The properties and behaviour of materials under extreme conditions are essential for energy systems such as fission and fusion reactors. However, accurately predicting the properties of materials at high temperatures remains a challenge. Direct measurements of these properties are limited by experimental instrumentation, and atomic-scale simulations based on empirical force fields are often unreliable due to a lack of precision.This problem can be solved using statistical learning techniques, which have recently seen their use explode in materials science. Force fields constructed by machine learning achieve the degree of accuracy of {it ab initio} calculations; however, their implementation in sampling methods is limited by high computational costs, generally several orders of magnitude higher than those of traditional force fields. To overcome this limitation, two objectives will be pursued in this thesis: (i) to improve active statistical learning force fields by finding a better accuracy-efficiency trade-off and (ii) to create accelerated free energy and kinetic path sampling methods to facilitate the use of computationally expensive statistical learning force fields.
For the first objective, we improve the construction of statistical learning force fields by focusing on three key factors: the database, the local atomic environment descriptor and the regression model. For the second objective, we will implement a fast and robust Bayesian sampling scheme to estimate the anharmonic free energy, which is crucial for understanding the effects of temperature on crystalline solids, using an adaptive bias force method that significantly improves convergence speed and overall accuracy.We will apply the methods developed to the calculation of free energy and its derivatives, physical quantities that give access to the thermo-elastic properties of alloys and the thermodynamic properties of point defects. To do this, we will use algorithmic extensions that allow us to sample a specific metastable state and also the transition paths to other energy basins, and thus to estimate the free energies of formation and migration of vacancy defects. The thermodynamic quantities calculated will then be used as input data for kinetic Monte Carlo methods, which will make it possible to measure the diffusion coefficients in complex alloys as a function of temperature.
One aim will be to try to relate the atomic transport properties to the complexity of the alloy. Since our approach is considerably faster than standard methods, we will be able to apply it to complex alloys comprising the elements W, Ti, V, Mo and Ta at temperatures and compositions that have not been studied experimentally.