Rational neural network advances partial differentiation equation learning

In the physical world, math is the language of the physical world, and Alex Townsend sees mathematical patterns everywhere: in weather, in the way sound waves move, and in the spots where zebra fish grow.

The associate professor of mathematics in the College of Arts and Sciences said that sinceNewton wrote down calculus, they have been creating differential equations to model physical phenomena.

If you already know the physics of the system, this method will work. What about learning about the physics of physical systems?

Calculating partial differential equation learning involves collecting data from natural systems and using trained computer neural networks to try to derive underlying mathematical equations. In a new paper, the University of Oxford and Christopher Earls, professor of civil and environmental engineering in the College of Engineering, collaborated to advance PDE learning with a novel neural network.

Deep learning will enhance scientific exploration of natural phenomena such as weather systems, climate change, fluid dynamics, genetics and more.

Neural networks are inspired by the simple animal brain mechanism. In the context of computerized neural networks, activated cells collect inputs from other cells. The weights are between the neurons and send signals to the next one.

You can come up with very complicated maps that take inputs to outputs, just like the brain might take a signal from the eye and turn it into an idea.

According to Townsend, mathematicians have been working with Green's functions for nearly 200 years. He uses a Green's function to quickly solve a differential equation. Earls wanted to use Green's functions to understand a differential equation rather than solve it.

The researchers created a rational neural network that can capture extreme physical behavior of Green's functions. Rational neural networks were introduced in a separate study.

There are different types of cells in the brain. Townsend said that they are not all the same.

Rational neural networks can be more flexible than standard neural networks.

One of the important mathematical ideas here is that we can change the activation function to capture what we expect from the Green. It doesn't know what it means. Humans can now look at the Green's function because we have learned something.

There is a different physics for each system. He is excited about the research because it will put his expertise in Green's functions to work in a modern way.

More information: Nicolas Boullé et al, Data-driven discovery of Green's functions with human-understandable deep learning, Scientific Reports (2022). DOI: 10.1038/s41598-022-08745-5 Journal information: Scientific Reports Citation: Rational neural network advances partial differentiation equation learning (2022, April 5) retrieved 6 April 2022 from https://phys.org/news/2022-04-rational-neural-network-advances-partial.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.