The lost art of mathematical modelling

Gyllingberg, Linnéa; Birhane, Abeba; Sumpter, David J. T.

doi:10.1016/j.mbs.2023.109033

Cited by 6 publications

(5 citation statements)

References 110 publications

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“…While reductionism would advocate for symmetry, 395 specific mixtures may require specific lenses for adequate representation. Hybrid multiscale ML models 396 with physics-based multiscale modeling which probes causality and mechanisms for emergence (from micro to macroscale) and immergence (from macro to microscale) comprehension. 397,398 Another important takeaway is that the Hamiltonian may serve as a pivotal concept between graph topology, state probability, phase space dynamics, game theory, 399 and optimization, adeptly portraying the complexity and symmetry-breaking inherent in mixtures.…”

Section: Lessons Learned and Outlookmentioning

confidence: 99%

“…While reductionism would advocate for symmetry, specific mixtures may require specific lenses for adequate representation. Hybrid multiscale ML models connect geometric deep learning with physics-based multiscale modeling which probes causality and mechanisms for emergence (from micro to macroscale) and immergence (from macro to microscale) comprehension. , …”

Section: Lessons Learned and Outlookmentioning

confidence: 99%

“…specific mixtures may require specific lenses for adequate representation. Hybrid multiscale ML models396 connect geometric deep learning…”

mentioning

confidence: 99%

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Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Nicolle,

Deng,

Ihme

et al. 2024

J. Chem. Inf. Model.

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Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the ’recomposition’ of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure–Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.

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Section: Lessons Learned and Outlookmentioning

confidence: 99%

Section: Lessons Learned and Outlookmentioning

confidence: 99%

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Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Nicolle,

Deng,

Ihme

et al. 2024

J. Chem. Inf. Model.

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“…(2009) pointed out that methods for quantitatively understanding fish shoal behavior patterns are still under development [14]. Gyllingberg critiques the prevailing focus within mathematical biology on model analysis over model formation, especially in the context of rapid advancements in modern machine learning, arguing that researchers are currently overly focused on model analysis at the expense of model formation [15].…”

Section: Introductionmentioning

confidence: 99%

Quantitative Assessment and Analysis of Fish Behavior in Closed Systems Using Information Entropy

Kadota,

Torisawa,

Takagi

2024

Fishes

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This study introduces a method for quantitatively assessing the complexity and predictability of fish behavior in closed systems through the application of information entropy, offering a novel lens through which to understand how fish adapt to environmental changes. Utilizing simulations rooted in a random walk model for fish movement, we delve into entropy fluctuations under varying environmental conditions, including responses to feeding and external stimuli. Our findings underscore the utility of information entropy in capturing the intricacies of fish behavior, particularly highlighting the synchrony in collective actions and adaptations to environmental shifts. This research not only broadens our comprehension of fish behavior but also paves the way for its application in fields like aquaculture and resource management. Through our analysis, we discovered that smaller grid sizes in simulations capture detailed local fluctuations, while larger grids elucidate general trends, pinpointing a 2.5 grid as optimal for our study. Moreover, changes in swimming speeds and behavioral adaptations during feeding were quantitatively analyzed, with results illustrating significant behavior modifications. Additionally, employing a Gaussian mixture model helped to clarify the nuanced changes in fish behavior in response to altered light conditions, demonstrating the layered complexity of fish responses to environmental stimuli. This investigation confirms the efficacy of information entropy as a robust metric for evaluating fish shoal behavior, offering a fresh methodology for ecological and environmental studies, with promising implications for sustainable management practices.

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“…We then introduce social interaction, and characterize the behaviour of a pair of fish as a function of key parameters. The aim of our study is primarily to investigate the mechanisms at work [58][59][60][61][62], rather than to compare the model in detail with data. Nonetheless, we show that the patterns of interactions created in the model mimic those observed in single and pairs of guppies.…”

Section: Introductionmentioning

confidence: 99%

Using neuronal models to capture burst-and-glide motion and leadership in fish

Gyllingberg

Szorkovszky

Sumpter

2023

J. R. Soc. Interface.

Self Cite

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While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh–Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader–follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

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The lost art of mathematical modelling

Cited by 6 publications

References 110 publications

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Quantitative Assessment and Analysis of Fish Behavior in Closed Systems Using Information Entropy

Using neuronal models to capture burst-and-glide motion and leadership in fish

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