New Scientist - 09.11.2019

14 | New Scientist | 9 November 2019

Maths

AI tackles thorny orbits

Artificial intelligence can solve hideously hard three-body puzzle

News

A NOTORIOUS maths problem

first posed by Isaac Newton has

become a lot easier thanks to

artificial intelligence. The

three-body problem – the

question of how three objects

orbit one another under their

own gravity – has baffled

physicists and mathematicians

for more than 300 years, but it

turns out a neural network can

find solutions remarkably quickly.

The problem is difficult because

three objects orbiting each other

form a chaotic system, meaning

a very precise understanding of

where the objects start is needed.

In a chaotic system, the “butterfly

effect” comes into play – even a

tiny starting error could result in

very different orbits. There is no

single equation to predict how the

objects will move and whether the

orbits will be stable over time.

Instead, mathematicians have

to meticulously test each scenario

iteratively, either by hand or using

computerised solvers, which can

be slow and energy intensive.

Philip Breen at the University of

Edinburgh, UK, and his colleagues

have come up with a new way to

solve it using a neural network,

which can be up to 100 million

times faster than the best

computerised solvers.

They trained their AI on a set

of 9900 three-body scenarios

generated by a state-of-the-art

solver called Brutus. The

researchers used 100 more

scenarios from Brutus to make

sure their system worked, and

then 5000 unsolved scenarios to

test it. It matched examples from

Brutus nearly exactly, showing

the neural network could provide

accurate and speedy solutions

to the three-body problem

(arxiv.org/abs/1910.07291).

The AI could improve our

understanding of how black holes

collide and form gravitational

waves, says Breen. Many of those

kind of complex systems can be

boiled down to a series of three-

body interactions that the neural

network can easily solve, he says.

“It’s astonishing to me to find

a totally new approach to this old

problem,” says Douglas Heggie at

the University of Edinburgh, who

wasn’t involved in the research.

One limitation is that the AI only

works for a finite length of time,

and if a particular three-body

problem hasn’t been studied

before, you don’t know in advance

how long it will take to figure out

what actually happens, he says.

The researchers have proposed

a solution to this: rather than

using the AI for the entire task,

just give it the hard bits – when the

three bodies make close passes.

Then give the problem back to

Brutus with that computational

bottleneck already solved.

This could provide any number

of solutions rapidly, even without a

long sought-after, neat three-body

equation, says Christopher Foley at

the University of Cambridge, who

also worked on the AI.

“It’s less about the elegance and

more about making progress and

advancing our understanding of

the building blocks of our physical

environment,” he says. “If I can get

the solutions, some would argue

that it doesn’t matter how I get

there, as long as they are right.” ❚

Leah Crane

JUPE/ALAMY STOCK PHOTO

DELIVERY drones could get a range

boost by taking the bus. Landing on

public transport means the flying

vehicles could travel four-and-a-

half times further, making them

more useful for carrying packages

over longer distances.

Drones are agile and fast, but

their measly battery life means they

can’t fly for long – considerably less

than an hour for most consumer

models. That is a problem if you

want to use them to deliver

packages across a large city.

To address this, Shushman

Choudhury and his colleagues at

Stanford University in California

devised a computer program

that plans deliveries by getting

drones to piggyback on buses

for a range boost. “We already

have this existing, generally decent

infrastructure for most good

cities and we’re just benefiting

from that,” says Choudhury.

The software has two tasks.

The first is to decide which drones

should deliver which packages and

the second is to set the route each

should take and when they should

hop on and off buses.

In simulations of San Francisco

and the Washington DC area, the

program typically took a few

seconds to do both tasks. Riding

buses boosted drone ranges by

up to 450 per cent. The largest

simulation involved 200 drones

delivering 5000 packages using a

bus network with 8000 stops on

it (arxiv.org/abs/1909.11840).

The research doesn’t deal with

practical considerations, such as

noise pollution, reliably landing

drones on buses and public

transport delays, says Choudhury.

“Exploiting predictable, existing

traffic flows is smart,” says Niels

Agatz at Erasmus University

Rotterdam in the Netherlands.

However, transit networks in many

areas wouldn’t be extensive enough

for this system to work, he says. ❚

If flying delivery

vehicles want

to extend their

reach, they

might have to

take the bus

OKTAY ORTAKCIOGLU/GETTY

Predicting how three

objects orbit each other

is a complex challenge

Edd Gent

Technology

Drones could ride on

public transport to

extend their reach