Written by Jennifer Chu, MIT News Office
Pushing a shovel through snow, planting an umbrella on the beach, wading through a ball pit, and driving over gravel all have one thing in common: They all are exercises in intrusion, with an intruding object exerting some force to move through a soft and granular material.
Predicting what it takes to push through sand, gravel, or other soft media can help engineers drive a rover over Martian soil, anchor a ship in rough seas, and walk a robot through sand and mud. But modeling the forces involved in such processes is a huge computational challenge that often takes days to weeks to solve.
Now, engineers at MIT and Georgia Tech have found a faster and simpler way to model intrusion through any soft, flowable material. Their new method quickly maps the forces it would take to push, wiggle, and drill an object through granular material in real-time. The method can apply to objects and grains of any size and shape, and does not require complex computational tools as other methods do.
“We now have a formula that can be very useful in settings where you have to check through lots of options as fast as possible,” says Ken Kamrin, professor of mechanical engineering at MIT.
“This is especially useful for applications such as real-time path-planning for vehicles traveling through vast deserts and other off-road terrains, that cannot wait for existing slower simulation methods to decide their path,” adds Shashank Agarwal SM ’19, PhD ’22.
Kamrin and Agarwal detail their new method in a study appearing this week in the journal Proceedings of the National Academy of Sciences. The study also includes Daniel I. Goldman, professor of physics at Georgia Tech.
A fluid connection
In order to know how much to push on an object to move it through sand, one could go grain by grain, using discrete element modeling, or DEM — an approach that systematically calculates each individual grain’s motion in response to a given force. DEM is precise but slow, and it can take weeks to fully solve a practical problem involving just a handful of sand. As a faster alternative, scientists can develop continuum models, which simulate granular behavior in generalized chunks, or grain groupings. This more simplified approach can still generate a detailed picture of how grains flow, in a way that can shave a weeks-long problem down to days or even hours.
“We wanted to see if we could do even better than that and cut that process down to seconds,” Agarwal says.
The team looked to previous work by Goldman. In 2014, he was studying how animals and robots move through dry, granular material such as sand and soil. In looking for ways to quantitatively describe their movements, he found he could do so with a quick relationship that was originally meant to describe fluid swimmers.
The formulation, Resistive Force Theory (RFT), works by considering an object’s surface as a collection of small plates. (Imagine representing a sphere as a soccer ball.) As an object moves through a fluid, each plate experiences a force, and RFT claims that the force on each plate depends only on its local orientation and movement. The equation takes all this into account, along with the fluid’s individual characteristics, to ultimately describe how the object as a whole moves through a fluid.
Surprisingly, Goldman found this simple approach was also accurate when applied to granular intrusion. Specifically, it predicted the forces lizards and snakes exert to slither through sand, as well as how small, legged robots walk over soil. The question, Kamrin says, was why?
“It was this weird mystery why this theory, which was originally derived for moving through viscous fluid, would even work at all in granular media, which has completely different flow behavior,” he says.
Kamrin took a closer look at the math and found a connection between RFT and a continuum model he had derived to describe granular flow. In other words, the physics checked out, and RFT could indeed be an accurate way to predict granular flow, in a simpler and faster way than conventional models. But there was one big limitation: The approach was mainly workable for two-dimensional problems.
To model intrusion using RFT, one needs to know what will happen if one moves a plate every which way possible — a task that is manageable in two dimensions, but not in three. The team then needed some shortcut to simplify 3D’s complexity.
In their new study, the researchers adapted RFT to 3D by adding an extra ingredient to the equation. That ingredient is a plate’s twist angle, measuring how plate orientation changes as the entire object is rotated. When they incorporated this extra angle, in addition to a plate’s tilt and direction of motion, the team had enough information to define the force acting on the plate as it moves through a material in 3D. Importantly, by exploiting the connection to continuum modeling, the resulting 3D-RFT is generalizable, and can be easily recalibrated to apply to many dry granular media on Earth, and even on other planetary bodies.
The researchers demonstrated the new method using a variety of three-dimensional objects, from simple cylinders and cubes to more complex bunny- and monkey-shaped geometries. They first tiled the objects, representing them each as a collection of hundreds to thousands of tiny plates. Then they applied the tweaked RFT formula to each individual plate and calculated the forces that would be needed over time to drill each plate, and ultimately the entire object, down through a bed of sand.
“For more wacky objects, like the bunny, you can imagine having to consistently shift your loads to keep drilling it straight down,” Kamrin says. “And our method can even predict those little wiggles, and the distribution of force all around the bunny, in less than a minute.”
The new approach provides a fast and accurate way to model granular intrusion, which can be applied to a host of practical problems, from driving a rover through Martian soil, to characterizing the movement of animals through sand, and even predicting what it would take to uproot a tree.
“Can I predict how hard it is to uproot natural plants? You might want to know, is this storm going to knock over this tree?” Kamrin says. “Here is a way to get an answer fast.”
This research was supported, in part, by the Army Research Office, the U.S. Army DEVCOM Ground Vehicle Systems Center, and NASA.
Study: Superconductivity switches on and off in “magic-angle” graphene
A quick electric pulse completely flips the material’s electronic properties, opening a route to ultrafast, brain-inspired, superconducting electronics
Written by Jennifer Chu, MIT News Office
With some careful twisting and stacking, MIT physicists have revealed a new and exotic property in “magic-angle” graphene: superconductivity that can be turned on and off with an electric pulse, much like a light switch.
The discovery could lead to ultrafast, energy-efficient superconducting transistors for neuromorphic devices — electronics designed to operate in a way similar to the rapid on/off firing of neurons in the human brain.
Magic-angle graphene refers to a very particular stacking of graphene — an atom-thin material made from carbon atoms that are linked in a hexagonal pattern resembling chicken wire. When one sheet of graphene is stacked atop a second sheet at a precise “magic” angle, the twisted structure creates a slightly offset “moiré” pattern, or superlattice, that is able to support a host of surprising electronic behaviors.
In 2018, Pablo Jarillo-Herrero and his group at MIT were the first to demonstrate magic-angle twisted bilayer graphene. They showed that the new bilayer structure could behave as an insulator, much like wood, when they applied a certain continuous electric field. When they upped the field, the insulator suddenly morphed into a superconductor, allowing electrons to flow, friction-free.
That discovery gave rise to “twistronics,” a field that explores how certain electronic properties emerge from the twisting and layering of two-dimensional materials. Researchers including Jarillo-Herrero have continued to reveal surprising properties in magic-angle graphene, including various ways to switch the material between different electronic states. So far, such “switches” have acted more like dimmers, in that researchers must continuously apply an electric or magnetic field to turn on superconductivity, and keep it on.
Now Jarillo-Herrero and his team have shown that superconductivity in magic-angle graphene can be switched on, and kept on, with just a short pulse rather than a continuous electric field. The key, they found was a combination of twisting and stacking.
In a paper appearing today in Nature Nanotechnology, the team reports that, by stacking magic-angle graphene between two offset layers of boron nitride — a two-dimensional insulating material — the unique alignment of the sandwich structure enabled the researchers to turn graphene’s superconductivity on and off with a short electric pulse.
“For the vast majority of materials, if you remove the electric field, zzzzip, the electric state is gone,” says Jarillo-Herrero, who is the Cecil and Ida Green Professor of Physics at MIT. “This is the first time that a superconducting material has been made that can be electrically switched on and off, abruptly. This could pave the way for a new generation of twisted, graphene-based superconducting electronics.”
His MIT co-authors are lead author Dahlia Klein, Li-Qiao Xia, and David MacNeill, along with Kenji Watanabe and Takashi Taniguchi of the National Institute for Materials Science in Japan.
Flipping the switch
In 2019, a team at Stanford University discovered that magic-angle graphene could be coerced into a ferromagnetic state. Ferromagnets are materials that retain their magnetic properties, even in the absence of an externally applied magnetic field.
The researchers found that magic-angle graphene could exhibit ferromagnetic properties in a way that could be tuned on and off. This happened when the graphene sheets were layered between two sheets of boron nitride such that the crystal structure of the graphene was aligned to one of the boron nitride layers. The arrangement resembled a cheese sandwich in which the top slice of bread and the cheese orientations are aligned, but the bottom slice of bread is rotated at a random angle with respect to the top slice. The result intrigued the MIT group.
“We were trying to get a stronger magnet by aligning both slices,” Jarillo-Herrero says. “Instead, we found something completely different.”
In their current study, the team fabricated a sandwich of carefully angled and stacked materials. The “cheese” of the sandwich consisted of magic-angle graphene — two graphene sheets, the top rotated slightly at the “magic” angle of 1.1 degrees with respect to the bottom sheet. Above this structure, they placed a layer of boron nitride, exactly aligned with the top graphene sheet. Finally, they placed a second layer of boron nitride below the entire structure and offset it by 30 degrees with respect to the top layer of boron nitride.
The team then measured the electrical resistance of the graphene layers as they applied a gate voltage. They found, as others have, that the twisted bilayer graphene switched electronic states, changing between insulating, conducting, and superconducting states at certain known voltages.
What the group did not expect was that each electronic state persisted rather than immediately disappearing once the voltage was removed — a property known as bistability. They found that, at a particular voltage, the graphene layers turned into a superconductor, and remained superconducting, even as the researchers removed this voltage.
This bistable effect suggests that superconductivity can be turned on and off with short electric pulses rather than a continuous electric field, similar to flicking a light switch. It isn’t clear what enables this switchable superconductivity, though the researchers suspect it has something to do with the special alignment of the twisted graphene to both boron nitride layers, which enables a ferroelectric-like response of the system. (Ferroelectric materials display bistability in their electric properties.)
“By paying attention to the stacking, you could add another tuning knob to the growing complexity of magic-angle, superconducting devices,” Klein says.
For now, the team sees the new superconducting switch as another tool researchers can consider as they develop materials for faster, smaller, more energy-efficient electronics.
“People are trying to build electronic devices that do calculations in a way that’s inspired by the brain,” Jarillo-Herrero says. “In the brain, we have neurons that, beyond a certain threshold, they fire. Similarly, we now have found a way for magic-angle graphene to switch superconductivity abruptly, beyond a certain threshold. This is a key property in realizing neuromorphic computing.”
This research was supported in part by the Air Force Office of Scientific Research, the Army Research Office, and the Gordon and Betty Moore Foundation.
When should data scientists try a new technique?
A new measure can help scientists decide which estimation method to use when modeling a particular data problem
Written by Adam Zewe, MIT News Office
If a scientist wanted to forecast ocean currents to understand how pollution travels after an oil spill, she could use a common approach that looks at currents traveling between 10 and 200 kilometers. Or, she could choose a newer model that also includes shorter currents. This might be more accurate, but it could also require learning new software or running new computational experiments. How to know if it will be worth the time, cost, and effort to use the new method?
A new approach developed by MIT researchers could help data scientists answer this question, whether they are looking at statistics on ocean currents, violent crime, children’s reading ability, or any number of other types of datasets.
The team created a new measure, known as the “c-value,” that helps users choose between techniques based on the chance that a new method is more accurate for a specific dataset. This measure answers the question “is it likely that the new method is more accurate for this data than the common approach?”
Traditionally, statisticians compare methods by averaging a method’s accuracy across all possible datasets. But just because a new method is better for all datasets on average doesn’t mean it will actually provide a better estimate using one particular dataset. Averages are not application-specific.
So, researchers from MIT and elsewhere created the c-value, which is a dataset-specific tool. A high c-value means it is unlikely a new method will be less accurate than the original method on a specific data problem.
In their proof-of-concept paper, the researchers describe and evaluate the c-value using real-world data analysis problems: modeling ocean currents, estimating violent crime in neighborhoods, and approximating student reading ability at schools. They show how the c-value could help statisticians and data analysts achieve more accurate results by indicating when to use alternative estimation methods they otherwise might have ignored.
“What we are trying to do with this particular work is come up with something that is data specific. The classical notion of risk is really natural for someone developing a new method. That person wants their method to work well for all of their users on average. But a user of a method wants something that will work on their individual problem. We’ve shown that the c-value is a very practical proof-of-concept in that direction,” says senior author Tamara Broderick, an associate professor in the Department of Electrical Engineering and Computer Science (EECS) and a member of the Laboratory for Information and Decision Systems and the Institute for Data, Systems, and Society.
She’s joined on the paper by Brian Trippe PhD ’22, a former graduate student in Broderick’s group who is now a postdoc at Columbia University; and Sameer Deshpande ’13, a former postdoc in Broderick’s group who is now an assistant professor at the University of Wisconsin at Madison. An accepted version of the paper is posted online in the Journal of the American Statistical Association.
The c-value is designed to help with data problems in which researchers seek to estimate an unknown parameter using a dataset, such as estimating average student reading ability from a dataset of assessment results and student survey responses. A researcher has two estimation methods and must decide which to use for this particular problem.
The better estimation method is the one that results in less “loss,” which means the estimate will be closer to the ground truth. Conder again the forecasting of ocean currents: Perhaps being off by a few meters per hour isn’t so bad, but being off by many kilometers per hour makes the estimate useless. The ground truth is unknown, though; the scientist is trying to estimate it. Therefore, one can never actually compute the loss of an estimate for their specific data. That’s what makes comparing estimates challenging. The c-value helps a scientist navigate this challenge.
The c-value equation uses a specific dataset to compute the estimate with each method, and then once more to compute the c-value between the methods. If the c-value is large, it is unlikely that the alternative method is going to be worse and yield less accurate estimates than the original method.
“In our case, we are assuming that you conservatively want to stay with the default estimator, and you only want to go to the new estimator if you feel very confident about it. With a high c-value, it’s likely that the new estimate is more accurate. If you get a low c-value, you can’t say anything conclusive. You might have actually done better, but you just don’t know,” Broderick explains.
Probing the theory
The researchers put that theory to the test by evaluating three real-world data analysis problems.
For one, they used the c-value to help determine which approach is best for modeling ocean currents, a problem Trippe has been tackling. Accurate models are important for predicting the dispersion of contaminants, like pollution from an oil spill. The team found that estimating ocean currents using multiple scales, one larger and one smaller, likely yields higher accuracy than using only larger scale measurements.
“Oceans researchers are studying this, and the c-value can provide some statistical ‘oomph’ to support modeling the smaller scale,” Broderick says.
In another example, the researchers sought to predict violent crime in census tracts in Philadelphia, an application Deshpande has been studying. Using the c-value, they found that one could get better estimates about violent crime rates by incorporating information about census-tract-level nonviolent crime into the analysis. They also used the c-value to show that additionally leveraging violent crime data from neighboring census tracts in the analysis isn’t likely to provide further accuracy improvements.
“That doesn’t mean there isn’t an improvement, that just means that we don’t feel confident saying that you will get it,” she says.
Now that they have proven the c-value in theory and shown how it could be used to tackle real-world data problems, the researchers want to expand the measure to more types of data and a wider set of model classes.
The ultimate goal is to create a measure that is general enough for many more data analysis problems, and while there is still a lot of work to do to realize that objective, Broderick says this is an important and exciting first step in the right direction.
This research was supported, in part, by an Advanced Research Projects Agency-Energy grant, a National Science Foundation CAREER Award, the Office of Naval Research, and the Wisconsin Alumni Research Foundation.
Computers that power self-driving cars could be a huge driver of global carbon emissions
Study shows that if autonomous vehicles are widely adopted, hardware efficiency will need to advance rapidly to keep computing-related emissions in check
Written by Adam Zewe, MIT News Office
In the future, the energy needed to run the powerful computers on board a global fleet of autonomous vehicles could generate as many greenhouse gas emissions as all the data centers in the world today.
That is one key finding of a new study from MIT researchers that explored the potential energy consumption and related carbon emissions if autonomous vehicles are widely adopted.
The data centers that house the physical computing infrastructure used for running applications are widely known for their large carbon footprint: They currently account for about 0.3 percent of global greenhouse gas emissions, or about as much carbon as the country of Argentina produces annually, according to the International Energy Agency. Realizing that less attention has been paid to the potential footprint of autonomous vehicles, the MIT researchers built a statistical model to study the problem. They determined that 1 billion autonomous vehicles, each driving for one hour per day with a computer consuming 840 watts, would consume enough energy to generate about the same amount of emissions as data centers currently do.
The researchers also found that in over 90 percent of modeled scenarios, to keep autonomous vehicle emissions from zooming past current data center emissions, each vehicle must use less than 1.2 kilowatts of power for computing, which would require more efficient hardware. In one scenario — where 95 percent of the global fleet of vehicles is autonomous in 2050, computational workloads double every three years, and the world continues to decarbonize at the current rate — they found that hardware efficiency would need to double faster than every 1.1 years to keep emissions under those levels.
“If we just keep the business-as-usual trends in decarbonization and the current rate of hardware efficiency improvements, it doesn’t seem like it is going to be enough to constrain the emissions from computing onboard autonomous vehicles. This has the potential to become an enormous problem. But if we get ahead of it, we could design more efficient autonomous vehicles that have a smaller carbon footprint from the start,” says first author Soumya Sudhakar, a graduate student in aeronautics and astronautics.
Sudhakar wrote the paper with her co-advisors Vivienne Sze, associate professor in the Department of Electrical Engineering and Computer Science (EECS) and a member of the Research Laboratory of Electronics (RLE); and Sertac Karaman, associate professor of aeronautics and astronautics and director of the Laboratory for Information and Decision Systems (LIDS). The research appears in the January-February issue of IEEE Micro.
The researchers built a framework to explore the operational emissions from computers on board a global fleet of electric vehicles that are fully autonomous, meaning they don’t require a back-up human driver.
The model is a function of the number of vehicles in the global fleet, the power of each computer on each vehicle, the hours driven by each vehicle, and the carbon intensity of the electricity powering each computer.
“On its own, that looks like a deceptively simple equation. But each of those variables contains a lot of uncertainty because we are considering an emerging application that is not here yet,” Sudhakar says.
For instance, some research suggests that the amount of time driven in autonomous vehicles might increase because people can multitask while driving and the young and the elderly could drive more. But other research suggests that time spent driving might decrease because algorithms could find optimal routes that get people to their destinations faster.
In addition to considering these uncertainties, the researchers also needed to model advanced computing hardware and software that doesn’t exist yet.
To accomplish that, they modeled the workload of a popular algorithm for autonomous vehicles, known as a multitask deep neural network because it can perform many tasks at once. They explored how much energy this deep neural network would consume if it were processing many high-resolution inputs from many cameras with high frame rates, simultaneously.
When they used the probabilistic model to explore different scenarios, Sudhakar was surprised by how quickly the algorithms’ workload added up.
For example, if an autonomous vehicle has 10 deep neural networks processing images from 10 cameras, and that vehicle drives for one hour a day, it will make 21.6 million inferences each day. One billion vehicles would make 21.6 quadrillion inferences. To put that into perspective, all of Facebook’s data centers worldwide make a few trillion inferences each day (1 quadrillion is 1,000 trillion).
“After seeing the results, this makes a lot of sense, but it is not something that is on a lot of people’s radar. These vehicles could actually be using a ton of computer power. They have a 360-degree view of the world, so while we have two eyes, they may have 20 eyes, looking all over the place and trying to understand all the things that are happening at the same time,” Karaman says.
Autonomous vehicles would be used for moving goods, as well as people, so there could be a massive amount of computing power distributed along global supply chains, he says. And their model only considers computing — it doesn’t take into account the energy consumed by vehicle sensors or the emissions generated during manufacturing.
Keeping emissions in check
To keep emissions from spiraling out of control, the researchers found that each autonomous vehicle needs to consume less than 1.2 kilowatts of energy for computing. For that to be possible, computing hardware must become more efficient at a significantly faster pace, doubling in efficiency about every 1.1 years.
One way to boost that efficiency could be to use more specialized hardware, which is designed to run specific driving algorithms. Because researchers know the navigation and perception tasks required for autonomous driving, it could be easier to design specialized hardware for those tasks, Sudhakar says. But vehicles tend to have 10- or 20-year lifespans, so one challenge in developing specialized hardware would be to “future-proof” it so it can run new algorithms.
In the future, researchers could also make the algorithms more efficient, so they would need less computing power. However, this is also challenging because trading off some accuracy for more efficiency could hamper vehicle safety.
Now that they have demonstrated this framework, the researchers want to continue exploring hardware efficiency and algorithm improvements. In addition, they say their model can be enhanced by characterizing embodied carbon from autonomous vehicles — the carbon emissions generated when a car is manufactured — and emissions from a vehicle’s sensors.
While there are still many scenarios to explore, the researchers hope that this work sheds light on a potential problem people may not have considered.
“We are hoping that people will think of emissions and carbon efficiency as important metrics to consider in their designs. The energy consumption of an autonomous vehicle is really critical, not just for extending the battery life, but also for sustainability,” says Sze.
This research was funded, in part, by the National Science Foundation and the MIT-Accenture Fellowship.
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