Fast Bayesian approach for parameter estimation
Fast Bayesian approach for parameter estimation
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DOI：
10.1002/nme.2319
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发表时间：
2008-10
影响因子：
2.9
通讯作者：
Bangti Jin
中科院分区：
文献类型：
--
作者：
Bangti Jin
本文提出了两种构造代理模型的技术，即真正交分解(POD)和随机配置法(SCM)，以加速偏微分方程参数估计问题的贝叶斯推理方法。POD是一种模型降阶技术，它使用最优的问题适应基础来推导降阶模型，从而显著减少问题的规模，从而减少计算成本。SCM是一种不确定性传播技术，它近似于参数化解，并将进一步的正解减少到函数求值。在淬火过程中产生的边界测量和无损评估中概率地校准标量Robin系数的非线性反问题上，评估了这些技术的实用性。该方法采用分层贝叶斯模型，灵活处理正则化参数和噪声水平，并采用马尔可夫链蒙特卡罗方法搜索后验状态空间。数值结果表明，在不牺牲精度的前提下，可以获得显著的计算增益。版权所有©2008 John Wiley&Sons，Ltd.
This paper presents two techniques, i.e. the proper orthogonal decomposition (POD) and the stochastic collocation method (SCM), for constructing surrogate models to accelerate the Bayesian inference approach for parameter estimation problems associated with partial differential equations. POD is a model reduction technique that derives reduced‐order models using an optimal problem‐adapted basis to effect significant reduction of the problem size and hence computational cost. SCM is an uncertainty propagation technique that approximates the parameterized solution and reduces further forward solves to function evaluations. The utility of the techniques is assessed on the non‐linear inverse problem of probabilistically calibrating scalar Robin coefficients from boundary measurements arising in the quenching process and non‐destructive evaluation. A hierarchical Bayesian model that handles flexibly the regularization parameter and the noise level is employed, and the posterior state space is explored by the Markov chain Monte Carlo. The numerical results indicate that significant computational gains can be realized without sacrificing the accuracy. Copyright © 2008 John Wiley & Sons, Ltd.