Day: October 30, 2020

https://www.wired.com/story/accessibility-video-games-ablegamers

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October 29, 2020 at 06:09AM

https://www.technologyreview.com/2020/10/30/1011435/ai-fourier-neural-network-cracks-navier-stokes-and-partial-differential-equations/

Unless you’re a physicist or an engineer, there really isn’t much reason for you to know about partial differential equations. I know. After years of poring over them in undergrad while studying mechanical engineering, I’ve never used them since in the real world.

But partial differential equations, or PDEs, are also kind of magical. They’re a category of math equations that are really good at describing change over space and time, and thus very handy for describing the physical phenomena in our universe. They can be used to model everything from planetary orbits to plate tectonics to the air turbulence that disturbs a flight, which in turn allows us to do practical things like predict seismic activity and design safe planes.

The catch is PDEs are notoriously hard to solve. And here, the meaning of “solve” is perhaps best illustrated by an example. Say you are trying to simulate air turbulence to test a new plane design. There is a known PDE called Navier-Stokes that is used to describe the motion of any fluid. “Solving” Navier-Stokes allows you to take a snapshot of the air’s motion (a.k.a. wind conditions) at any point in time and model how it will continue to move, or how it was moving before.

These calculations are highly complex and computationally intensive, which is why disciplines that use a lot of PDEs often rely on supercomputers to do the math. It’s also why the AI field has taken a special interest in these equations. If we could use deep learning to speed up the process of solving them, it could do a whole lot of good for scientific inquiry and engineering.

Now researchers at Caltech have introduced a new deep-learning technique for solving PDEs that is dramatically more accurate than deep-learning methods developed previously. It’s also much more generalizable, capable of solving entire families of PDEs—such as the Navier-Stokes equation for any type of fluid—without needing retraining. Finally, it is 1,000 times faster than traditional mathematical formulas, which would ease our reliance on supercomputers and increase our computational capacity to model even bigger problems. That’s right. Bring it on.

Hammer time

Before we dive into how the researchers did this, let’s first appreciate the results. In the gif below, you can see an impressive demonstration. The first column shows two snapshots of a fluid’s motion; the second shows how the fluid continued to move in real life; and the third shows how the neural network predicted the fluid would move. It basically looks identical to the second.

The paper has gotten a lot of buzz on Twitter, and even a shout-out from rapper MC Hammer. Yes, really.

Fourier Neural Operator for Parametric Partial Differential Equations #Hamm400aos https://t.co/ABYRwadcT7

— MC HAMMER (@MCHammer) October 22, 2020

Okay, back to how they did it.

When the function fits

The first thing to understand here is that neural networks are fundamentally function approximators. (Say what?) When they’re training on a data set of paired inputs and outputs, they’re actually calculating the function, or series of math operations, that will transpose one into the other. Think about building a cat detector. You’re training the neural network by feeding it lots of images of cats and things that are not cats (the inputs) and labeling each group with a 1 or 0, respectively (the outputs). The neural network then looks for the best function that can convert each image of a cat into a 1 and each image of everything else into a 0. That’s how it can look at a new image and tell you whether or not it’s a cat. It’s using the function it found to calculate its answer—and if its training was good, it’ll get it right most of the time.

Conveniently, this function approximation process is what we need to solve a PDE. We’re ultimately trying to find a function that best describes, say, the motion of air particles over physical space and time.

Now here’s the crux of the paper. Neural networks are usually trained to approximate functions between inputs and outputs defined in Euclidean space, your classic graph with x, y, and z axes. But this time, the researchers decided to define the inputs and outputs in Fourier space, which is a special type of graph for plotting wave frequencies. The intuition that they drew upon from work in other fields, says Anima Anandkumar, a Caltech professor who oversaw the research, is that something like the motion of air can actually be described as a combination of wave frequencies. The general direction of the wind at a macro level is like a low frequency with very long, lethargic waves, while the little eddies that form at the micro level are like high frequencies with very short and rapid ones.

Why does this matter? Because it’s far easier to approximate a Fourier function in Fourier space than to wrangle with PDEs in Euclidean space, which greatly simplifies the neural network’s job. Cue major accuracy and efficiency gains: in addition to its huge speed advantage over traditional methods, their technique achieves a 30% lower error rate when solving Navier-Stokes than previous deep-learning methods.

The whole thing is extremely clever, and also makes the method more generalizable. Previous deep-learning methods had to be trained separately for every type of fluid, whereas this one only needs to be trained once to handle all of them, as confirmed by the researchers’ experiments. Though they haven’t yet tried extending this to other examples, it should also be able to handle every earth composition when solving PDEs related to seismic activity, or every material type when solving PDEs related to thermal conductivity.

Super-simulation

Anandkumar and the lead author of the paper, Zongyi Li, a PhD student in her lab, didn’t do this research just for the theoretical fun of it. They want to bring AI to more scientific disciplines. It was through talking to various collaborators in climate science, seismology, and materials science that Anandkumar first decided to tackle the PDE challenge with her students. They’re now working to put their method into practice with other researchers at Caltech and the Lawrence Berkeley National Laboratory.

One research topic Anandkumar is particularly excited about: climate change. Navier-Stokes isn’t just good at modeling air turbulence; it’s also used to model weather patterns. “Having good, fine-grained weather predictions on a global scale is such a challenging problem,” she says, “and even on the biggest supercomputers, we can’t do it at a global scale today. So if we can use these methods to speed up the entire pipeline, that would be tremendously impactful.”

There are also many, many more applications, she adds. “In that sense, the sky’s the limit, since we have a general way to speed up all these applications.”

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October 30, 2020 at 04:06AM

https://www.popsci.com/story/technology/robotic-hawk-drone/

The LisHawk. (Enrico Ajanic, EPFL/)

Drones are common enough that it’s easy to picture their basic design variations. Fixed-wing drones look like miniature airplanes. Others use propellers—typically four of them—to pull themselves up into the sky, kind of like helicopters. A few drones combine those ideas by using props to get off the ground and then rotating position as they fly, so the sides of the drone can act like wings and provide lift. Amazon’s package delivery drone does this, and so does a big cargo carrier from Bell.

Now picture how a bird soars through the air, with all the ways that its wings and tail can move. Biological flight like that feels pretty different from the way those other gadgets whiz around. But engineers in Switzerland have unveiled a robotic bird that emulates the way a hawk flies. Their results are published today in the journal Science Robotics.

Their goal was to create a bird-like drone that’s capable of both cruising long distances at high speeds (like a fixed-wing plane) while remaining highly maneuverable. Their creation was inspired by a real bird called the northern goshawk.

“This bird hunts in forests, so it’s super agile,” says Enrico Ajanic, a doctoral student and roboticist at the Swiss Federal Institute of Technology in Lausanne. They wanted to be able to determine: “Why is this northern goshawk so agile? But at the same time, [it] can also be quite efficient—it’s also a migratory bird.” By creating a robot that can accomplish those varied flight goals, Ajanic says they can make a flying machine that’s the best of both worlds.

A northern goshawk. (Ondrej Prosicky / Deposit Photos/)

A drone that could do that, he argues, would be fantastic at cruising through an urban environment. “Big cities require a drone which can fly long distances, so you have to be very efficient,” he says. “But at the same time, you also need to avoid obstacles, because these cities are cluttered.”

The result is a creation made from carbon fiber and other materials that’s called LisHawk. At its largest, the wingspan is 3.4 feet across. In some ways, the robo-hawk is a lot like a real northern goshawk. Its tail, which can fan outwards, is about the same length—around .8 feet. And the outer portion of its wing (called the chord) is about a foot long, roughly the same as its biological counterpart. The wings can extend outwards or tuck inwards. The tail can fan out, and move up and down and side-to-side. That morphing ability gives the LisHawk the ability to widen the spectrum of the type of flying that it’s good at; a typical drone can’t morph like that.

Enrico Ajanic and the LisHawk. (EPFL/)

There are challenges, though, with trying to duplicate nature with artificial materials. The main one is that the robotic hawk doesn’t flap its wings—it uses a propeller. “The propeller is quite efficient, and from a mechanical engineer point of view, it’s a simple system,” he says. A drone that flapped its wing would be difficult to create, and picturing the opposite scenario is just funny: a bird with a propeller sticking out of its beak.

Overall, Ajanic is pleased with how well they accomplished the goal of creating a shape-shifting, bio-inspired aircraft. He says that tech like this could be used with other drones to “improve their flight performance.”

For fast cruise flight, he says the ideal configuration is with the wings and tail tucked inwards, a position in which the minimum speed is 17 miles per hour. For slower but more agile flight, the speed decreases to 9 mph, with the tail and wings extended. Changing wing shape in the air that way in aviation is a rarity: planes like the F-14, the fighter jets from the original Top Gun, did it.

The LisHawk follows in the feathery footsteps of a similar robo-bird called the PigeonBot, which debuted back in January. Unlike the PigeonBot, this robot-hawk doesn’t use actual feathers from a real bird—Ajanic’s team devised an artificial solution.

Realistically, we’re unlikely to see hawk- or pigeon-like robots zipping through cities anytime soon, if ever—fixed-wing drones and quadcopters remain the industry norm, and rural areas are safer settings for them, and a better flight area from a regulatory standpoint. But that doesn’t change the fact that a robotic creation that finds its inspiration in biology is, to put it simply, very cool.

via Popular Science – New Technology, Science News, The Future Now https://www.popsci.com

October 28, 2020 at 03:31PM