Memristive devices are the subject of research and development by the Industry and Academy because of promising applications connected to non-volatile memory ICs, neuromorphic engineering, hardware cryptography, and radio-frequency switches1. Here, we present results linked to devices based on the Au/Ti/h-BN/Au stack2 (see Figure 1a). An h-BN multilayer grown by chemical vapor deposition (18 layers approximately, see Figures 1a and b) was placed on top of the bottom electrode by wet transfer. The I-V curves, obtained under ramped voltage stress are shown in Figure 1c. In Figure 1d the HRS and LRS resistances are shown versus cycle number. The inset shows the cumulative distribution function (CDF) of the same data, highlighting the cycle-to-cycle uniformity and a wide memory window. Several negative voltage pulse trains have been applied to our devices (see Figure 2) to assess synaptic depression, after set processes. Both the pulse voltage and frequency have been changed to analyze the conductance modulation in depth. To quantitatively evaluate the dynamics of synaptic depression, the evolution of the device current as a function of the applied pulse number was modeled using an exponential decay function (Equation 1). The experimental current (colored symbols) for each pulse train is fitted using Equation 1 (see Figure 3). The τ values (blue triangles) extracted exhibit a clear inverse relationship with the applied voltage well-described by a linear fit (see the red dashed line). A simulation of the devices under study has been performed by means of COMSOL Multiphysics. The simulation domain is shown in Figure 4. The ultra-fine local mesh triangulation is critical for accurately solving the physical singularities at the Conductive NanoFilament (CNF) tip, such as intense electric field enhancement and extreme localized Joule heating gradients. The material physical properties are included: most data belong to the COMSOL material database, although some physical properties are changed following previous results in the literature. The Poisson and heat equations are solved in addition to the continuity equations in a 3D self-consistent approach. In this study we consider an anisotropic thermal conductivity for the h-BN (a tensor in this case), and also an isotropic thermal conductivity for the sake of comparison. The experimental data are correctly reproduced as shown in Figure 1c with the anisotropic thermal approach. Figure 5 depicts how the Joule heat is g