# Computer models

By Marcus Wilson 18/08/2010

For the last couple of days, I’ve been engaged with a student of mine on a computer-modelling problem. Specifically, it’s an electromagnetic problem, working out how the electric field behaves between an array of electrodes. It’s a useful thing to do, because the outputs of the model will help guide future experimental work, and help us to interpret the results.

Computer models are well used in science, particularly in physics. I’ve used lots in my time as a researcher, and they fall into many different varieties  (my classification based on experience).

First there are the computer models that use well-known physics that is described by known equations. My student’s work is one of these. Electromagnetism is described by Maxwell’s equations. There is no dispute about this (unless if you get into quantum effects, etc). If your computer programme is solving Maxwell’s equations, it will work out for sure your electric fields (so long as you’ve specified your problem correctly). There’s not a great deal of scope for things going wrong, though that shouldn’t mean that you can just take your result for granted as correct.

Then there are the computer models that use well-known physics, but in problems that are really quite hard to specify. Fluid flow and movement of particles in fluids falls into this category. I’ve done a bit of this kind of modelling too – for example looking at the movement of airborne bacteria in a food-production building – with a view to identifying high-risk regions of the building where bacteria might accumulate. Here the equations are fairly well established (e.g. Navier Stokes equation for fluid flow) but some parts of them are uncertain. Exactly how does a bacterium respond to moving air? A tricky one – not least because they have a variety of sizes, shapes and textures, and this can influence how they move. There are various sub-models around of how to do this, but there is room for debate.

Moreover, in this kind of model you can have problems specifying the problem.  Do you have to model every tiny piece of machinery (geometry) in the room? Sometimes a small change in geometry can lead to a large change in the behaviour of fluid flow. And the reality is, on a production line, things change all the time, so the poor modeller never knows what his problem really is anyway.

But it can get worse for the modeller. There are those models (such as the models I work with for looking at the electrical currents in the brain) where the equations themselves aren’t robustly established. Here the modeller is, in a sense, having to make up his own equations, drawing from what data is known about the brain (and there is a lot). This kind of modelling has a huge uncertainty associated with it, as it is loaded with assumptions. Get your underlying equations wrong, and you might end up with predictions that are just utterly disconnected from reality. A modeller can ask the question ‘how close do my equations have to be to reality?’ The answer to that one is often ‘it depends on what you are going to use the model for’.  Sometimes we need really accurate physical models, that are based on pain-staking experiments, and sometimes we don’t. That will control how much effort goes into developing them.

Overall, then, ‘computer modelling’ is a many-faceted beast which hides a multitude of skills. I would say it is an area of science in itself