数値解析・応用解析セミナー

1月16日(木) 15:00 -- 16:30  Michael C. Koch  (京都大学農学研究科) 
            ``Development of Hamiltonian Monte Carlo based inverse methods 
              for parameter identification in geomechanical problems.''

＜研究発表要旨＞
General inverse problems in geomechanics are solved in a Bayesian framework 
to yield probabilistic descriptions of the underlying posterior probability 
distributions. Exploration of such probability distributions is usually 
done through Markov Chain Monte Carlo (MCMC) methods, which are prohibitively 
expensive. Methods are developed for the solution of three inverse problems 
in a Hamiltonian Monte Carlo (HMC) framework, which is a statistically 
efficient variant of MCMC. Firstly, efficient identification of spatial 
field parameters (e.g. elastic modulus) is attempted from elastic wave 
propagation data. An adjoint HMC algorithm is developed that combines the 
Karhunen-Loeve expansion for dimensionality reduction and adjoint method 
for efficient gradient computation. The second problem involves the 
explicit identification of solid-void interfaces. A novel parameter 
update from a reference configuration is designed to maintain HMC 
reversibility. Finite element mesh quality is maintained through mesh 
moving methods and HMC gradients are computed using shape derivatives.
Finally, these two methods are combined for simultaneous estimation of
spatial field (hydraulic conductivity) and solid-void interface (piping
zone) in two ways: approximate and exact, whose sampling efficiency is
compared.

●セミナー室: 京都大学 総合研究12号館 2階203号
              （応用解析学講座セミナー室）

●総合研究12号館はキャンパスマップでは「京都大学本部構内 54番建物」です。
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セミナー連絡先: 京都大学大学院 情報学研究科 先端数理科学専攻
                 磯 祐介    e-mail; iso@i.kyoto-u.ac.jp