In dilute turbulent particle-laden flows, such as atmospheric dispersion of pollutants or virus particles, the dynamics of tracer-like to low inertial particles are significantly altered by the fluctuating motion of the carrier fluid phase. Neglecting the effects of fluid velocity fluctuations on particle dynamics causes poor prediction of particle transport and dispersion. To account for the effects of fluid phase fluctuating velocity on the particle transport, stochastic differential equations coupled with large-eddy simulation are proposed to model the fluid velocity seen by the particle. The drift and diffusion terms in the stochastic differential equation are modeled using neural networks (“neural stochastic differential equations”). The neural networks are trained with direct numerical simulations (DNS) of decaying homogeneous isotropic turbulence at low and moderate Reynolds numbers. The predictability of the proposed models is assessed against DNS results through a priori analyses and a posteriori simulations of decaying homogeneous isotropic turbulence at low-to-high Reynolds numbers. Total particle fluctuating kinetic energy is under-predicted by 40% with no model, compared to the DNS data. In contrast, the proposed model predictions match total particle fluctuating kinetic energy to within 5% of the DNS data for low- to high-inertia particles. For inertial particles, the model matches the variance of uncorrelated particle velocity to within 10% of DNS results, compared to 60%–70% under-prediction with no model. It is concluded that the proposed model is applicable for flow configurations involving tracer and inertial particles, such as transport and dispersion of pollutants or virus particles.