**About this Abstract** |

**Meeting** |
**2022 TMS Annual Meeting & Exhibition
** |

**Symposium
** |
**Hume-Rothery Symposium on Connecting Macroscopic Materials Properties to Their Underlying Electronic Structure: The Role of Theory, Computation, and Experiment
** |

**Presentation Title** |
Machine Learning in Diffusivity Calculations Using a Variational Principle |

**Author(s)** |
Dallas R. Trinkle |

**On-Site Speaker (Planned)** |
Dallas R. Trinkle |

**Abstract Scope** |
Computing mesoscale diffusivity requires scaling up from microstates and transition rates at the atomistic scale. In particular, we need to solve the master equation, which describes the time-evolution of probability, and find the long-time "near equilibrium" steady-state solution. The general solution involves the inversion of rate matrix: the Green function. However, while the rate matrix is typically sparse, its inverse is not; moreover, efficient calculation of the Green function is tractable only for dilute concentrations. By recasting the calculation of transport coefficients as a variational problem, we can compute transport coefficients from thermal average quantities instead of trajectory-based calculations. Moreover, it provides a framework for understanding and improving kinetic Monte Carlo calculations of diffusivity. A "hybrid" approach to diffusivity, using kinetic Monte Carlo of short trajectories followed by machine learning optimization can produce diffusivity values that are equivalent to those from significantly longer time trajectories. |

**Proceedings Inclusion?** |
Planned: |

**Keywords** |
Computational Materials Science & Engineering, Machine Learning, |