Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data

Prokop, Bartosz; Gelens, Lendert; Pelz, Peter F.; Friesen, John W.

doi:10.1103/physreve.107.064305

Cited by 3 publications

(3 citation statements)

References 47 publications

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Section: Resultsmentioning

confidence: 99%

“…Insufficient resolution Sufficient resolution plays a crucial role in model identification in general and for SINDy in particular; SINDy reportedly struggles in low-data scenarios (50,66,67), which has led to proposals to extend the method (49,68,69). However, the limitations of SINDy and the proposed extensions have not been sufficiently studied, and their proof of concept has been done on generic examples, such as the Lorenz system.…”

Section: Resultsmentioning

confidence: 99%

“…However, the SINDy method has been scarcely applied to real data. Examples include data from generic systems (48,49), settlement data (50), gene expression data (51) and mainly experimental data from predator-prey dynamics (52)(53)(54), where SINDy was able to identify relevant aspects of the respective biological systems.…”

Section: Data-driven Model Inference In Biologymentioning

confidence: 99%

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From biological data to oscillator models using SINDy

Prokop,

Gelens

2023

Preprint

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A large number of important dynamical biological processes, such as the early embryonic cell cycle, cardiac rhythms, or circadian rhythms, are dominated by periodic changes, also called oscillations. It has been a long-standing interest of scientists to understand the underlying mechanisms that describe and regulate this dynamic behavior, usually using classical model identification techniques. The recent rise of data-driven methods, also called machine learning, has fundamentally changed model identification, allowing models to be inferred directly from data with almost no prior knowledge. An example is the data-driven white-box approach SINDy, which despite its recent popularity, has been mainly applied to synthetic data and has yet to prove successful on data from real (biological) experiments. In this work, we explore the limitations of the SINDy approach in the specific context of (biological) oscillatory systems. By directly applying SINDy to experimental data, we define the main limiting aspects: data availability and quality, complexity of interactions, and dimensionality (number of variables) of systems. We study these limiting factors using a set of commonly used, generic oscillator models of different complexity and/or dimensionality. From this, we formulate specific mitigation approaches leading to a step-by-step guide for model inference from real biological data, whose effectiveness we demonstrate using data of glycolytic oscillations in yeast as a test example.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Data-driven Model Inference In Biologymentioning

confidence: 99%

See 1 more Smart Citation

From biological data to oscillator models using SINDy

Prokop,

Gelens

2023

Preprint

Self Cite

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From biological data to oscillator models using SINDy

Prokop,

Gelens

2024

iScience

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Enhancing model identification with SINDy via nullcline reconstruction

Prokop,

Frolov,

Gelens

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse Identification of Nonlinear Dynamics (SINDy). This paper illustrates the importance of accurately determining the system’s limit cycle position in phase space for identifying sparse and effective models. We introduce a method for identifying the limit cycle position and the system’s nullclines by applying SINDy to datasets adjusted with various offsets. This approach is evaluated using three criteria: model complexity, coefficient of determination, and generalization error. We applied this method to several models: the oscillatory FitzHugh–Nagumo model, a more complex model consisting of two coupled cubic differential equations with a single stable state, and a multistable model of glycolytic oscillations. Our results confirm that incorporating detailed information about the limit cycle in phase space enhances the accuracy of model identification in oscillatory systems.

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Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data

Cited by 3 publications

References 47 publications

From biological data to oscillator models using SINDy

From biological data to oscillator models using SINDy

From biological data to oscillator models using SINDy

Enhancing model identification with SINDy via nullcline reconstruction

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