Inverse problems are addressed in numerous areas of physics, with the analytic continuation of the imaginary Green’s function into the real frequency domain being an especially significant example. Be that as it may, the analytic continuation problem is poorly characterized, and presently, no analytic change for unraveling it is known.

As a part of the semester project, an EPFL student named Romain Fournier applied machine learning to the problem of analytic continuation. He has shown that deep learning can be used to analytically connect digital simulations and experimental results more quickly and reliably than conventional methods.

Fournier said, “The main challenge in the translation process is that there’s an unlimited number of mathematical solutions to a given problem. It’s a little like, instead of being asked what 2+2 equals, you were asked what math operation answers 4. Among the many possible answers, we’re only interested in the one that makes sense in the physical world. So we’re talking about an ill-defined problem, which is a common situation in science.”

This new approach involves teaching a neural network to run the translation process by feeding it examples of data simulations that could be obtained experimentally.

Fournier said, “It’s very easy to go from experimental data to imaginary-time data, and so we were able to quickly build up a big database that we could use to train our model.”

Unlike conventional methods, this new method provides more reliable answers than traditional methods and does so more quickly.

Oleg Yazyev, an assistant professor, said, “The fact that an ordinary semester project can turn into a scientific advancement worthy of being published in a leading journal is a real source of motivation for our students. That doesn’t happen every day, of course. But when it does, it provides our up-and-coming researchers with a real career boost. On top of that, more experienced researchers like me can use these kinds of projects to test some of our crazier ideas.”

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Prosthetic limbs are getting better every year, but the strength and precision they gain doesn’t always translate to easier or more effective use, as amputees have only a basic level of control over them. One promising avenue being investigated by Swiss researchers is having an AI take over where manual control leaves off.

To visualize the problem, imagine a person with their arm amputated above the elbow controlling a smart prosthetic limb. With sensors placed on their remaining muscles and other signals, they may fairly easily be able to lift their arm and direct it to a position where they can grab an object on a table.

But what happens next? The many muscles and tendons that would have controlled the fingers are gone, and with them the ability to sense exactly how the user wants to flex or extend their artificial digits. If all the user can do is signal a generic “grip” or “release,” that loses a huge amount of what a hand is actually good for.

Here’s where researchers from École polytechnique fédérale de Lausanne (EPFL)  take over. Being limited to telling the hand to grip or release isn’t a problem if the hand knows what to do next — sort of like how our natural hands “automatically” find the best grip for an object without our needing to think about it. Robotics researchers have been working on automatic detection of grip methods for a long time, and it’s a perfect match for this situation.

Prosthesis users train a machine learning model by having it observe their muscle signals while attempting various motions and grips as best they can without the actual hand to do it with. With that basic information the robotic hand knows what type of grasp it should be attempting, and by monitoring and maximizing the area of contact with the target object, the hand improvises the best grip for it in real time. It also provides drop resistance, being able to adjust its grip in less than half a second should it start to slip.

The result is that the object is grasped strongly but gently for as long as the user continues gripping it with, essentially, their will. When they’re done with the object, having taken a sip of coffee or moved a piece of fruit from a bowl to a plate, they “release” the object and the system senses this change in their muscles’ signals and does the same.

It’s reminiscent of another approach, by students in Microsoft’s Imagine Cup, in which the arm is equipped with a camera in the palm that gives it feedback on the object and how it ought to grip it.

It’s all still very experimental, and done with a third-party robotic arm and not particularly optimized software. But this “shared control” technique is promising and could very well be foundational to the next generation of smart prostheses. The team’s paper is published in the journal Nature Machine Intelligence.

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