In modern engineering applications, the generation of high-dimensional snapshots can be time and/or resource-demanding. The spatio-temporal data comes as snapshots containing spatial information for each time instant.

Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal data generated from dynamical systems and infer different scenarios for said systems. Modern computational science and engineering applications are being improved by the advances in scientific machine learning. We introduce measure-preserving extended dynamic mode decomposition ($ exttt$ on a range of challenging examples, its increased robustness to noise compared with other DMD-type methods, and its ability to capture the energy conservation and cascade of experimental measurements of a turbulent boundary layer flow with Reynolds number $> 6 imes 10^4$ and state-space dimension $>10^5$. However, Koopman operators are infinite-dimensional, and computing their spectral information is a considerable challenge. Koopman operators globally linearize nonlinear dynamical systems and their spectral information is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. Published by Oxford University Press on behalf of Royal Society of Tropical Medicine and Hygiene.

DMD is poised to be an effective and efficient computational analysis tool for the study of infectious disease. We demonstrate how DMD can aid in the analysis of spatial-temporal disease data. For each case, we describe the utility of the method for surveillance and resource allocation. We demonstrate the method on three different infectious disease sets including Google Flu Trends data, pre-vaccination measles in the UK, and paralytic poliomyelitis wild type-1 cases in Nigeria. The algorithm has a number of advantages including a rigorous connection to the analysis of nonlinear systems, an equation-free architecture, and the ability to efficiently handle high-dimensional data. The development and application of quantitative methods to understand disease dynamics and plan interventions is becoming increasingly important in the push toward eradication of human infectious diseases, exemplified by the ongoing effort to stop the spread of poliomyelitis.ĭynamic mode decomposition (DMD) is a recently developed method focused on discovering coherent spatial-temporal modes in high-dimensional data collected from complex systems with time dynamics.

Tor eckhoff grave