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Estimating initial conditions for dynamical systems with incomplete information

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  • Farmer, J. Doyne
  • Kolic, Blas
  • Sabuco, Juan

Abstract

In this paper we study the problem of inferring the initial conditions of a dynamical system under incomplete information. Studying several model systems, we infer the latent microstates that best reproduce an observed time series when the observations are sparse, noisy and aggregated under a (possibly) nonlinear observation operator. This is done by minimizing the least-squares distance between the observed time series and a model-simulated time series using gradient-based methods. We validate this method for the Lorenz and Mackey-Glass systems by making out-of-sample predictions. Finally, we analyze the predicting power of our method as a function of the number of observations available. We find a critical transition for the MackeyGlass system, beyond which it can be initialized with arbitrary precision.

Suggested Citation

  • Farmer, J. Doyne & Kolic, Blas & Sabuco, Juan, 2021. "Estimating initial conditions for dynamical systems with incomplete information," INET Oxford Working Papers 2021-20, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    • Handle: RePEc:amz:wpaper:2021-20
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    File URL: https://www.inet.ox.ac.uk/files/Microstates_Initialization-4-00000002.pdf
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    1. Sylvain Barde, 2012. "Back to the future: economic rationality and maximum entropy prediction," Studies in Economics 1202, School of Economics, University of Kent.
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