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Parameter estimation in systems exhibiting spatially complex solutions via persistent homology and machine learning

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  • Calcina, Sabrina S.
  • Gameiro, Marcio

Abstract

We use persistent homology to extract topological information from complex spatio-temporal data generated by differential equations and use this information to estimate the corresponding parameters of the differential equation using regression methods in machine learning. We apply this technique to a predator–prey system and to the complex Ginzburg–Landau equation.

Suggested Citation

  • Calcina, Sabrina S. & Gameiro, Marcio, 2021. "Parameter estimation in systems exhibiting spatially complex solutions via persistent homology and machine learning," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 719-732.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:719-732
    DOI: 10.1016/j.matcom.2021.01.013
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    References listed on IDEAS

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    1. Zixuan Cang & Lin Mu & Guo-Wei Wei, 2018. "Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening," PLOS Computational Biology, Public Library of Science, vol. 14(1), pages 1-44, January.
    2. Xiaolei Xun & Jiguo Cao & Bani Mallick & Arnab Maity & Raymond J. Carroll, 2013. "Parameter Estimation of Partial Differential Equation Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1009-1020, September.
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