  A predictive, point-cloud tracer is presented that determines with a
quantified uncertainty the Lagrangian motion of a group of point-particles
within a finite region. The tracer assumes a random forcing within confidence
intervals to account for the empiricism of data-driven force models and
stochasticity related to the chaotic nature of the subcloud scale dynamics. It
builds on the closed Subgrid Particle-Averaged Reynolds Stress-Equivalent
(SPARSE) formulation presented in Dom\'inguez-V\'azquez~\textit{et al.}
[\textit{Int. J. Multiph. Flow.} 161, 104375] that assumes a deterministic
forcing. SPARSE describes the first two moments of particle clouds with moment
equations in closed-form, with a theoretical third-order convergence rate with
respect to the standard deviations of the cloud variables. The cloud model
alleviates computational cost and enhances the convergence rate as compared to
Monte Carlo (MC) based point-particle methods. The randomness in the forcing
model leads to virtual stresses that correlate random forcing and field
fluctuations. These stresses strain and rotate the random cloud as compared to
a deterministically forced cloud and thus determine to what extent the random
forcing propagates into the confidence intervals of the dispersed solution. In
symmetric flows the magnitude of the virtual stress is zero. Tests in
analytical carrier-fields and in a decaying homogeneous isotropic turbulence
flow computed with a discontinuous Galerkin (DG) compressible DNS solver are
performed to verify and validate the SPARSE method for randomly forced
particles.
