Modular Operator Superposition (MOS): Physics-Guided ML Addressing Dimensionality Curse

Multiphase flow prediction consistently finds itself torn between two extremes: machine-learning (ML) surrogates that generalize poorly beyond narrow, small-scale configurations, and physics-based solvers that cannot meet real-time computation demands. To bridge this trade-off, we introduce Modular Operator Superposition (MOS), a physics-guided, AI-augmented framework. MOS learns only recurring flow primitives (e.g., single-cylinder or sphere cross-flow) as modular operators, thereby decoupling total offline cost from system complexity. In the online stage, these operators are superposed via pairwise interaction physics to approximate arbitrary, unseen flow fields. In a 2D channel populated with 1~15,000 randomly placed cylinders, MOS achieves (i) 3~5 orders of magnitude speedup over OpenFOAM, (ii) R^2 > 0.85 accuracy across the domain, and (iii) >10^3 times reduction in memory footprint. Moreover, MOS seamlessly accommodates polydispersity and moving particles. When embedded in an Euler-Lagrange solver, it closes pseudo-turbulent Reynolds stresses and recovers subgrid flow features at "particle-resolved" fidelity, without retraining or mesh refinement.