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Principled Model Selection for Stochastic Dynamics.

Andonis Gerardos1, Pierre Ronceray1

  • 1Aix Marseille Université, CNRS, CINAM, Turing Center for Living Systems, Marseille, France.

Physical Review Letters
|October 31, 2025
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Summary
This summary is machine-generated.

We introduce parsimonious stochastic inference (PASTIS) to prevent overfitting in complex dynamical systems modeled by stochastic differential equations. PASTIS effectively identifies minimal models from data, even with noise or sparse sampling.

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Area of Science:

  • Dynamical Systems and Complexity
  • Computational Statistics
  • Theoretical Ecology

Background:

  • Complex systems (macromolecules to ecosystems) are often modeled using stochastic differential equations.
  • Learning these models from data typically involves sparse selection from extensive function libraries, which can lead to overfitting.
  • Overfitting stems from both individual model complexity and the combinatorial explosion of potential models.

Purpose of the Study:

  • To develop a principled method for learning parsimonious models of complex dynamical systems from data.
  • To address the overfitting problem inherent in sparse selection methods for stochastic differential equations.
  • To improve the reliability and accuracy of model identification in the presence of noise and limited data.

Main Methods:

  • Introduction of parsimonious stochastic inference (PASTIS), a novel statistical framework.
  • Combination of likelihood-estimation statistics with extreme value theory to penalize superfluous parameters.
  • Application and validation across various complex systems, including stochastic partial differential equations.

Main Results:

  • PASTIS significantly outperforms existing methods in identifying minimal models.
  • The method demonstrates robustness even with low sampling rates and substantial measurement error.
  • Successful application to ecological networks and reaction-diffusion dynamics, showcasing broad applicability.

Conclusions:

  • Parsimonious stochastic inference (PASTIS) provides a robust and effective solution to overfitting in complex dynamical systems.
  • The method enables reliable identification of essential model components, leading to more interpretable and generalizable models.
  • PASTIS offers a significant advancement for data-driven modeling in diverse scientific fields involving stochastic processes.