Computational studies of anisotropic thermal conductivity in two-dimensional materials have become increasingly important for understanding heat dissipation in nanoscale devices and optimizing thermal management systems. The unique structural characteristics of 2D materials such as graphene and molybdenum disulfide (MoS2) lead to direction-dependent thermal transport properties, necessitating advanced modeling techniques to capture their behavior accurately.

First-principles calculations based on density functional theory (DFT) provide a fundamental approach to studying thermal conductivity in 2D materials. These methods compute interatomic force constants and phonon dispersion relations, which are essential for evaluating lattice thermal conductivity through the Boltzmann transport equation (BTE). In graphene, for instance, first-principles calculations predict an ultrahigh in-plane thermal conductivity of approximately 2000–4000 W/mK at room temperature due to strong sp2 carbon bonds and long phonon mean free paths. However, the out-of-plane thermal conductivity is orders of magnitude lower, typically below 10 W/mK, because of weak van der Waals interactions between layers. Similarly, monolayer MoS2 exhibits anisotropic thermal conductivity, with in-plane values around 80–100 W/mK and out-of-plane values below 2 W/mK. These discrepancies arise from differences in phonon group velocities and scattering rates along different crystallographic directions.

Machine learning potentials have emerged as a powerful tool to overcome the computational limitations of first-principles methods while retaining high accuracy. Neural network potentials and Gaussian approximation potentials trained on DFT datasets enable large-scale molecular dynamics (MD) simulations that capture phonon-phonon scattering and defect interactions more efficiently than classical force fields. For example, machine learning-assisted MD simulations of graphene have reproduced experimental thermal conductivity trends while revealing the effects of grain boundaries and edge scattering. In MoS2, such approaches have quantified the reduction in thermal conductivity due to sulfur vacancies, showing a decrease of up to 30% at a defect concentration of 1%. These methods are particularly valuable for investigating temperature-dependent behavior, as they can simulate systems with thousands of atoms over nanosecond timescales, which is impractical with pure DFT calculations.

Defects and strain significantly influence anisotropic thermal transport in 2D materials. Point vacancies, adatoms, and substitutional dopants introduce phonon scattering centers that reduce thermal conductivity. DFT and MD studies demonstrate that even low defect concentrations (below 0.1%) can decrease graphene's in-plane thermal conductivity by 20–50%, depending on the defect type. Stone-Wales defects, for instance, disrupt phonon propagation more severely than single vacancies due to their larger distortion of the lattice. In MoS2, sulfur vacancies dominate thermal resistance, with simulations showing a stronger impact on the cross-plane direction than the in-plane direction. Strain engineering further modulates thermal conductivity anisotropy. Uniaxial tensile strain of 5% in graphene reduces in-plane thermal conductivity by 15–20%, whereas biaxial strain has a more pronounced effect due to uniform softening of phonon modes. MoS2 exhibits a non-monotonic strain response, with thermal conductivity initially increasing under small tensile strain (below 2%) before decreasing at higher strains because of altered phonon dispersion and enhanced anharmonicity.

The role of substrate interactions and interfacial thermal resistance is another critical aspect of anisotropic heat transport in 2D materials. Simulations incorporating substrate phonon coupling reveal that supported graphene sheets experience a substantial reduction in in-plane thermal conductivity compared to freestanding layers. For example, graphene on a SiO2 substrate shows a thermal conductivity reduction of up to 60% due to phonon leakage into the substrate and increased scattering at the interface. Similar effects are observed in MoS2, where the substrate interaction suppresses out-of-plane phonon modes more strongly than in-plane modes, exacerbating anisotropy.

Multiscale modeling approaches combine first-principles calculations, machine learning potentials, and continuum models to bridge the gap between atomic-scale mechanisms and macroscopic thermal properties. These methods are particularly useful for predicting the performance of 2D materials in device configurations, where edge effects, contact resistance, and finite-size effects become significant. For instance, multiscale simulations of graphene ribbons reveal that thermal conductivity scales with ribbon width due to edge scattering, following a power-law relationship that depends on the specularity of phonon reflection. In MoS2 nanoribbons, the anisotropy ratio between armchair and zigzag directions becomes more pronounced as the width decreases below 50 nm, highlighting the interplay between dimensionality and thermal transport.

Future computational efforts will likely focus on improving the accuracy of machine learning potentials for defect-rich systems and extending simulations to heterostructures and twisted bilayers, where interlayer coupling introduces additional complexity to thermal transport. The integration of high-throughput computational screening with experimental validation will further advance the design of 2D materials with tailored anisotropic thermal properties for applications in flexible electronics, thermoelectric devices, and thermal interface materials.

In summary, computational studies provide critical insights into the anisotropic thermal conductivity of 2D materials by elucidating the roles of phonon dynamics, defects, strain, and interfacial effects. First-principles calculations establish foundational understanding, while machine learning potentials enable large-scale simulations that capture realistic conditions. Defects and strain serve as tunable parameters to modulate thermal transport, with implications for material design and device optimization. Continued advancements in computational methods will enhance predictive capabilities and facilitate the development of next-generation nanomaterials with controlled thermal properties.