| It is often said that kinetic Monte Carlo (kMC) methods are ways to extend the timeframe of molecular dynamics (MD) simulations, to scales that allow the study of diffusion-driven processes in materials (e.g. precipitation or segregation). The time gain in kMC methods comes essentially from the decision to neglect atomic oscillations in the dynamic description of the system, retaining only their "by-products", i.e. diffusion jumps of point defects. These are treated in kMC as thermally activated processes, governed chiefly by activation energies, that depend on the local environment (i.e. on which atoms surround the "jumping" defect and how they are distributed). In practice, most of the commonly used kMC schemes are rigid lattice models which neglect much more than just atomic oscillations. Typically, the activation energies are calculated by including only the effect on them of close neighbours (1st and 2nd shell) and/or by neglecting completely the effect of strain fields. A real extension of molecular dynamics, though, should include these effects explicitly. The problem is that, if these effects are taken into account, the price to be paid is a heavy reduction of the timescales that the model can cover, or of the volumes that can be studied, because the CPU time required increases enormously. Atomistic kMC models limited to close neighbour shells avoid this problem. They also have the advantage that their parameters can be fitted directly to ab initio calculations, instead of using interatomic potentials. However, a true extension of MD simulations should be using the same description of the total energy, which is an interatomic potential in 99% of the cases. It is of course in the interest of the reliability of both MD simulations and kMC simulations used to extend them, that the interatomic potential should be as reliable as possible. The reliability of an interatomic potential is indeed a delicate issue. Here, however, we shall assume that a reliable potential is available and explain how it has been possible, exploiting it, to develop an atomistic kMC model that can be truly considered an extension of MD, without paying the price of an unaffordable CPU time. The key has been the use of artificial neural networks (ANNs) as universal regression tools to approximate, to high degree of precision, the unknown functions expressing the activation energy for point-defect diffusion in terms of local environment. A few examples will be shown of the application of this method to precise cases, in which very good agreement with experiments was achieved. In addition, examples will be given of how else ANNs can be of further help in developing models that describe the nanostructural and microchemical evolution of materials. The essential point is the recognition that unknown complex functions are best regressed with advanced numerical tools, without this jeopardising the physical understanding of the phenomena to be studied. The limitation is given by how far the complexity can be pushed: this, however, can be only discovered by direct experience. Whenever the limit seems to have been reached, the key is to simplify slightly the description of the system based on physical considerations. ANNs are a powerful numerical tool, but they do not replace physics. |
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