Encoding multiphase dynamics to predict spatiotemporal evolution via latent-space operators

Modeling complex multiphase flows relies on solving partial-differential equations (PDEs) that capture the intricate transfers of mass, momentum, and energy among the interacting phases. These systems typically involve intricate couplings between gas, liquid, and solid phases, exhibiting dynamics that diverge from those of single-phase flows. We propose a two-stage decoupled training paradigm that independently optimizes a Kolmogorov–Arnold autoencoder for spatial reduced-order representation and a latent-space operator network for initial-to-future dynamics. Systematic comparisons of bubble rise, particle deposition, and fluidized bed demonstrate that the width of layer dominates encoder fidelity, whereas operator accuracy depends on balancing expressiveness and overfitting. In addition, compared with fully connected and convolutional baselines, MultiOKAN reduces the reconstruction error by a significant margin while maintaining a similar computational cost. Latent projection also endows the model with strong resilience to noise and modest data budgets, preserving accuracy even under substantial perturbations or when trained on a fraction of the original samples. The proposed reduced-order and fusion schemes for multiphase problems characterize the accuracy-efficiency trade-off. These schemes enable either lightweight training through shared latent reconstruction or higher-fidelity prediction via enhanced cross-phase coupling in latent dynamics.