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A numerical method for solving a stochastic inverse problem for parameters.

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  • 1Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712, United States.

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|December 19, 2013
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Summary
This summary is machine-generated.

This study introduces a novel method for the stochastic inverse problem, determining input parameter variations to match output variations in models like the Brusselator. The approach offers a computational solution with error analysis for improved accuracy.

Keywords:
A posteriori error analysisAdjoint problemDensity estimationInverse sensitivity analysisNonparametric density estimationSensitivity analysis

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Area of Science:

  • Applied Mathematics
  • Chemical Kinetics
  • Computational Science

Background:

  • Stochastic inverse problems are crucial for understanding systems with inherent randomness.
  • Accurate determination of input parameter variations is essential for model validation and prediction.
  • The Brusselator model serves as a complex test case for evaluating new computational methods.

Purpose of the Study:

  • To present a new formulation and solution for the stochastic inverse parameter determination problem.
  • To apply this method to the Brusselator model for practical demonstration.
  • To develop a computational approach for approximating probability measures in inverse problems.

Main Methods:

  • Formulating the problem as an inverse problem for an integral equation using the Law of Total Probability.
  • Constructing a systematic method for approximating set-valued inverse solutions.
  • Developing a computational approach for measure-theoretic approximation of probability measures.

Main Results:

  • A viable computational method for solving stochastic inverse problems was developed.
  • The approach was successfully applied to the Brusselator model.
  • Convergence and a posteriori error analyses were performed on the computed probability distributions.

Conclusions:

  • The proposed method provides a robust framework for addressing stochastic inverse problems.
  • The computational approach offers accurate approximations of probability measures.
  • This work advances the understanding and solution of parameter determination in complex systems.