[p2] Ideas for new applications


[p2-24]

Uncertainty quantification based on second-order adjoint method for data assimilation using massive autonomous systems

S. Ito (The University of Tokyo), H. Nagao (The University of Tokyo), A. Yamanaka (Tokyo University of f Agriculture and Technology), Y. Tsukada (Nagoya University), T. Koyama (Nagoya University), M. Kano (The University of Tokyo), and J. Inoue (The University of Tokyo)

 
Abstract

Uncertainty quantification (UQ) of unobservable state and parameters involved in simulation models is one of the significant issues in data assimilation. However, conventional UQ methods need huge computational costs especially in the cases of massive simulation models. We propose an adjoint-based data assimilation method available for autonomous simulation models that provides optimum estimates and their uncertainties within practical computational time and resources. The uncertainties are given as diagonal components of an inverse Hessian, which corresponds to the covariance matrix of a multivariate Gaussian that approximates a target posterior probability density function in the neighborhood of the optimum. The proposed method using a second-order adjoint method allows us to directly evaluate the desired diagonal components of the inverse Hessian avoiding a computation of all its components. Our method drastically saves the computational cost comparing with conventional approaches owing to the effective usage of the second-order adjoint method. The proposed method is validated through numerical tests based on synthetic data generated by a massive two-dimensional Kobayashi's phase-field model. We confirm that our method correctly reproduces assumed true parameter and initial state, and appropriately evaluates the uncertainty of the parameter.