AI Reveals Unsuspected Math Underlying The Search For Exoplanets (2024)

Artificial intelligence (AI) algorithms trained on real astronomical observations now outperform astronomers in sifting through massive amounts of data.

AI helps them to find new exploding stars, identify new types of galaxies and detect the mergers of massive stars, accelerating the rate of new discovery in the world’s oldest science.

But AI, also called machine learning, can reveal something deeper, University of California, Berkeley, astronomers found: unsuspected connections hidden in the complex mathematics arising from general relativity — in particular, how that theory is applied to finding new planets around other stars.

In a paper appearing this week in the journal Nature Astronomy, the researchers describe how an AI algorithm developed to more quickly detect exoplanets when such planetary systems pass in front of a background star and briefly brighten it — a process called gravitational microlensing — revealed that the decades-old theories now used to explain these observations are woefully incomplete.

In 1936, Albert Einstein himself used his new theory of general relativity to show how the light from a distant star can be bent by the gravity of a foreground star, not only brightening it as seen from Earth, but often splitting it into several points of light or distorting it into a ring, now called an Einstein ring. This is similar to the way a hand lens can focus and intensify light from the sun.

But when the foreground object is a star with a planet, the brightening over time — the light curve — is more complicated. What’s more, there are often multiple planetary orbits that can explain a given light curve equally well — so called degeneracies. That’s where humans simplified the math and missed the bigger picture.

The AI algorithm, however, pointed to a mathematical way to unify the two major kinds of degeneracy in interpreting what telescopes detect during microlensing, showing that the two “theories” are really special cases of a broader theory that, the researchers admit, is likely still incomplete.

“A machine learning inference algorithm we previously developed led us to discover something new and fundamental about the equations that govern the general relativistic effect of light- bending by two massive bodies,” Joshua Bloom wrote in a blog post last year when he uploaded the paper to a preprint server, arXiv. Bloom is a UC Berkeley professor of astronomy and chair of the department.

He compared the discovery by UC Berkeley graduate student Keming Zhang to connections that Google’s AI team, DeepMind, recently made between two different areas of mathematics. Taken together, these examples show that AI systems can reveal fundamental associations that humans miss.

“I argue that they constitute one of the first, if not the first time that AI has been used to directly yield new theoretical insight in math and astronomy,” Bloom said. “Just as Steve Jobs suggested computers could be the bicycles of the mind, we’ve been seeking an AI framework to serve as an intellectual rocket ship for scientists.”

“This is kind of a milestone in AI and machine learning,” emphasized co-author Scott Gaudi, a professor of astronomy at The Ohio State University and one of the pioneers of using gravitational microlensing to discover exoplanets. “Keming’s machine learning algorithm uncovered this degeneracy that had been missed by experts in the field toiling with data for decades. This is suggestive of how research is going to go in the future when it is aided by machine learning, which is really exciting.”

Discovering exoplanets with microlensing

More than 5,000 exoplanets, or extrasolar planets, have been discovered around stars in the Milky Way, though few have actually been seen through a telescope — they are too dim. Most have been detected because they create a Doppler wobble in the motions of their host stars or because they slightly dim the light from the host star when they cross in front of it — transits that were the focus of NASA’s Kepler mission. Little more than 100 have been discovered by a third technique, microlensing.

One of the main goals of NASA’s Nancy Grace Roman Space Telescope, scheduled to launch by 2027, is to discover thousands more exoplanets via microlensing. The technique has an advantage over the Doppler and transit techniques in that it can detect lower-mass planets, including those the size of Earth, that are far from their stars, at a distance equivalent to that of Jupiter or Saturn in our solar system.

Bloom, Zhang and their colleagues set out two years ago to develop an AI algorithm to analyze microlensing data faster to determine the stellar and planetary masses of these planetary systems and the distances the planets are orbiting from their stars. Such an algorithm would speed analysis of the likely hundreds of thousands of events the Roman telescope will detect in order to find the 1% or fewer that are caused by exoplanetary systems.

One problem astronomers encounter, however, is that the observed signal can be ambiguous. When a lone foreground star passes in front of a background star, the brightness of the background stars rises smoothly to a peak and then drops symmetrically to its original brightness. It’s easy to understand mathematically and observationally.

But if the foreground star has a planet, the planet creates a separate brightness peak within the peak caused by the star. When trying to reconstruct the orbital configuration of the exoplanet that produced the signal, general relativity often allows two or more so-called degenerate solutions, all of which can explain the observations.

To date, astronomers have generally dealt with these degeneracies in simplistic and artificially distinct ways, Gaudi said. If the distant starlight passes close to the star, the observations could be interpreted either as a wide or a close orbit for the planet — an ambiguity astronomers can often resolve with other data. A second type of degeneracy occurs when the background starlight passes close to the planet. In this case, however, the two different solutions for the planetary orbit are generally only slightly different.

According to Gaudi, these two simplifications of two-body gravitational microlensing are usually sufficient to determine the true masses and orbital distances. In fact, in a paper published last year, Zhang, Bloom, Gaudi and two other UC Berkeley co-authors, astronomy professor Jessica Lu and graduate student Casey Lam, described a new AI algorithm that does not rely on knowledge of these interpretations at all. The algorithm greatly accelerates analysis of microlensing observations, providing results in milliseconds, rather than days, and drastically reducing the computer crunching.

Zhang then tested the new AI algorithm on microlensing light curves from hundreds of possible orbital configurations of star and exoplanet and noticed something unusual: There were other ambiguities that the two interpretations did not account for. He concluded that the commonly used interpretations of microlensing were, in fact, just special cases of a broader theory that explains the full variety of ambiguities in microlensing events.

“The two previous theories of degeneracy deal with cases where the background star appears to pass close to the foreground star or the foreground planet,” Zhang said. “The AI algorithm showed us hundreds of examples from not only these two cases, but also situations where the star doesn’t pass close to either the star or planet and cannot be explained by either previous theory. That was key to us proposing the new unifying theory.”

Gaudi was skeptical, at first, but came around after Zhang produced many examples where the previous two theories did not fit observations and the new theory did. Zhang actually looked at the data from two dozen previous papers that reported the discovery of exoplanets through microlensing and found that, in all cases, the new theory fit the data better than the previous theories.

“People were seeing these microlensing events, which actually were exhibiting this new degeneracy but just didn’t realize it,” Gaudi said. “It was really just the machine learning looking at thousands of events where it became impossible to miss.”

Zhang and Gaudi have submitted a new paper that rigorously describes the new mathematics based on general relativity and explores the theory in microlensing situations where more than one exoplanet orbits a star.

The new theory technically makes interpretation of microlensing observations more ambiguous, since there are more degenerate solutions to describe the observations. But the theory also demonstrates clearly that observing the same microlensing event from two perspectives — from Earth and from the orbit of the Roman Space Telescope, for example — will make it easier to settle on the correct orbits and masses. That is what astronomers currently plan to do, Gaudi said.

“The AI suggested a way to look at the lens equation in a new light and uncover something really deep about the mathematics of it,” said Bloom. “AI is sort of emerging as not just this kind of blunt tool that’s in our toolbox, but as something that’s actually quite clever. Alongside an expert like Keming, the two were able to do something pretty fundamental.”

A ubiquitous unifying degeneracy in two-body microlensing systems


AI Reveals Unsuspected Math Underlying The Search For Exoplanets (2024)


AI Reveals Unsuspected Math Underlying The Search For Exoplanets? ›

In a paper appearing this week in the journal Nature Astronomy, the researchers describe how an AI algorithm developed to more quickly detect exoplanets when such planetary systems pass in front of a background star and briefly brighten it — a process called gravitational microlensing — revealed that the decades-old ...

What is the biggest problem with finding exoplanets? ›

The major problem astronomers face in trying to directly image exoplanets is that the stars they orbit are millions of times brighter than their planets. Any light reflected off of the planet or heat radiation from the planet itself is drowned out by the massive amounts of radiation coming from its host star.

What is the math behind AI? ›

Linear algebra is the field of applied mathematics that AI experts can't live without. You will never become a good AI specialist without mastering this field. Linear algebra helps in generating new ideas, that's why it is a must-learn thing for AI scientists and researchers.

Why is it difficult for scientist to find exoplanets? ›

Not only are they really far away, but planets are really dim compared to their parent stars so they're really hard to see. Indirect observations (such as the Doppler technique, transits, and eclipses) are much more commonly used when searching for exoplanets.

What method is used to detect exoplanets? ›

Most early exoplanet discoveries were made using this so-called radial velocity method. The first detections using transit photometry were made in 1999. 'Transiting' exoplanets are detected as they pass in front of – transit – their host star, causing a dip in the starlight as seen from the observer's viewpoint.

Will humans ever live on another planet? ›

No other planet in our solar system currently has the conditions to support life as we know it on Earth. Even if scientists discover another habitable planet outside of our solar system, humans do not yet have the technology to visit it.

Why can't we go to exoplanets? ›

Will a person ever go to an exoplanet? Not anytime soon, given the enormous distances between the stars and the time it would take to travel between them with our current technology. Perhaps one day a robot will visit an exoplanet like the rovers on Mars. But that day too is still very far in the future.

What is the AI that proves math? ›

Symbolab is a powerful online math solver that provides step-by-step solutions for a wide range of mathematical problems. It goes beyond simply giving answers, offering detailed explanations and multiple solution methods, making it ideal for building problem-solving skills.

Is AI heavy on math? ›

You don't need to be really into math to see why this stuff is potentially very exciting. Math is really, really hard for AI models. Complex math, such as geometry, requires sophisticated reasoning skills, and many AI researchers believe that the ability to crack it could herald more powerful and intelligent systems.

What AI can solve math? ›

Julius is the most accurate AI tool for solving math equations — in a recent test, Julius was over 31% more accurate than GPT-4o, while also beating out Mathway and Symbolab. From geometry and trigonometry to algebra and calculus, Julius is the ultimate AI for mathematics.

Why can't we take pictures of exoplanets? ›

In order to capture an exoplanet image through the solar gravitational lens, a telescope would have to be placed at least 14 times farther away from the sun than Pluto, past the edge of our solar system, and further than humans have ever sent a spacecraft.

Can we actually see exoplanets? ›

In some cases, we can actually see exoplanets next to their host stars and track their orbits.

What are the easiest exoplanets to detect? ›

Hot Jupiters are the easiest exoplanets to study, because they block more of their star's light than smaller planets do, and you can see the change in brightness of their star very frequently.

What is the biggest problem to detect exoplanets? ›

But exoplanets, which orbit distant stars, are more difficult to directly observe, because they are much farther away and close to their extremely bright stars. Instead, astronomers often detect exoplanets indirectly, through the effect they have on their host star.

Why is Pluto no more a planet? ›

According to the IAU, Pluto is technically a “dwarf planet,” because it has not “cleared its neighboring region of other objects.” This means that Pluto still has lots of asteroids and other space rocks along its flight path, rather than having absorbed them over time, like the larger planets have done.

What type of planet is most likely to be habitable? ›

Many rocky planets have been detected in Earth's size-range: a point in favor of possible life. Based on what we've observed in our own solar system, large, gaseous worlds like Jupiter seem far less likely to offer habitable conditions.

What are the two major challenges of directly detecting exoplanets? ›

Challenges in Detecting Exoplanets
  • Brightness of Stars: Stars are much brighter than the planets that orbit them. ...
  • Small Size and Mass: Many exoplanets, especially those similar in size to Earth, exert only a tiny gravitational effect on their host stars, making them harder to detect through the radial velocity method.
Oct 18, 2023

How hard is it to find an exoplanet? ›

Because exoplanets exist outside our solar system, orbiting other stars, they can be hard to capture with a telescope. In fact, even Neptune, in our own solar system, is a blurry blue ball when viewed form Earth's orbit. Because of this, it can be hard to find exoplanets.

Why is it difficult to observe an exoplanet directly through a telescope? ›

Planets can be billions of times dimmer than their host stars, so they're usually lost in the glare. But by blocking the star's light using a coronagraph or starshade, astronomers can image fainter planets in orbit.

What are two problems astronomers face in observing such planets directly? ›

Answer : First, since stars are too bright for direct observation, astronomers have difficulties seeing such planets clearly. Secondly, because these planets are too brilliant to picture, it is challenging to document them. These two issues are related to each other and hinder direct observation of these planets.

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