Data-driven prediction in dynamical systems: recent developments

Ghadami, Amin; Epureanu, Bogdan I.

doi:10.1098/rsta.2021.0213

Cited by 39 publications

(18 citation statements)

References 189 publications

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“…5). These observations call for empirical estimation of developmental maps, for instance, via the rapidly developing methods to estimate dynamic equations from data (Schmidt and Lipson, 2009; Brunton et al ., 2016; Ghadami and Epureanu, 2022, and papers in the special issue). Overall, our analysis finds that development has major evolutionary consequences.…”

Section: Discussionmentioning

confidence: 99%

How development affects evolution

González-Forero¹,

Gardner²

2021

Preprint

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How development affects evolution. A mathematical framework that explicitly integrates development into evolution has recently been derived. Here we use this framework to analyse how development affects evolution. We show that, whilst selection pushes genetic and phenotypic evolution uphill on the fitness landscape, development determines the admissible evolutionary pathway, such that evolutionary outcomes occur at path peaks, which need not be peaks of the fitness landscape. Development can generate path peaks, triggering adaptive radiations, even on constant, single-peak landscapes. Phenotypic plasticity, niche construction, extra-genetic inheritance, and developmental bias variously alter the evolutionary path and hence the outcome. Selective development, whereby phenotype construction may point in the adaptive direction, may induce evolution either towards or away landscape peaks depending on the developmental constraints. Additionally, developmental propagation of phenotypic effects over age allows for the evolution of negative senescence. These results help explain empirical observations including punctuated equilibria, the paradox of stasis, the rarity of stabilizing selection, and negative senescence, and show that development has a major role in evolution.

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Section: Discussionmentioning

confidence: 99%

How development affects evolution

González-Forero¹,

Gardner²

2021

Preprint

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“…The current developments of information technology and artificial intelligence have brought new tools and approaches in relation to the detection, classification, understanding, prediction and control of the dynamics of complex systems. In order to achieve an accurate and computationally tractable prediction of dynamical systems, it is necessary to develop low-dimensional models that are easy to handle but that provide a good approximation of the underlying dynamics [13]. A major challenge in the study of complex system dynamics through data-driven approaches is the large amounts of data that are generated.…”

Section: Introductionmentioning

confidence: 99%

Learning complex systems dynamics from vector fields over discrete measure spaces

Solis

Rossem

Madeleine

et al. 2023

Preprint

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A complex system is formed by entities that, through their interactions and dependencies, give rise to a unified whole with properties and behaviour distinct from those of its constituent parts. Examples of complex systems include the human brain, living cells, organisms, soft matter materials, the Earth’s global climate, ecosystems and the economy. A large number of entities and dependencies produce high dimensional non-linear dynamics, which make the modelling, classification and prediction of complex systems dynamics a major challenge. Advances in modern information technology have made possible a successful use of data-driven approaches to the study of dynamical systems. However, in the particular case of complex systems there are still important open questions to address such as large and complex data sets analysis, dimensionality reduction, phase space reconstruction and global attractor classification. In this paper we introduce the theory of vector fields over discrete measure spaces to analyse data structurally complex, such as images, image gradients, and real and vector valued functions over simplicial complexes. We apply our framework to the analysis of data obtained from numerical solutions of equations commonly used in biology and physics to model a variety of complex systems. We show that our geometric framework, together with multidimensional scaling, an unsupervised learning method, can be successfully used in the analysis of large data sets for dimensionality reduction, mode decomposition and global attractor characterisation of complex systems dynamics. These results pave the way towards the characterisation and understanding of a number of complex dynamical systems.

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“…Modern machine learning methods have made significant progress in the black box prediction performance of many tasks, but the simplified closed form of the internal governing equations of the systems is still unclear or partially unknown. Therefore, it is necessary to study how to explore the governing equations of systems, which contain the underlying governing equation, from the observed data [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Governing equation discovery based on causal graph for nonlinear dynamic systems

Jia,

Zhou,

et al. 2023

Mach. Learn.: Sci. Technol.

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The governing equations of nonlinear dynamic systems is of great significance for understanding the internal physical characteristics. In order to learn the governing equations of nonlinear systems from noisy observed data, we propose a novel method named governing equation discovery based on causal graph that combines spatio-temporal graph convolution network with governing equation modeling. The essence of our method is to first devise the causal graph encoding based on transfer entropy to obtain the adjacency matrix with causal significance between variables. Then, the spatio-temporal graph convolutional network is used to obtain approximate solutions for the system variables. On this basis, automatic differentiation is applied to obtain basic derivatives and form a dictionary of candidate algebraic terms. Finally, sparse regression is used to obtain the coefficient matrix and determine the explicit formulation of the governing equations. We also design a novel cross-combinatorial optimization strategy to learn the heterogeneous parameters that include neural network parameters and control equation coefficients. We conduct extensive experiments on seven datasets from different physical fields. The experimental results demonstrate the proposed method can automatically discover the underlying governing equation of the systems, and has great robustness.

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Data-driven prediction in dynamical systems: recent developments

Cited by 39 publications

References 189 publications

How development affects evolution

How development affects evolution

Learning complex systems dynamics from vector fields over discrete measure spaces

Governing equation discovery based on causal graph for nonlinear dynamic systems

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