Version 1
: Received: 5 October 2024 / Approved: 7 October 2024 / Online: 7 October 2024 (15:32:26 CEST)
How to cite:
Fortela, D. L.; Mikolajczyk, A.; Hernandez, R.; Revellame, E.; Sharp, W.; Holmes, W.; Zappi, M. E. Dynamic Time Warping as Elementary Effects Metric for Morris-based Global Sensitivity Analysis of High-dimension Dynamical Models. Preprints2024, 2024100502. https://doi.org/10.20944/preprints202410.0502.v1
Fortela, D. L.; Mikolajczyk, A.; Hernandez, R.; Revellame, E.; Sharp, W.; Holmes, W.; Zappi, M. E. Dynamic Time Warping as Elementary Effects Metric for Morris-based Global Sensitivity Analysis of High-dimension Dynamical Models. Preprints 2024, 2024100502. https://doi.org/10.20944/preprints202410.0502.v1
Fortela, D. L.; Mikolajczyk, A.; Hernandez, R.; Revellame, E.; Sharp, W.; Holmes, W.; Zappi, M. E. Dynamic Time Warping as Elementary Effects Metric for Morris-based Global Sensitivity Analysis of High-dimension Dynamical Models. Preprints2024, 2024100502. https://doi.org/10.20944/preprints202410.0502.v1
APA Style
Fortela, D. L., Mikolajczyk, A., Hernandez, R., Revellame, E., Sharp, W., Holmes, W., & Zappi, M. E. (2024). Dynamic Time Warping as Elementary Effects Metric for Morris-based Global Sensitivity Analysis of High-dimension Dynamical Models. Preprints. https://doi.org/10.20944/preprints202410.0502.v1
Chicago/Turabian Style
Fortela, D. L., William Holmes and Mark E. Zappi. 2024 "Dynamic Time Warping as Elementary Effects Metric for Morris-based Global Sensitivity Analysis of High-dimension Dynamical Models" Preprints. https://doi.org/10.20944/preprints202410.0502.v1
Abstract
This work focused on demonstrating the use of dynamic time warping (DTW) as metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics is the modeling of parameter perturbation effects propagated to all model outputs while capturing time-dependent patterns. The study establishes and demonstrates the use of DTW as metric of elementary effects across the time domain and the multivariate output domain, which are all aggregated together via the DTW cost function into a single metric value. Unlike the commonly studied coefficient-based functional approximation, and covariance decomposition methods, this new DTW-based Morris GSA algorithm implements curve alignment via dynamic programing for cost computation in every parameter perturbation trajectory, which captures the essence of “elementary effect” in the original Morris formulation. This new algorithm eliminates approximations and assumptions about the model outputs while achieving the objective of capturing perturbations across time and the array of model outputs. The technique was demonstrated using ordinary differential equation (ODE) system of a mixed-order adsorption kinetics, Monod-type microbial kinetics, and the Lorenz attractor for chaotic solutions. DTW as Morris-based GSA metric enables the modeling of parameter sensitivity effects on the entire array of model output variables evolving in time domain resulting to parameter rankings attributed to the entire model dynamics.
Keywords
multivariate dynamical systems; system identification; functional data analysis
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
