Last week, I introduced Emmy Noether, an extraordinary figure in the fields of mathematics and physics. To understand Noether’s reasoning, we need to talk a bit more about the fundamentals of ...

Artificial intelligence (AI) systems, particularly artificial neural networks, have proved to be highly promising tools for uncovering patterns in large amounts of data that would otherwise be ...

Maxwell’s equations of electromagnetism and the Euler equation top a poll to find the greatest equations of all time. Robert P Crease discusses the results of his reader survey First among equals – ...

Physics-Informed Neural Networks (PINNs) augment traditional neural architectures by embedding the governing equations of physical systems directly into the loss function. Instead of solely minimising ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...