Inverse design of particle shapes with target sphericity and packing fraction using variational autoencoders

Sphericity and packing fraction are fundamental properties governing the behavior of granular materials in many engineering applications. Conventional methods for designing particles with these target properties usually suffer from limited accuracy, diversity, and interpretability due to complex relationships between particle shape and properties. To address this, we propose an inverse design framework based on deep learning. First, a rotation- and reflection-invariant variational autoencoder (VAE) parameterizes two-dimensional convex particle shapes into a low-dimensional latent space, enabling accurate reconstruction and capturing geometric interpretations such as sphericity and symmetry. Second, a conditional variational autoencoder (CVAE) facilitates inverse design by generating particle shapes corresponding to target sphericity or packing fraction, and also enables the coupling control of both properties. Trained on a dataset of over 1600 convex shapes, the framework demonstrates robustness and universality. The rotation- and reflection-invariant architecture consistently maps different orientations of the same shape to a unified representation, which enhances interpretability. The main contribution in artificial intelligence lies in developing invariant generative models that learn shape representations and enable property-driven shape generation. The engineering contribution is providing a precise and efficient tool for the inverse design of particle shapes with target properties, supporting the optimization of granular materials in engineering applications.