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A dynamical low-rank approximation is developed for reduced-order modelling (ROM) of the filtered density function (FDF) transport equation, which is utilised for large eddy simulation (LES) of turbulent reacting flows. In this methodology, the evolution of the composition matrix describing the FDF transport via a set of Langevin equations is con- strained to a low-rank matrix manifold. The composition matrix is approximated using a low-rank factorisation, which consists of two thin, time-dependent matrices repre- senting spatial and composition bases, along with a small time-dependent coefficient matrix. The evolution equations for spatial and composition subspaces are derived by projecting the composition transport equation onto the tangent space of the low-rank matrix manifold. Unlike conventional ROMs, such as those based on principal com- ponent analysis, both subspaces are time-dependent and the ROM does not require any prior data to extract the low-dimensional subspaces. As a result, the constructed ROM adapts on the fly to changes in the dynamics. For demonstration, LES via the time-dependent bases (TDB) is conducted of the canonical configuration of a tempo- rally developing planar CO/H2 jet flame. The flame is rich with strong flame-turbulence interactions resulting in local extinction followed by re-ignition. The combustion chem- istry is modelled via the skeletal kinetics, containing 11 species with 21 reaction steps. It is shown that the FDF-TDB yields excellent predictions of various sta