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The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models
John T Nardini1,2, D M Bortz3
1Statistical and Applied Mathematical Sciences Institute, 4501 Research Commons, Suite 300 79 T.W. Alexander Drive, PO Box 110207 Durham, NC 27709, United States of America.
Inverse Problems
|June 14, 2021
Summary
Numerical error in advection equation solutions can impact parameter estimation. This study develops a statistical model to improve accuracy and provides guidelines for identifying error sources in scientific inference.
Area of Science:
- Numerical analysis
- Scientific computing
- Partial differential equations
Background:
- Advective partial differential equations model numerous scientific processes.
- Parameter inference from experimental data is challenged by measurement noise and numerical errors.
- The impact of numerical error on parameter estimation and uncertainty quantification in inverse problems is not well understood.
Purpose of the Study:
- To analyze the behavior of least squares cost functions and parameter estimators under numerical error in advection equation solutions.
- To understand how numerical error affects parameter estimation and uncertainty quantification.
- To provide practical guidelines for error assessment and improvement in scientific inference.
Main Methods:
- Analytical and computational investigation of parameter estimation with numerical error.
- Analysis of residual patterns to develop a statistical model.
- Derivation of an autocorrelative statistical model for improved estimation and confidence intervals.
Main Results:
- Characterization of the influence of numerical error on parameter estimation accuracy.
- Development of an autocorrelative statistical model to enhance parameter estimation and confidence interval computation.
- Identification of conditions under which numerical error dominates experimental error.
Conclusions:
- Numerical error significantly affects parameter estimation in advection-dominated processes.
- The derived statistical model offers a method to improve inference accuracy and quantify uncertainty.
- Guidelines are provided for practitioners to diagnose and mitigate error sources for more reliable scientific results.
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