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Maximally predictive ensemble dynamics from data

View ORCID ProfileAntonio Carlos Costa, View ORCID ProfileTosif Ahamed, David Jordan, View ORCID ProfileGreg J Stephens
doi: https://doi.org/10.1101/2021.05.26.445816
Antonio Carlos Costa
1 Ecole Normale Superieure Paris;
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  • For correspondence: antonio.costa@phys.ens.fr
Tosif Ahamed
2 Lunenfeld-Tanenbaum Research Institute: Toronto, ON, CA;
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David Jordan
3 Gurdon Institute, University of Cambridge;
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Greg J Stephens
4 Vrije Universiteit Amsterdam, Okinawa Institute of Science and Technology Graduate University
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Abstract

We leverage the interplay between microscopic variability and macroscopic order to connect physical descriptions across scales directly from data, without underlying equations. We reconstruct a state space by concatenating measurements in time, building a maximum entropy partition of the resulting sequences, and choosing the sequence length to maximize predictive information. Trading non-linear trajectories for linear, ensemble evolution, we analyze reconstructed dynamics through transfer operators. The evolution is parameterized by a transition time τ: capturing the source entropy rate at small τ and revealing timescale separation with collective, coherent states through the operator spectrum at larger τ. Applicable to both deterministic and stochastic systems, we illustrate our approach through the Langevin dynamics of a particle in a double-well potential and the Lorenz system. Applied to the behavior of the nematode worm C. elegans, we derive a "run-and-pirouette" navigation strategy directly from posture dynamics. We demonstrate how sequences simulated from the ensemble evolution capture both fine scale posture dynamics and large scale effective diffusion in the worm's centroid trajectories and introduce a top-down, operator-based clustering which reveals subtle subdivisions of the "run" behavior.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • https://github.com/AntonioCCosta/predictive_ensemble_dynamics/

  • https://zenodo.org/record/4778712#.YK5oBn0zbok

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license.
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Posted September 26, 2021.
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Maximally predictive ensemble dynamics from data
Antonio Carlos Costa, Tosif Ahamed, David Jordan, Greg J Stephens
bioRxiv 2021.05.26.445816; doi: https://doi.org/10.1101/2021.05.26.445816
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Maximally predictive ensemble dynamics from data
Antonio Carlos Costa, Tosif Ahamed, David Jordan, Greg J Stephens
bioRxiv 2021.05.26.445816; doi: https://doi.org/10.1101/2021.05.26.445816

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