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Automated adaptive inference of phenomenological dynamical models

Author

Listed:
  • Bryan C. Daniels

    (Center for Complexity and Collective Computation, Wisconsin Institute for Discovery, University of Wisconsin)

  • Ilya Nemenman

    (Emory University
    Emory University)

Abstract

Dynamics of complex systems is often driven by large and intricate networks of microscopic interactions, whose sheer size obfuscates understanding. With limited experimental data, many parameters of such dynamics are unknown, and thus detailed, mechanistic models risk overfitting and making faulty predictions. At the other extreme, simple ad hoc models often miss defining features of the underlying systems. Here we develop an approach that instead constructs phenomenological, coarse-grained models of network dynamics that automatically adapt their complexity to the available data. Such adaptive models produce accurate predictions even when microscopic details are unknown. The approach is computationally tractable, even for a relatively large number of dynamical variables. Using simulated data, it correctly infers the phase space structure for planetary motion, avoids overfitting in a biological signalling system and produces accurate predictions for yeast glycolysis with tens of data points and over half of the interacting species unobserved.

Suggested Citation

  • Bryan C. Daniels & Ilya Nemenman, 2015. "Automated adaptive inference of phenomenological dynamical models," Nature Communications, Nature, vol. 6(1), pages 1-8, November.
  • Handle: RePEc:nat:natcom:v:6:y:2015:i:1:d:10.1038_ncomms9133
    DOI: 10.1038/ncomms9133
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    Cited by:

    1. Aguilar-Canto, Fernando Javier & Brito-Loeza, Carlos & Calvo, Hiram, 2024. "Model discovery of compartmental models with Graph-Supported Neural Networks," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    2. Wei, Baolei, 2022. "Sparse dynamical system identification with simultaneous structural parameters and initial condition estimation," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Fernández de la Mata, Félix & Gijón, Alfonso & Molina-Solana, Miguel & Gómez-Romero, Juan, 2023. "Physics-informed neural networks for data-driven simulation: Advantages, limitations, and opportunities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    4. Zhao Chen & Yang Liu & Hao Sun, 2021. "Physics-informed learning of governing equations from scarce data," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    5. Charles D. Brummitt & Andres Gomez-Lievano & Ricardo Hausmann & Matthew H. Bonds, 2018. "Machine-learned patterns suggest that diversification drives economic development," Papers 1812.03534, arXiv.org.
    6. Mikhail Genkin & Owen Hughes & Tatiana A. Engel, 2021. "Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories," Nature Communications, Nature, vol. 12(1), pages 1-9, December.

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