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Filtering the passive scalar transport equation in the large-eddy simulation(LES) of turbulent transport gives rise to the closure term corresponding tothe unresolved scalar flux. Understanding and respecting the statisticalfeatures of subgrid-scale (SGS) flux is a crucial point in robustness andpredictability of the LES. In this work, we investigate the intrinsic nonlocalbehavior of the SGS passive scalar flux through studying its two-pointstatistics obtained from the filtered direct numerical simulation (DNS) datafor passive scalar transport in homogeneous isotropic turbulence (HIT).Presence of long-range correlations in true SGS scalar flux urges to go beyondthe conventional local closure modeling approaches that fail to predict thenon-Gaussian statistical features of turbulent transport in passive scalars.Here, we propose an appropriate statistical model for microscopic SGS motionsby taking into account the filtered Boltzmann transport equation (FBTE) forpassive scalar. In FBTE, we approximate the filtered equilibrium distributionwith an $\alpha$-stable Levy distribution that essentially incorporates apower-law behavior to resemble the observed nonlocal statistics of SGS scalarflux. Generic ensemble-averaging of such FBTE lets us formulate a continuumlevel closure model for the SGS scalar flux appearing in terms offractional-order Laplacian that is inherently nonlocal. Through a data-drivenapproach, we infer the optimal version of our SGS model using the high-fidelitydata for the two-point correlation function between the SGS scalar flux andfiltered scalar gradient, and sparse linear regression. In an \textit{a priori}test, the optimal fractional-order model yields a promising performance inreproducing the probability distribution function (PDF) of the SGS dissipationof the filtered scalar variance compared to its true PDF obtained from thefiltered DNS data.

Data-Driven Fractional Subgrid-scale Modeling for Scalar Turbulence: A Nonlocal LES Approach