A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis

نویسندگان

  • J. Breidt
  • Troy D. Butler
  • Donald J. Estep
چکیده

We consider the inverse sensitivity analysis problem of quantifying the uncertainty of inputs to a deterministic map given specified uncertainty in a linear functional of the output of the map. This is a version of the model calibration or parameter estimation problem for a deterministic map. We assume that the uncertainty in the quantity of interest is represented by a random variable with a given distribution, and we use the law of total probability to express the inverse problem for the corresponding probability measure on the input space. Assuming that the map from the input space to the quantity of interest is smooth, we solve the generally ill-posed inverse problem by using the implicit function theorem to derive a method for approximating the set-valued inverse that provides an approximate quotient space representation of the input space. We then derive an efficient computational approach to compute a measure theoretic approximation of the probability measure on the input space imparted by the approximate set-valued inverse that solves the inverse problem.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Measure-Theoretic Computational Method for Inverse Sensitivity Problems III: Multiple Quantities of Interest

We consider inverse problems for a deterministic model in which the dimension of the output quantities of interest computed from the model is smaller than the dimension of the input quantities for the model. In this case, the inverse problem admits set-valued solutions (equivalence classes of solutions). We devise a method for approximating a representation of the set-valued solutions in the pa...

متن کامل

Solving a nonlinear inverse system of Burgers equations

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

متن کامل

Inverse Laplace transform method for multiple solutions of the fractional Sturm-Liouville problems

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.

متن کامل

A Computational Measure Theoretic Approach to Inverse Sensitivity Problems II: A Posteriori Error Analysis

In part one of this paper [T. Butler and D. Estep, SIAM J. Numer. Anal., to appear], we develop and analyze a numerical method to solve a probabilistic inverse sensitivity analysis problem for a smooth deterministic map assuming that the map can be evaluated exactly. In this paper, we treat the situation in which the output of the map is determined implicitly and is difficult and/or expensive t...

متن کامل

A novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem

Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and league championship algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we u...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • SIAM journal on numerical analysis

دوره 49 5  شماره 

صفحات  -

تاریخ انتشار 2011