The Navier–Stokes partial differential equation was developed in the early 19th century by Claude-Louis Navier and George Stokes. It has proved its worth for modelling incompressible fluids in ...

Artificial intelligence (AI) is increasingly prevalent, integrated into phone apps, search engines and social media platforms ...

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When you think about how a neural network can beat a Go champion or otherwise accomplish tasks that would be impractical for most computers, it's tempting to attribute the success to math. Surely it's ...

Abstract: There has been significant recent work on solving PDEs using neural networks on infinite dimensional spaces. In this talk we consider two examples. First, we prove that transformers can ...

More than 70 years ago, researchers at the forefront of artificial intelligence research introduced neural networks as a revolutionary way to think about how the brain works. In the human brain, ...

The challenge of speeding up AI systems typically means adding more processing elements and pruning the algorithms, but those approaches aren’t the only path forward. Almost all commercial machine ...

In this article, sufficient conditions for fixed-time synchronization of time-delayed quaternion-valued neural networks (QVNNs) are derived. Firstly, QVNNs are decomposed into four real-valued systems ...

Here’s a challenge for the mathematically inclined among you. Solve the following differential equation for y: You have 30 seconds. Quick! No dallying. The answer, of course, is: If you were unable to ...

Over the last few years, we've heard a lot about neural networks, whether its Google's Deep Dream software creating horrifying digital dreamscapes or composites of pop songs written by a machine. But ...