AN EFFECTIVE METHOD FOR PARAMETER ESTIMATION WITH PDE CONSTRAINTS WITH MULTIPLE RIGHT-HAND SIDES

作者：Haber Eldad^*; Chung Matthias; Herrmann Felix

来源：SIAM Journal on Optimization, 2012, 22(3): 739-757.

DOI：10.1137/11081126X

• PDE constrained optimization
• stochastic optimization
• stochastic approximation
• sample average approximation
• inverse problems
• parameter estimation
• large scale problems
• DC resistivity
• seismic tomography
• multiple right hand sides

Often, parameter estimation problems of parameter-dependent PDEs involve multiple right-hand sides. The computational cost and memory requirements of such problems increase linearly with the number of right-hand sides. For many applications this is the main bottleneck of the computation. In this paper we show that problems with multiple right-hand sides can be reformulated as stochastic programming problems by combining the right-hand sides into a few %26quot;simultaneous%26quot; sources. This effectively reduces the cost of the forward problem and results in problems that are much cheaper to solve. We discuss two solution methodologies: namely sample average approximation and stochastic approximation. To illustrate the effectiveness of our approach we present two model problems, direct current resistivity and seismic tomography.

• 出版日期2012
• 单位Virginia Tech; 美国弗吉尼亚理工大学(Virginia Tech)