Active subspaces are part of an emerging set of tools for subspace-based dimension reduction in complex simulation models in science and engineering. This repository contains data sets and associated Jupyter notebooks that apply active subspace methods to a wide range of science and engineering models. The Python implementations of the methods are available on Github. More information on active subspaces can be found at activesubspaces.org.
Each directory contains a data set as a CSV file and a Jupyter notebook (.ipynb). Github allows you view the notebook by simply clicking the .ipynb file. However, Github's rendering of mathematical expressions is not as robust as the rendering at nbviewer.jupyter.org. We recommend you copy the link to the notebook you wish to view and paste it in the box at nbviewer.jupyter.org. Each notebook also has links to associated publications for more details.
The repository contains Jupyter notebooks for the following models / data sets.
- Ebola: a 9-parameter dynamical system model for the geographic spread of Ebola. [paper]
- HIV: a 21-parameter dynamical system model for in-host HIV. [paper]
- HyShotII: a 7-parameter multiphysics model of a hypersonic scramjet. [paper]
- Hydrology: a 20-parameter integrated surface/subsurface hydrologic model. [paper]
- Lithium_Battery: an 18-parameter model of a lithium-ion battery. [paper]
- MCMC: exploiting active subspaces to apply MCMC in a 100-parameter PDE model. [paper]
- MHD: a 5-parameter magnetohydrodynamics power generation model. [paper]
- NACA0012: an 18-parameter model for a two-spatial-dimensional airfoil. [chapter 5]
- NREL_Wind: a 5-parameter model of off-shore wind turbine fatige. [paper]
- ONERA-M6: a 60-parameter model for a three-spatial-dimensional transonic wing. [paper]
- Reentry_freestream_conditions: a 7-parameter model for an atmostpheric re-entry vehicle.
- SingleDiodePV: a 5-parameter model for a lumped-parameter single-diode photovoltaic solar cell. [paper]
- Stomatal_Resistance: a 20-parameter model of stomatal resistance in an integrated surface/subsurface hydrologic model. [thesis]
- Subsurface_Permeability: a 100-parameter model for subsurface permeability for groundwater flow. [paper]
If you have a data set from a model, and you find evidence of an active subspace, feel free to contribute a notebook to our repository. Contact Paul Constantine at Colorado School of Mines with questions or comments. Ryan Howard at Colorado School of Mines created the notebooks from the associated publications and data sets over the summer of 2016.
This material is based upon work supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC-0011077.