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 present MultiOKAN, a novel deep learning framework that integrate a Kolmogorov-Arnold autoencoder with a latent-space operator network to approximate the mappings from initial state to future evolution, which aims to substitute traditional PDEs solver. The encoder compresses initial volume fraction fields into a low-dimensional latent representation, which is fed into operator to predict the future morphology evolution. 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. One of the important features of current framework is its multiphase compatibility with new structured latent representation acquisition strategies. This work opens a promising pathway toward leveraging neural operators for real-time spatiotemporal prediction of multiphase systems.