Data-driven inference of complex system dynamics: A mini-review

Gao, Ting-Ting; Yan, Gang

doi:10.1209/0295-5075/acc3bf

Cited by 6 publications

(2 citation statements)

References 68 publications

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“…Currently, the three main classes of methods to learn equations from data are symbolic regression [65], neural-network approaches [13], and library-based sparse regression [12]. Recent reviews of these categories and their overlaps can be found in [66,67].…”

Section: Discussionmentioning

confidence: 99%

Distilling identifiable and interpretable dynamic models from biological data

Massonis,

Villaverde,

Banga

2023

PLoS Comput Biol

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Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam’s razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable.

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Section: Discussionmentioning

confidence: 99%

Distilling identifiable and interpretable dynamic models from biological data

Massonis,

Villaverde,

Banga

2023

PLoS Comput Biol

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“…Alternatively, some methods restrict inferences to statistical arguments with uncertainty in order to remove the dependence on a priori information. For the interested reader, a comprehensive review and discussion on data-driven network inference has also been given by Gao & Yan [13].…”

Section: Introductionmentioning

confidence: 99%

A Backpropagation Algorithm for Inferring Disentagled Nodal Dynamics and Connectivity Structure of Dynamical Networks

Tan,

Corrêa,

Stemler

et al. 2024

IEEE Trans. Netw. Sci. Eng.

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Dynamical networks are versatile models that describe a variety of behaviours such as synchronisation and feedback in networks of coupled dynamical components. However, applying these models in real systems is difficult as prior information of the connectivity structure or local dynamics is often unknown and must be inferred from node state observations. Additionally, the influence of coupling interactions complicates the isolation of local node dynamics. Given the architectural similarities between dynamical networks and recurrent neural networks (RNNs), we propose a network inference method based on the backpropagation through time (BPTT) algorithm used to train RNNs. This method aims to simultaneously infer both the connectivity structure and isolated local node dynamics from node state observations. An approximation of local node dynamics is first constructed using a neural network. This is alternated with an adapted BPTT algorithm to regress corresponding network weights by minimising prediction errors of the network based on the previously constructed local models until convergence. This method was successful in identifying the connectivity structure for coupled networks of chaotic oscillators. Freerun prediction performance with the resulting local models and weights was comparable to the true system with noisy initial conditions. The method is also extended to asymmetric negative coupling.

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Identification of network interactions from time series data: An iterative approach

Singhal,

Li,

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The first step toward advancing our understanding of complex networks involves determining their connectivity structures from the time series data. These networks are often high-dimensional, and in practice, only a limited amount of data can be collected. In this work, we formulate the network inference task as a bilinear optimization problem and propose an iterative algorithm with sequential initialization to solve this bilinear program. We demonstrate the scalability of our approach to network size and its robustness against measurement noise, hyper-parameter variation, and deviations from the network model. Results across experimental and simulated datasets, comprising oscillatory, non-oscillatory, and chaotic dynamics, showcase the superior inference accuracy of our technique compared to existing methods.

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Data-driven inference of complex system dynamics: A mini-review

Cited by 6 publications

References 68 publications

Distilling identifiable and interpretable dynamic models from biological data

Distilling identifiable and interpretable dynamic models from biological data

A Backpropagation Algorithm for Inferring Disentagled Nodal Dynamics and Connectivity Structure of Dynamical Networks

Identification of network interactions from time series data: An iterative approach

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