Conceptual Models

Conceptual Apps - a new approach for science and education

To understand how a system works - the climate system, the interaction between sharks and fish, the growth of bacteria, the dispersion of plastics through the ocean - we build conceptual models in our heads. How does one part of a system interact with another? What factors control those interactions? For those who understand higher-level maths, particularly differential equations (which describe how things change over time or distance), conceptual models can be translated into equations. These equations can then be used to build computer-based simulations. The simulations allow us to test whether our conceptual understanding matches the real world. What elements are our models missing? Do the system interactions lead to unexpected behaviour? What happens when we tweak our conceptual model?

With recent advances in AI, the ability to turn conceptual models into working computer-based simulations - or conceptual apps - has become far easier. AI can handle the underlying maths and help us build interactive tools. This opens up new and better ways to do research, allowing us to apply tools traditionally reserved for physics and engineering to any discipline.

Conceptual apps can also boost teaching. New concepts can be visualised and manipulated, making understanding easier, and workflows can be gamified. Students can even build conceptual apps themselves, essentially learning by developing tools for others.

Types of conceptual model architectures

I use three types of models (there are more):

• Box models: These track the evolution of important system components and how they interact (often expressed using differential equations, but AI can help us build these without needing the maths). Examples include predator-prey models or simple climate models.
• Agent-based models: Here we simulate the behaviour of individual agents based on personal rules, then observe what happens when multiple agents interact. Examples include disease spread through populations or traffic behaviour on roads.
• Statistical models: These include regression models, machine learning models, or Monte Carlo simulations. They look for patterns in data without necessarily requiring a mechanistic understanding of how the system works.

Let's work through some examples

First, let's build a simple teaching app to help students understand wave interaction - superposition. For simple apps like this, we can build everything in a single HTML webpage using JavaScript (JS, a language commonly used in web pages). We don't need to know HTML or JS - we just need to clearly articulate what we want and carefully validate the product. Important tip: Don't try to build your app in one shot. It's an iterative process of refining and validating. Here's my dialogue with ChatGPT to create the app…

Next, let's try a conceptual model from an ecological research paper that examines predator-prey interactions and population dynamics over time. The paper is maths-heavy, so we'll first use AI to help understand the paper, extract and explain the relevant equations, then recreate the conceptual model as a web app that makes it far more intuitive to understand...

Now let’s try an agent based model. Here we’ll start with a random distribution of agents (simulating fish or birds). They each follow a set of rules like: look around at nearby neighbours, try to align motion with neighbours, move towards the centre of groups and avoid over crowding. We’ll then add some additional complexity - a predator! Again we gradually build up the complexity of the simulation leading to some amazing emergent behaviour …