Title: Uncertainty quantification for parameters and time series forecasting based on data assimilation
Authors: Hiromichi Nagao - The University of Tokyo (Japan) [presenting]
Shin-ichi Ito - The University of Tokyo (Japan)
Abstract: Data assimilation (DA) is a computational technique that integrates numerical simulation models and observation data based on Bayesian statistics. DA is mainly applied in the weather forecasting, in which the simulation model consists of a set of differential equations that describe time evolution of the Earth's atmosphere. DA has been expanding its application fields to various areas such as seismology, biology and materials science. When DA is applied to a large-scale simulation model, the four-dimensional variational method (4DVar) is often used to optimize parameters and initial conditions in the simulation model, rapidly and accurately computing the derivative of a cost function that measures the difference between the model and data. The conventional 4DVar can obtain only the optima of the parameters and time series forecasting but never evaluates their uncertainties. We propose a new 4DVar that enables us to evaluate the uncertainties by using the second-order adjoint method. We demonstrate the validity of the proposed method by applying to the phase-field models, which are Allen-Cahn-type differential equations often used to simulate the time evolution of grain growths in materials.