Machine learning algorithm points to problems in mathematical theory for interpreting microlenses.
Artificial intelligence (AI) systems trained on real astronomical observations now surpass astronomers in filtering through massive amounts of data to find new exploding stars, identify new types of galaxies, and detect the mergers of massive stars, boosting the rate of new discovery in the world’s oldest science.
But a type of AI called machine learning can reveal something deeper,
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
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
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
Zhang then tested the new AI algorithm on microlensing light curves from hundreds of possible orbital configurations of star and exoplanet and discovered 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.”
Reference: “A ubiquitous unifying degeneracy in two-body microlensing systems” by Keming Zhang, B. Scott Gaudi and Joshua S. Bloom, 23 May 2022, Nature Astronomy.
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