Bayesian Data Assimilation of Temperature Dependence of Solid–Liquid Interfacial Properties of Nickel

Abstract

Temperature dependence of solid–liquid interfacial properties during crystal growth in nickel was investigated by ensemble Kalman filter (EnKF)-based data assimilation, in which the phase-field simulation was combined with atomic configurations of molecular dynamics (MD) simulation. Negative temperature dependence was found in the solid–liquid interfacial energy, the kinetic coefficient, and their anisotropy parameters from simultaneous estimation of four parameters. On the other hand, it is difficult to obtain a concrete value for the anisotropy parameter of solid–liquid interfacial energy since this factor is less influential for the MD simulation of crystal growth at high undercooling temperatures. The present study is significant in shedding light on the high potential of Bayesian data assimilation as a novel methodology of parameter estimation of practical materials an out of equilibrium condition.

Fast-Decoding Algorithm for Electrode Processes at Electrified Interfaces by Mean-Field Kinetic Model and Bayesian Data Assimilation: An Active-Data-Mining Approach for the Efficient Search and Discovery of Electrocatalysts

“…The probability distribution function after the prediction step is given as where δ is the Dirac delta function, and y 1: t –1 represents observational data from t = 1 to t – 1. In the filtering step, states vector is updated as , where K t is the ensemble approximation of Kalman gain defined as V t | t –1 is the sample covariance matrixes of state vector and R t is the observation error defined as Finally, smoothing is performed using the ensemble Kalman smoother (EnKS) . The ensemble member of smoothed distribution at time s ( s < t ) is given as This process plays a role in smoothing previously estimated data and stabilizing sequential data of the estimated values.…”

“…In the early stage, data assimilation achieved great success mainly in geophysics . Recently, data assimilation-based techniques are put in use in the field of materials science. − Above considerations, as well as recent progress in data-driven science, drove us to build a fast-decoding algorithm combined with a data-driven approach of data assimilation for extracting microscopic kinetic features from current–potential profiles of complicated electrode processes. To the best of our knowledge, this work is the first attempt to use Bayesian data assimilation for electrochemical data to extract microscopic kinetic features.…”

Large-scale phase-field simulations for dendrite growth: A review on current status and future perspective

“…Yamanaka has been conducting pioneering work in introducing data assimilation into the PF simulations [134][135][136][137]. Ohno et al developed a novel inference method using an ensemble Karman filter (EnKF) of the solid-liquid interfacial parameters of a pure metal by coupling PF and MD simulations [138,139].…”

Preliminary system for data assimilation to infer material parameters from directional solidification experiments: twin experimental study using phase-field method

“…Data assimilation [16] has been attracting attention as a promising method for integrating numerical simulations and experiments. Ohno et al developed a method for estimating interfacial properties by combining molecular dynamics and PF simulations with an ensemble Kalman filter (EnKF) and applied it to pure iron and nickel [17,18]. Yamanaka et al employed the local ensemble transform Kalman filter to dendritic solidification to efficiently estimate material parameters [19,20].…”