Fig. 5: NeuralDEM training methodology.

Using the presented continuous physics representation, we model the Lagrangian discretization of DEM as an assumed underlying field. The approximator maps the encoded representation to one that can be decoded at any specified spatial location \(j{\prime}\). The multi-branch neural operator is a family of deep learning architectures that processes multi-physics quantities and can distinguish between primary quantities, used to model the core physics in the main branches, and secondary quantities, which are used to predict additional desired quantities in the off-branches, both modeled as fields. The quantities come, e.g., from DEM simulations with coupled particles and fluid, which the architecture handles using specialized encoders and decoders. All modules processing the primary quantities influence each other. In contrast, those that process secondary quantities are independent and use the tokens from the primary branch as additional information but cannot affect them.