Accelerating particle-resolved simulations of dense suspensions with hybrid GNN–U-Net neural networks

Particle-resolved simulations are essential for studying dense-suspension rheology because they resolve the microstructure that controls macroscopic stress, but their computational cost remains substantial due to the tight two-way coupling between the fluid and the suspended particles. In the OpenFOAM-based fictitious-domain solver considered here, the dominant cost is the iterative determination of the forcing field that couples the two phases by enforcing rigid-body motion inside the particles. We address this bottleneck by learning a solver-internal quantity rather than replacing the solver itself: a hybrid graph neural network (GNN) and U-Net model predicts how the forcing field changes each time step and initializes the solver’s existing iteration. The governing equations, solver loop, and convergence criterion remain unchanged. On simulation intervals not used during training, the learned initializer cuts the mean forcing error – an accuracy measure – by about 95% relative to naive persistence (repeating the previous value). Embedded in the full solver, it yields an iteration-reduction factor of 2.54 and an overall speedup of 2 . 1 3 × after accounting for inference cost. The time-averaged shear stress changes by only −1.65% relative to the unmodified solver. Trained on a single simulation, the model retains iteration speedups between 1 . 4 8 × and 2 . 7 8 × across six further test cases, not used for training, that vary the initial configuration, domain size, volume fraction, friction coefficient, particle–particle interactions, and imposed flow type. These results indicate that an accurate learned initializer can accelerate the original solver without altering its governing equations or convergence criterion.