AI has Cracked a Key Mathematical Puzzle for Understanding our World: Partial Differential Equations (PDEs)

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve.

As reported by MIT Technology Review: 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.

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 is that something like the motion of air can actually be described as a combination of wave frequencies, says Anima Anandkumar, a Caltech professor who oversaw the research alongside her colleagues, professors Andrew Stuart and Kaushik Bhattacharya. 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

The professors and their PhD students 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 colleagues and 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.”

Harley-Davidson Officially Spins Off New Electric Bicycle Company (Serial 1 Cycle) with Stunning First Model

 

As reported by Electrek: This is it. Harley-Davidson has been teasing us with the prospect of their own in-house electric bicycles for over two years. And today the bar-and-shield motorcycle manufacturer has finally announced its new dedicated electric bicycle brand known as Serial 1 Cycle Company.

The brand’s name is an homage to the very first motorcycle ever built by Harley-Davidson in 1903, named “Serial Number One.”

Back then, motorcycles were essentially just bicycles with a small engine placed in front of the pedals.

And so it is fitting that the company’s first electric bicycle is a nod to that very first H-D motorcycle. Check out both in the video below to see how well they nailed the tribute.

As Serial 1 Cycle Company’s brand director Aaron Frank explained in a statement provided to Electrek:

When Harley-Davidson first put power to two wheels in 1903, it changed how the world moved, forever. Inspired by the entrepreneurial vision of Harley-Davidson’s founders, we hope to once again change how cyclists and the cycling-curious move around their world with a Serial 1 eBicycle.

The new e-bike brand from H-D actually began life as a skunkworks project in Harley-Davidson’s Product Development Center.

As the company explained, they began with “a small group of passionate motorcycle and bicycle enthusiasts working with a single focus to design and develop an eBicycle worthy of the Harley-Davidson name.”

Ultimately, they decided along with H-D to spin off the brand into a dedicated electric bicycle company that could focus purely on delivering a premium e-bike product and experience.

In addition to Aaron Frank, other major players from H-D’s in-house e-bike program that made the jump to Serial 1 Cycle Company include Jason Huntsman, president; Ben Lund, vice president; and Hannah Altenburg, lead brand marketing specialist.

Serial 1 will officially debut its first electric bicycle models for consumers in March 2021. For now, the company is showing off its first prototype model, which the brand describes as “a styling exercise, not necessarily intended for mass production.”

This prototype has been styled after that original 1903 Serial Number One motorcycle from Harley-Davidson. But interestingly, we can see that it shares the same frame as one of the original three electric bicycle prototypes that I spied last year at the 2019 EICMA Milan Motorcycle Show.

That means that while this specific styling likely won’t see showroom floors, the bike it is based on very well may be here this spring.

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As we’ve previously seen, the design includes a mid-drive motor, a belt drive system that looks very much like a Gates Carbon Drive setup (which would make sense, as Harley-Davidson’s other belt-driven motorcycles including the all-electric LiveWire also uses belt drive systems from Gates), frame-integrated headlights and taillights, thru-axle wheel hubs, what appear to be Tektro dual-piston hydraulic disc brakes on 203 mm rotors, a Brooks leather saddle, and beautifully wrapped leather handgrips.

I’m still left with many questions. Will these parts make it onto Serial 1 Cycle Company’s production models? What power level is the motor? What is the battery capacity? How much will the e-bikes cost?

For these questions and more, we still have no answers. But at least now we have a better idea of when to expect answers, and who we will be receiving them from. Stay tuned, because as soon as Serial 1 has more details for us, we’ll be back to share them with you.

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GM Sells Out First Year of Electric Hummer Production

 As reported by Reuters: General Motors Co said it has sold out the first year’s worth of its hulking GMC Hummer EV electric pickup truck after a splashy video reveal on Tuesday.

The least expensive Hummer EV, starting at $79,995, is scheduled to go into production in the spring of 2024, GM said.

The Hummer EV was designed and engineered in 18 months, GM officials said during a presentation on Wednesday. The brawny truck can “crab walk” sideways on rough terrain using its four-wheel steering system, and has a “Watts to Freedom” mode that accelerates the truck to 60 miles per hour (97 kph) in 3 seconds.

The Hummer EV is in part a response to Tesla Inc's Cybertruck, which has a very different but equally eye-grabbing design and a bevy of extreme performance features. The Cybertruck's starting price is $39,900, though a model with 500 miles of range starts at $69,900.

Tesla has begun building a factory in Austin, Texas to build the Cybertruck starting in late 2021.

The head of GM’s GMC division, Duncan Aldred, said about half the brand’s dealers have agreed to sell the Hummer EV lineup. GM is taking orders on its website, and Aldred said the company’s intent is to offer no-haggle prices. The online reservations and firm pricing are similar to the Tesla approach.

High-performance electric pickup trucks could be a crowded niche in the U.S. market, with eight companies promising to launch models by the end of 2021.

Ford Motor Co is promising an electric version of its F-series pickup, though Ford has said its electric pickup will be aimed at customers who want to use the truck for work. GM has Chevrolet versions of its electric truck in the works.

Startups Rivian, Nikola Corp and Lordstown Motors are among other companies that have electric pickups in development.

Nokia Wins NASA Contract to put a 4G Network on the Moon. Yes, Really.

 As reported by Mashable: Soon, astronauts on moon missions won't have any excuse for not answering their texts.

NASA has awarded Nokia of America $14.1 million to deploy a cellular network on the moon. The freaking moon. The grant is part of $370 million worth of contracts signed under NASA's "Tipping Point" selections, meant to advance research and development for space exploration. 

Nokia's plan is to build a 4G/LTE network, and eventually transition to 5G (just like the rest of us). It will be "the first LTE/4G communications system in space," according to NASA's announcement.

"The system could support lunar surface communications at greater distances, increased speeds, and provide more reliability than current standards," the announcement also reads.

To the moon! 🌕

We are excited to have been named by @NASA as a key partner to advance “Tipping Point” technologies for the moon, to help pave the way towards sustainable human presence on the lunar surface.

So, what technology can you expect to see? (1/6) pic.twitter.com/wDNwloyHdP

— Bell Labs (@BellLabs) October 15, 2020

Nokia's research arm, Bell Labs, provided more details in a Twitter thread. The company intends for the network to support wireless operation of lunar rovers and navigation, as well as streaming video.

The network is built to be compact and efficient, as well as "specially designed to withstand the extreme temperature, radiation and vacuum conditions of space."

According to UPI, NASA said in a live broadcast of the announcement that the network would extend to spacecraft, and help develop technology fit for the moon. While there aren't details about the timeline of this project becoming a reality, it's all in support of NASA's goal of having a lunar base on the moon by 2028, NASA Administrator Jim Bridenstine said in the broadcast. After all, how else would the astronauts be able to Instagram their moon walks?!

Former SpaceX Engineers Tout New Microreactor

Radiant’s microreactor is being developed for use in locations where other forms of power generation may not be practical, or even available. The company’s 1-MW-plus design makes it suitable to power small neighborhoods, remote commercial sites, and military bases. Courtesy: Radiant

As reported by Powermag.com: A California company is gathering funding for development of a portable nuclear microreactor, designed for use in areas where other forms of power generation are not practical.

Radiant, founded by former SpaceX engineers, on Sept. 22 said it has raised $1.2 million from angel investors as it designs what the company calls a “clean energy alternative to fossil fuels for military and commercial applications.” Radiant executives said the funding is a combination of cash and cost-share commitments to support development of its more than 1-MW microreactor.

“Radiant is developing the first power generation system that can go anywhere,” company co-founder Doug Bernauer told POWER in an interview on Sept. 21. Bernauer is a former SpaceX engineer who while there worked on developing energy sources for an eventual Mars colony. Bernauer said he thinks microreactors hold the most promise to supply power for settlements on Mars, and during his research he saw an immediate opportunity to utilize the technology on Earth, which led him to found Radiant along with two other SpaceX colleagues.

“A lot of the microreactors being developed are fixed location,” Bernauer said. “Nobody has a [commercial] system yet, so there’s kind of a race to be the first.”

Patents for Upgrades

Radiant on Tuesday announced it has received two provisional patents for its advances in portable nuclear reactors. One of the technical upgrades decreases the time and cost for refueling the reactor; the other enables more-efficient heat transport from the reactor core.

Battelle Energy Alliance, the contractor that manages operations at the Idaho National Laboratory, and Radiant recently signed a memorandum of understanding seeking collaboration for development and testing of the technology.

“The National Reactor Innovation Center (NRIC) looks forward to working with Radiant to test its portable nuclear microreactor at Idaho National Laboratory. It’s part of our mission to empower innovators, and deliver successful outcomes. This is an opportunity to innovate in ways that bring a cleaner energy future,” said Dr. Ashley Finan, Director of NRIC at INL, in a statement.

INL earlier this year chose an Oklo-designed microreactor as the first to receive high-assay, low-enriched uranium, or HALEU, nuclear fuel from the laboratory to support a first-of-its-kind demonstration of Oklo’s Aurora microreactor.

The use of microreactors to expand distributed power generation is part of a trend toward providing electricity to remote areas, as well as to military bases and commercial operations that need access to power but are far from the traditional grid.

“Cost optimization, a reduced power peaking factor … that’s all part of our design,” Bernauer said, noting the microreactor’s portability provides “freedom and optimization. One of the benefits of the portable system is that it’s so small, we can autonomously operate it.”

DOD a Primary Customer

Bernauer said Radiant is operating under the auspices of the U.S. Department of Energy during testing, and looking at the Department of Defense (DOD) as its primary market, as the DOD seeks a way to provide power to military bases in areas where access to electricity is not available.

The DOD, like other enterprises, also is looking at ways to reduce or eliminate the use of diesel and other fuels to provide power generation in remote areas.

“We target 72 hours from setting it down onsite, to full power production capacity,” Bernauer said of Radiant’s microreactor. He said the unit could be moved to a new location “after waiting just one week. It’s a self-contained system after you hit your site. The operating life is four to eight years, and that’s of course demand dependent. It can sync with other units and with the grid as well.”

Bernauer said portability of Radiant’s microreactor is key to its deployment, unlike small modular reactors that may be designed specifically to scale up. “We can do a modular configuration, but we’re more interested in keeping it portable,” he said.

“In some areas of the world, reliance on diesel fuel is untenable, and solar and wind power are either unavailable or impractical,” said Jess Gehin, PhD, Chief Scientist, Nuclear Science & Technology Directorate at INL. “Clean, safe nuclear microreactors are emerging as the best alternative for these environments.”

Eliminating Emissions, Fuel Transport Concerns

Diesel has long been the fuel of choice to run generators at remote sites. That brings both logistical challenges and environmental concerns, and the transport of fuel is a specific issue.

The U.S. Army in October 2018 published a report, titled “Mobile Nuclear Power Plants For Ground Operations,” that said about half of the 36,000 casualties in a nine-year period during the war in Iraq earlier this century came during land transport missions.

Microreactor developers have cited several important benefits, touting not only that the energy is clean, but that fuel can last four-plus years, refueling is not difficult, and the technology can work in areas with no sun or wind—even underground.

Radiant’s microreactor “is designed to power about 1,000 homes continuously for up to eight years,” according to the company. The microreactor is designed to fit in a shipping container—”single-high 8[feet] x 20 [feet], 9-and-a-half-feet high,” Bernauer said. It could be transported by air, ship, and road.

The company has said its microreactor is also safer than traditional nuclear power plant designs, leveraging particle fuel that withstands high temperatures and does not melt down. The use of helium coolant greatly reduces corrosion, boiling, and contamination risks associated with more traditional water coolant.

“We will be using a very well-established, extensively tested fuel, that’s already had hundreds of million of dollars of DOE testing,” Bernauer said. “We are taking what exists now and making it purely able to compete on cost.”

A company investor said the engineering and aerospace background of the Radiant team is an important aspect of his decision to support the effort.

“The innovative and ambitious team at Radiant has expertise from SpaceX as well as impressive nuclear industry credentials,” said investor Tom McInerney. “They have what it takes to bring new clean-energy solutions to market, and I’m excited to be part of their journey.”

“The nuclear industry can benefit greatly from aerospace technologies and software developments that have occurred over the past 20 years, and have not made their way into nuclear,” Bernauer said. He said that unlike some other microreactor developers, who may have academic backgrounds, his group is “engineers making an engineering product.”

Nikola Announces Deal with GM to Engineer and Produce its Electric/Hydrogen Pickup Truck

As reported by electrek: Nikola Motor (NKLA) announced a partnership with GM that will result in the latter engineering and manufacturing its upcoming Badger electric/hydrogen pickup truck, and maybe eventually its other vehicles.

Before Tesla unveiled the Cybertruck last year, Trevor Milton, founder of Nikola Motors, tweeted renders of a pickup truck that the company created and suggested that Tesla could use those for the Cybertruck since Nikola didn’t plan to build a pickup truck.

The comment appeared to be tongue-in-cheek since Nikola also accuses Tesla of stealing its design for its electric semi-truck.

However, after Tesla unveiled the Cybertruck and its polarizing design, Milton said that he planned for Nikola to build the vehicle, named Badger:

We were not planning on it if he built a good-looking truck. I was waiting to be first on the list, but I would never buy a Cybertruck. The Badger is what I was hoping Tesla would build design-wise. So if he won’t, I will. Now our interest is sky-high and why wouldn’t I?

In February, Nikola announced its plans for the Badger with a battery/fuel-cell hybrid powertrain enabling 600 miles of range, 0-60 mph acceleration in 2.9 seconds, and released a few renders.

A few months later, Nikola started taking $100 to $5,000 deposits for the pickup truck and launched a massive marketing campaign to try to accumulate reservations.

It included giving stock to the Diesel Brothers for promotion and a lot of online ads:

However, they don’t actually plan to bring this truck to market themselves, and now they are announcing their engineering and manufacturing partner: General Motors.

Nikola and GM have announced this morning a new wide-ranging partnership to manufacture and engineering the vehicle:

Nikola Corporation (NASDAQ: NKLA) and General Motors Co. (NYSE: GM) today announced a strategic partnership that begins with the Nikola Badger and carries cost reductions through Nikola’s programs, including: Nikola Badger, Nikola Tre, Nikola One, Nikola Two, and NZT. As part of the agreement, Nikola will utilize General Motors’ Ultium battery system and Hydrotec fuel cell technology, representing a key commercialization milestone for General Motors.

Here are the bulletpoints from the new deal between the two companies:

• General Motors to receive $2 billion equity stake in Nikola in exchange for certain in-kind contributions
• General Motors to engineer, validate, homologate, and build the Nikola Badger for both the battery electric vehicle and fuel cell electric vehicle variants as part of the in-kind services
• Nikola anticipates saving over $4 billion in battery and powertrain costs over 10 years and over $1 billion in engineering and validation costs
• General Motors expects to receive in excess of $4 billion of benefits between the equity value of the shares, contract manufacturing of the Badger, supply contracts for batteries and fuel cells, and EV credits retained over the life of the contract
• General Motors to be exclusive supplier of fuel cells globally (outside of Europe) to Nikola for Class 7/8 trucks, providing validation and scale in a multi-billion dollar total addressable market
• Badger is anticipated to enter production by year-end 2022

Nikola Founder and Executive Chairman Trevor Milton commented:

Nikola is one of the most innovative companies in the world. General Motors is one of the top engineering and manufacturing companies in the world. You couldn’t dream of a better partnership than this. By joining together, we get access to their validated parts for all of our programs, General Motors’ Ultium battery technology and a multibillion-dollar fuel cell program ready for production. Nikola immediately gets decades of supplier and manufacturing knowledge, validated and tested production-ready EV propulsion, world-class engineering and investor confidence. Most importantly, General Motors has a vested interest to see Nikola succeed. We made three promises to our stakeholders and have now fulfilled two out of three promises ahead of schedule. What an exciting announcement.

General Motors Chairman and CEO Mary Barra added:

This strategic partnership with Nikola, an industry leading disrupter, continues the broader deployment of General Motors’ all-new Ultium battery and Hydrotec fuel cell systems. We are growing our presence in multiple high-volume EV segments while building scale to lower battery and fuel cell costs and increase profitability. In addition, applying General Motors’ electrified technology solutions to the heavy-duty class of commercial vehicles is another important step in fulfilling our vision of a zero-emissions future.

The agreement apparently also involves Nikola using GM’s fuel cell technology in its trucks, which have been marketed as the company’s main products for which they had apparently developed their own hydrogen technology.

GM added:

“This strategic collaboration continues the broader deployment of GM’s all-new modular platform and Ultium battery and Hydrotec fuel cell systems. Nikola using GM’s Ultium platform and Hydrotec fuel-cell technology, represents a key commercialization milestone for us. In addition, applying GM’s electrified technology solutions to the heavy-duty class of commercial vehicles is another important step in fulfilling our vision of a zero emissions future. Fuel cells will become increasingly important to the semi-truck market because they are more efficient than gas or diesel. GM sees additional growth opportunities in multiple transportation, stationary and mobile-power end markets. Longer-term, there are substantial financial benefits to GM. This includes ongoing profitability from GM serving as the exclusive fuel-cell supplier in all markets except Europe.  GM will also receive accretive revenue and earnings from Badger and fuel cell manufacturing and becomes the largest non-management shareholder in Nikola.”

Electrek’s Take

Well, this seems to have confirmed what I suspected for a long time: Nikola has essentially nothing.

I understand going with a manufacturing partner, but this announcement makes it sounds like GM is doing everything here.

Nikola is even using their battery and hydrogen technology – both things that Milton has been claiming they had been working for years to perfect at Nikola.

I remember Milton tweeting pictures of their battery packs claiming that they were the best ever made. You remember last year when Milton claimed that Nikola achieved a “major battery breakthrough” and now they are just going to use GM’s Ultimum batteries? Even the fuel cells will be from GM.

Years ago, they hired Bosch to help devlop their own fuel cell technology and now they are just going to use GM’s.

This seems ridiculous on the surface.

The press release makes it sound like Nikola is basically a branding company now:

“Nikola will be responsible for the sales and marketing for the Badger and will retain the Nikola Badger brand. “

But if the deal also extends to Nikola’s other vehicles, including its commercial trucks, what is happening with the technology that they claim to be developing for the past 5 years? Where is any stockholder value?

As for GM, they get roughly 11% of Nikola in return. That’s a horrible way to spend $2B if you ask me.

I think Barra is really trying to be relevant in electrification, but this is not the way to do it in my opinion. GM is going to lose important resources to that deal that they could have spent on building and marketing their own electric vehicles. What do they get in return? GM says:

GM also gets ongoing profitability from serving as the exclusive fuel-cell supplier in all markets except Europe. GM will also receive accretive revenue and earnings from Badger and fuel cell manufacturing, as well as becoming the largest non-management shareholder in Nikola.

But what does that all mean? They now own 11% of a controversial and polarizing brand they could have built themselves for much less money.