English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Mathematical modelling of biological population dynamics often involvesproposing high fidelity discrete agent-based models that capture stochasticityand individual-level processes. These models are often considered inconjunction with an approximate coarse-grained differential equation thatcaptures population-level features only. These coarse-grained models are onlyaccurate in certain asymptotic parameter regimes, such as enforcing that thetime scale of individual motility far exceeds the time scale of birth/deathprocesses. When these coarse-grained models are accurate, the discrete modelstill abides by conservation laws at the microscopic level, which implies thatthere is some macroscopic conservation law that can describe the macroscopicdynamics. In this work, we introduce an equation learning framework to findaccurate coarse-grained models when standard continuum limit approaches areinaccurate. We demonstrate our approach using a discrete mechanical model ofepithelial tissues, considering a series of four case studies that considerproblems with and without free boundaries, and with and without proliferation,illustrating how we can learn macroscopic equations describing mechanicalrelaxation, cell proliferation, and the equation governing the dynamics of thefree boundary of the tissue. While our presentation focuses on this biologicalapplication, our approach is more broadly applicable across a range ofscenarios where discrete models are approximated by approximate continuum-limitdescriptions. All code and data to reproduce this work are available athttps://github.com/DanielVandH/StepwiseEQL.jl.

Pushing coarse-grained models beyond the continuum limit using equation learning