Anisotropic and isotropic elasticity and thermal transport in monolayer C$_{24}$ networks from machine-learning molecular dynamics

Two-dimensional fullerene networks have recently attracted increasing interest due to their diverse bonding topologies and mechanically robust architectures. In this work, we develop an accurate machine-learned potential NEP-C$_{24}$ for both the quasi-hexagonal phase (qHP) and the quasi-tetragonal phase (qTP) C$_{24}$ monolayers, based on the neuroevolution potential (NEP) framework. Using this NEP-C$_{24}$ model, we systematically investigate the elastic and thermal transport properties. Compared with C$_{60}$ monolayers, both C$_{24}$ phases exhibit markedly enhanced stiffness, arising from the combination of reduced molecular size and increased density of covalent bonds. The qTP C$_{24}$ monolayer shows nearly isotropic elastic properties and thermal conductivities along its two principal axes owing to its four-fold symmetry, whereas the chain-like, misaligned bonding topology of the qHP C$_{24}$ monolayer leads to pronounced in-plane anisotropy. Homogeneous nonequilibrium molecular dynamics and spectral decomposition analyses reveal that low-frequency ($<5$ THz) acoustic phonons dominate heat transport, with directional variations in phonon group velocity and mean free path governing the anisotropic response in qHP C$_{24}$. Real-space heat flow visualizations further show that, in these fullerene networks, phonon transport is dominated by strong inter-fullerene covalent bonds rather than weak van der Waals interactions. These findings establish a direct link between intermolecular bonding topology and phonon-mediated heat transport, providing guidance for the rational design of fullerene-based two-dimensional materials with tunable mechanical and thermal properties.