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Ghost hunting in the nonlinear dynamic machine

Author

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  • Jonathan E Butner
  • Ascher K Munion
  • Brian R W Baucom
  • Alexander Wong

Abstract

Integrating dynamic systems modeling and machine learning generates an exploratory nonlinear solution for analyzing dynamical systems-based data. Applying dynamical systems theory to the machine learning solution further provides a pathway to interpret the results. Using random forest models as an illustrative example, these models were able to recover the temporal dynamics of time series data simulated using a modified Cusp Catastrophe Monte Carlo. By extracting the points of no change (set points) and the predicted changes surrounding the set points, it is possible to characterize the topology of the system, both for systems governed by global equation forms and complex adaptive systems. RESULTS: The model for the simulation was able to recover the cusp catastrophe (i.e. the qualitative changes in the dynamics of the system) even when applied to data that have a significant amount of error variance. To further illustrate the approach, a real-world accelerometer example was examined, where the model differentiated between movement dynamics patterns by identifying set points related to cyclic motion during walking and attraction during stair climbing. These example findings suggest that integrating machine learning with dynamical systems modeling provides a viable means for classifying distinct temporal patterns, even when there is no governing equation for the nonlinear dynamics. Results of these integrated models yield solutions with both a prediction of where the system is going next and a decomposition of the topological features implied by the temporal dynamics.

Suggested Citation

  • Jonathan E Butner & Ascher K Munion & Brian R W Baucom & Alexander Wong, 2019. "Ghost hunting in the nonlinear dynamic machine," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-21, December.
  • Handle: RePEc:plo:pone00:0226572
    DOI: 10.1371/journal.pone.0226572
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    References listed on IDEAS

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    1. Vivien Marx, 2013. "The big challenges of big data," Nature, Nature, vol. 498(7453), pages 255-260, June.
    2. Sims, Christopher A, 1971. "Discrete Approximations to Continuous Time Distributed Lags in Econometrics," Econometrica, Econometric Society, vol. 39(3), pages 545-563, May.
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    2. Tarkocin, Coskun & Donduran, Murat, 2024. "Constructing early warning indicators for banks using machine learning models," The North American Journal of Economics and Finance, Elsevier, vol. 69(PB).
    3. Leal Filho, Walter & Wall, Tony & Rui Mucova, Serafino Afonso & Nagy, Gustavo J. & Balogun, Abdul-Lateef & Luetz, Johannes M. & Ng, Artie W. & Kovaleva, Marina & Safiul Azam, Fardous Mohammad & Alves,, 2022. "Deploying artificial intelligence for climate change adaptation," Technological Forecasting and Social Change, Elsevier, vol. 180(C).

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