Predicting the weather is hard. It requires a lot of physics, a lot of maths, a whole lot of data, and a huge amount of computing power. That's why researchers are now investigating whether artificial intelligence can help with the task.

Leading researchers from industry and universities came together to discuss the latest advances in this area at the *Deep learning for environmental problems workshop* organised by the Mathematics for Deep Learning (Maths4DL) research programme. Members of the Maths4DL team helped us take a peak into this rapidly evolving field and here is what we learnt.

Can artificial intelligence help predict the weather? — With better algorithms, more computing power, and more data available, things are looking optimistic.

Catching clouds with artificial intelligence — Clouds are one phenomenon that traditional forecasting models struggle with. Here's a look at how artificial intelligence could help.

Mathematical snapshots: Teo Deveney — Teo Deveney works for the Maths4DL project. Here's a look at the kind of things he is interested in and the perks that come with the job of an early career reseaercher.

### Background briefing

#### What is deep learning?

Maths in a minute: Machine learning — A quick look at the type of artificial intelligence people are proposing to use in weather forecasting. And yes, it can involve cats.

Maths in a minute: Deep learning — It's machine learning with lots and lots of layers, making it extremely powerful.

#### How do we forecast the weather?

Maths in a minute: Numerical weather prediction — Here is how weather forecasts are currently made, using physics, maths, and lots of computing power.

Maths in a minute: The Navier-Stokes equations — Central to traditional weather forecasting are the Navier-Stokes equations, which unfortunately are incredibly difficult to solve.

Maths in a minute: Mathematical chaos and the butterfly effect — The butterfly effect is another factor that makes weather forecasting hard. Here's a quick introduction.

Maths in a minute: Ensemble forecasting — Ensemble forecasting is one way to mitigate the butterfly effect. Instead of just producing one forecast, produce many!

#### Other important ideas

Maths in a minute: Thermodynamics — Tea gone cold? Don't worry, you can cheer yourself up with the theory of thermodynamics, the theory of heat and heat flow.

Maths in a minute: Fluid dynamics and the Euler equations — How does water, or indeed any fluid, move? The Euler equations let us look beneath the surface and mark the beginning of modern fluid dynamics.

Maths in a minute: Percentage error — How good is your estimate?

*We produced this collection of content as part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme, which brings together researchers from the universities of Bath and Cambridge, and University College London. Maths4DL aims to combine theory, modelling, data and computation to unlock the next generation of deep learning. You can see more content produced with Maths4DL here.*