its stability and generalization ability in the optimization process.Moreover,we apply the genetic algorithm to the densest packing problems for packing optimization,trying to explore the configuration with higher packing density.We reduce the number of optimization variables and dimension of solution space by applying the tangent constraint to ellipsoids or viewing two tetrahedrons as a dimer,which improves the convergency of the genetic algorithm.Numerical examples show that the method reaches the optimal result for several packing optimization problems,while the risk of falling into local optimal solution still remains.