# The Lost Art of Mathematical Modelling

arXiv: https://arxiv.org/abs/2301.08559 · HTML: https://mlsanity.com/paper/2301.08559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 150 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 8 of 8)

- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Scale-free networks are rare](https://mlsanity.com/paper/1801.03400/) (2018)
- [Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks](https://mlsanity.com/paper/2202.01723/) (2022)
- [Mapping the stereotyped behaviour of freely-moving fruit flies](https://mlsanity.com/paper/1310.4249/) (2013)
- [Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach](https://mlsanity.com/paper/2207.05779/) (2022)
- [Evolutionary games on multilayer networks: A colloquium](https://mlsanity.com/paper/1504.04359/) (2015)
- [The games we play: critical complexity improves machine learning](https://mlsanity.com/paper/2205.08922/) (2022)

## Abstract (arXiv)

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities -- (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data -- inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomena can be modelled in an infinite number of different ways, through the adoption of an open/pluralistic approach. We explain the open approach using fish locomotion as a case study and illustrate some of the pitfalls -- universalism, creating models of models, etc. -- that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling. This article is dedicated to the memory of Edmund Crampin.