Projection-based model-order reduction methods have almost exclusively been applied to mesh-based computational multi-physics numerical schemes. This work presents a modal decomposition approach that constitutes the first major step toward developing nonlinear projection-based model-order reduction for multiphase fluid flows modeled by smoothed-particle hydrodynamics (SPH), a meshless and nonlocal computational multi-physics method. A modal decomposition approach based on mapping Lagrangian particles to a fixed frame of reference is shown to be capable of capturing Eulerian field variables, and is performed as a post-processing procedure. The Lagrangian-to-Eulerian mapping is applied to Rayleigh-B\'{e}nard convection solutions of two immiscible fluids using SPH to demonstrate and showcase this new approach to perform modal decomposition and dimensional reduction for meshless methods.