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A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

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Parameter Estimation of Partial Differential Equation Models.

Xiaolei Xun¹, Jiguo Cao², Bani Mallick³

¹Beijing Novartis Pharma Co. Ltd., Pudong New District, Shanghai, 201203, China.

Journal of the American Statistical Association

|December 24, 2013

Summary

This summary is machine-generated.

This study introduces two novel methods, parameter cascading and Bayesian approaches, to accurately estimate parameters in complex partial differential equation (PDE) models. These methods improve accuracy and reduce computational load for dynamic system modeling.

Keywords:

Asymptotic theory Basis function expansion Bayesian method Differential equations Measurement error Parameter cascading

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Area of Science:

Applied mathematics
Computational science
Scientific modeling

Background:

Partial differential equation (PDE) models are crucial for dynamic systems in biology and finance.
Estimating unknown parameters in these models is challenging due to lack of analytical solutions and measurement errors.
Current parameter estimation methods for PDEs are computationally intensive.

Purpose of the Study:

To develop efficient and accurate methods for estimating parameters in partial differential equation (PDE) models.
To address the high computational cost associated with traditional PDE parameter estimation.
To provide robust techniques applicable to real-world data, such as LIDAR measurements.

Main Methods:

Representing the dynamic process using basis function expansion for both proposed methods.
Developing a parameter cascading method with nested optimization levels.
Implementing a Bayesian approach with a joint data-PDE model and a hierarchical model for Markov chain Monte Carlo (MCMC) inference.

Main Results:

Both the parameter cascading and Bayesian methods demonstrate high estimation accuracy.
The proposed methods outperform existing techniques for PDE parameter estimation.
The effectiveness of the methods is validated using LIDAR data for parameter estimation in a PDE model.

Conclusions:

The developed parameter cascading and Bayesian methods offer significant improvements in estimating parameters for partial differential equation models.
These novel approaches provide more accurate and computationally efficient alternatives to existing methods.
The techniques are practical and effective, as shown by their application to real-world LIDAR data analysis.