Bayesian Numerical Homogenization
主 题: Bayesian Numerical Homogenization
报告人: 张镭 (上海交通大学)
时 间: 2014-10-28 10:00-11:00
地 点: 数学学院理科一号楼1418室（主持人：李若）
Recently, we proposed the so-call RPS (rough polyharmonic splines)
basis,
which has the optimal accuracy and localization property for
the numerical
homogenization of divergence form elliptic equation with
rough (L^\infty)
coefficients. The construction is found by the
compactness of solution space.
Surprisingly, this basis can be obtained
by the reformulation of the numerical
homogenization problem as a Bayesian
Inference problem in which a given
PDE with rough coefficients (or mult
i-scale op-
erator) is excited with noise
(random right hand side/source term)
and one tries to
estimate the value
of the solution at a given point based on a finite num
ber of obser-
inference
problem: given a finite number of observations, the basis is
the conditional
expectation when the right hand side of the PDE is
replaced by a Gaussian
random field. This formulation can be applied to
general linear integro-differential
equations, and can be further
extended to finite temperature systems.
报告人简介：张镭，
上海交通大学数学系、自然科学研究院特别研究员，美国加州理工学院博士。
研究方向：
着眼于解决多尺度建模，分析和
计算的根本性问题，内容包括偏微分方程，
数值分析，以及在材料科学，地球物理科学，生命科学等领域中的广泛应用问题。
