Learning Equations from Biological Data with Limited Time Samples

Nardini, John T.; Lagergren, John; Hawkins-Daarud, Andrea; Curtin, Lee; Morris, Bethan; Rutter, Erica M.; Swanson, Kristin R.; Flores, Kevin

doi:10.1007/s11538-020-00794-z

Cited by 19 publications

(17 citation statements)

References 42 publications

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“…These two investigations, Q4 and Q5, suggest important future work must be performed to determine strategic (and not necessarily uniform) samples of the ABM that are informative and capture all dynamic regimes of the data). Some preliminary work towards these questions for PDE models has been investigated in [56]. A limitation of EQL methods, as opposed to ABM simulation and mean-field models, is that it may not be able to accurately extrapolate to unobserved data and parameters, as we observed in Case study 3b.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…ABMs are a useful intermediate step to test the predictions of mathematical methods because ABMs emulate the stochastic and discrete nature of many biological processes and allow researchers to alter aspects of the data. Biological data present many practical challenges for modellers, including only partial observations of the process under consideration or sparse sampling of the data [56]. We will use this case study to consider the performance of the EQL methods in the face of both limited data sampling and partial data observations.…”

Section: Case Study 3: Learning Agent-based Model Dynamics From Sparsmentioning

confidence: 99%

“…We note alternative methods of numerical differentiation can be used to improve EQL results with limited time samples here. As an example, we have recently introduced an ANN approach that has proven successful in learning equations from sparse PDE data [56]. This method would likely outperform the finite difference scheme used for differentiation throughout this study.…”

Section: Case Study 3: Learning Agent-based Model Dynamics From Sparsmentioning

confidence: 99%

“…This method would likely outperform the finite difference scheme used for differentiation throughout this study. We point the interested reader to [24,56] for more information on this ANN approach.…”

Section: Case Study 3: Learning Agent-based Model Dynamics From Sparsmentioning

confidence: 99%

“…Including data past the inflection point appears necessary to capture how C ABM (t) becomes concave down before reaching the carrying capacity. Further investigation into informative datasets for EQL training have been explored elsewhere [56]. The learned DE model for these different data percentages and their MSEs on the test data set are summarized in table 4.…”

Section: Case Study 3b: Predicting Unobserved Birth-deathmigration Dymentioning

confidence: 99%

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Learning differential equation models from stochastic agent-based model simulations

Nardini

Baker

Simpson

et al. 2021

J. R. Soc. Interface.

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Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology and epidemiology. Analysis of the model dynamics can be challenging due to their inherent stochasticity and heavy computational requirements. Common approaches to the analysis of agent-based models include extensive Monte Carlo simulation of the model or the derivation of coarse-grained differential equation models to predict the expected or averaged output from the agent-based model. Both of these approaches have limitations, however, as extensive computation of complex agent-based models may be infeasible, and coarse-grained differential equation models can fail to accurately describe model dynamics in certain parameter regimes. We propose that methods from the equation learning field provide a promising, novel and unifying approach for agent-based model analysis. Equation learning is a recent field of research from data science that aims to infer differential equation models directly from data. We use this tutorial to review how methods from equation learning can be used to learn differential equation models from agent-based model simulations. We demonstrate that this framework is easy to use, requires few model simulations, and accurately predicts model dynamics in parameter regions where coarse-grained differential equation models fail to do so. We highlight these advantages through several case studies involving two agent-based models that are broadly applicable to biological phenomena: a birth–death–migration model commonly used to explore cell biology experiments and a susceptible–infected–recovered model of infectious disease spread.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Case Study 3: Learning Agent-based Model Dynamics From Sparsmentioning

confidence: 99%

Section: Case Study 3: Learning Agent-based Model Dynamics From Sparsmentioning

confidence: 99%

Section: Case Study 3: Learning Agent-based Model Dynamics From Sparsmentioning

confidence: 99%

Section: Case Study 3b: Predicting Unobserved Birth-deathmigration Dymentioning

confidence: 99%

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Learning differential equation models from stochastic agent-based model simulations

Nardini

Baker

Simpson

et al. 2021

J. R. Soc. Interface.

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Learning Biological Dynamics From Spatio-Temporal Data by Gaussian Processes

Han

Dinh

et al. 2022

Bull Math Biol

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Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data

2023

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Learning Equations from Biological Data with Limited Time Samples

Cited by 19 publications

References 42 publications

Learning differential equation models from stochastic agent-based model simulations

Learning differential equation models from stochastic agent-based model simulations

Learning Biological Dynamics From Spatio-Temporal Data by Gaussian Processes

Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data

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