Rapid Random Packing of Poly-disperse Spheres using Adam Stochastic Optimization

This paper introduces a machine learning-based approach to solving the 3D sphere packing problem, with a particular focus on applications in Discrete Element Method (DEM) simulations. Diverging from traditional methods that explore abstract mathematical spaces and higher-dimensional constructs, we propose a practical strategy: (1) using generic triangular meshes of convex shapes as containers, and (2) adhering to a predefined size distribution. This approach is highly relevant for real-world applications in engineering and computer graphics. Our methodology defines an objective function to penalize both inter-particle overlap and violations of the container’s boundary, then minimizes this function using the modern stochastic optimization algorithm, Adam. To achieve high efficiency, we rely on a collective arrangement technique that enables the rapid packing of large numbers of spheres in a feasible time. We further enhance scalability by iteratively adding and optimizing batches of particles, allowing our implementation to handle large packed beds. The paper presents a detailed description of the algorithm and a thorough numerical evaluation that validates the results and provides insights into performance. With this algorithm, we successfully packed 200,000 particles in a tall vertical container box with a square base in 1 hour and 17 minutes, achieving an average core packing density of approximately 0.6. Finally, we also demonstrate the applicability of the method to complex and real-world configurations.