Method of Uncertainty Minimization using Polynomial Chaos Expansions

David A. Sheen

National Institute of Standards and Technology

Last Revision September 20, 2018

Download this software from GitHub

Welcome to the home page for the Method of Uncertainty Minimization using Polynomial Chaos Expansions (MUM-PCE). This software is a Python package that implements the methodology presented in Sheen & Wang (2011), Wang & Sheen (2015), and Sheen & Manion (2014). The software does the following things:

• Compiles a database of experimental measurements
• Constrains a physical model against the measurements in the database (optimization)
• Determines the uncertainty in the physical model parameters based on the uncertainty in the measurements (uncertainty analysis)
• Identifies measurements that are inconsistent with the constrained model (outlier detection)
• Identifies measurements that do not strongly constrain the constrained model (experimental design)

This implementation cannot be used out of the box. Instead, it is necessary for the user to create an interface to the user’s own code, which will be specific to that application. Two examples of how to do this are provided. One is a toy model which demonstrates how an interface might be written; it is intended to be as complete as possible while also being simple. The other example is an interface to the reaction kinetics program Cantera; this sort of interface probably represents the worst use case possible, with multiple heterogeneous measurements and a highly complex interface to a detailed model.

The package is implemented in a way to be as general as possible, which means that efficiency is often sacrificed in order to implement this generality. Expert users may be able to modify the code in such a way as to make it more efficient for their particular application. No support is provided for this adventure, but please let me know if you are successful.

Legal

This software is subject to the NIST Software License (revised as of July 2017). This license can be found in the GitHub repo in the file named LICENSE.

Contents

• Projects and Solutions
  • Creating Projects
  • Solving Projects to create Solutions
  • Project method summary
  • Project class
  • Solution class
• Measurements and Models
  • Measurements
  • Models and Response Surfaces
  • Function summary
  • Measurement class
  • Generic model class
  • Response surface class
• A toy example using MUM-PCE
  • Example usage and output
  • Defining models
  • The initialization function
  • Creating a Project
  • Solving the Project
  • Function summary
• The Cantera interface to MUM-PCE
  • Generic chemistry interface for Cantera
  • Shock tube models
  • Laminar flame speeds
  • Reaction Rate Measurements
  • Examples input for the Cantera interface
  • The initialization function
  • Model classes in the Cantera interface
  • Function summary

Contact

David Sheen

• Email
• NIST Staff Page
• GitHub profile

Links

NIST GitHub Organization

NIST Chemical Informatics Research Group

NIST home page

Indices and tables

• Index
• Module Index
• Search Page