AI Exoplanet

Wow! AI reveals unsuspected math underlying search for exoplanets

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

Astronomers say AI can reveal some­thing deep­er like unsus­pect­ed con­nec­tions hid­den in the com­plex math­e­mat­ics aris­ing from gen­er­al par­tic­u­lar, how that the­o­ry is applied to find­ing new plan­ets around oth­er stars.

What is an AI algorithm?

AI algorithm

An AI algo­rithm is a set of math­e­mat­i­cal instruc­tions based upon some pat­tern or prob­lem; and that the per­son cre­at­ing the algo­rithm wants to solve. To do this, it uses known data sets (e.g., many dif­fer­ent train­ing sets) to solve sim­i­lar prob­lems by search­ing for pat­terns in the data. When giv­en a new prob­lem, it search­es through its train­ing data sets; and it uti­lizes what­ev­er solu­tion it finds to com­pare its new unknown results with.

It then uses this com­par­i­son to alter its approach in an attempt to improve its solu­tion for all future com­par­isons that use sim­i­lar approach­es. In prac­tice, this means it will adjust itself based upon his­tor­i­cal per­for­mance of the approach; it also makes future com­par­isons more accu­rate than past ones.

New finding: AI reveals unsuspected math underlying search for exoplanets

In reveal­ing unsus­pect­ed math under­ly­ing search for exo­plan­ets, AI can offer insights into obser­va­tions of mas­sive stars and their rem­nants, includ­ing black holes and neu­tron stars. More­over, AI can be used to devel­op more effi­cient ways for dis­cov­er­ing new exo­plan­ets; and pos­si­bly, we can use it for dis­cov­er­ing life out­side our solar system.

In a paper pub­lished this week in the jour­nal Nature Astron­o­my, the researchers have described 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. It’s a process called grav­i­ta­tion­al microlens­ing. It revealed that the decades-old the­o­ries now used to explain these obser­va­tions are woe­ful­ly incomplete.

Albert Ein­stein him­self in 1936 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. Researchers say this is sim­i­lar to the way a hand lens can focus and inten­si­fy light from the sun.

Major degeneracies and their unification

Degen­era­cies are the col­lec­tive phe­nom­e­non aris­ing from the mas­sive stars in the cen­ter of the image. They cause light rays to split into many images that are seen as a ring.

An event relat­ed to grav­i­ta­tion­al microlens­ing was observed in 1987. At that time, two mas­sive stars col­lid­ed and caused their respec­tive Ein­stein rings to merge into a sin­gle dis­tort­ed ring. These events are called ‘sym­bi­ot­ic’ grav­i­ta­tion­al microlens­ing events. It’s because, researchers say, they unite (or “sym­bol­ize”) sev­er­al degen­er­ate objects into a sin­gle one.

These degen­era­cies have no the­o­ry under­ly­ing them, so explain­ing them was thought impos­si­ble until now. AI has revealed hid­den struc­ture in this com­plex math. And that may show how it works for both gen­er­al rel­a­tiv­i­ty and for quan­tum mechanics.

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.

Also read: How can we make sure that AI does what it is supposed to do?

But the AI ​​algo­rithm 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 .

Now, pro­fes­sion­al astronomers say that a machine learn­ing infer­ence algo­rithm, which was 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.

Authors of the paper claim that this is kind of a mile­stone in AI and machine learn­ing. They say Keming’s machine learn­ing algo­rithm uncov­ered that degen­er­a­cy that had been missed by experts in the field toil­ing with data for decades. And this was sug­ges­tive of how research is going to go in the future when it is aid­ed by machine learn­ing, which is real­ly exciting.

Discovery of exoplanets to-date and future plans

To-date, more than 5,000 exo­plan­ets, or extra­so­lar plan­ets, have been dis­cov­ered around stars in the Milky Way. How­ev­er, few of them have actu­al­ly been seen through a tele­scope and they are too dim. Most of them 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. And only a few more than 100 have been dis­cov­ered by a third tech­nique, microlens­ing.

NASA’s Nan­cy Grace Roman Space Tele­scope is sched­uled to launch by 2027. It has the main goal to dis­cov­er thou­sands more exo­plan­ets via microlens­ing. NASA states that the tech­nique has an advan­tage over the Doppler and tran­sit tech­niques. It’s 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.

Astronomers’ previous attempts to develop an AI algorithm

The team of 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. They say that 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.

But one prob­lem astronomers encounter 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 it 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. While 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.

View of astronomers on the issue

Scott Gau­di, co-author of the paper, a pro­fes­sor of astron­o­my at The Ohio State Uni­ver­si­ty and one of the pio­neers of using grav­i­ta­tion­al microlens­ing to dis­cov­er exo­plan­ets, said that astronomers have gen­er­al­ly dealt with these degen­era­cies in sim­plis­tic and arti­fi­cial­ly dis­tinct ways to date. If the dis­tant starlight pass­es close to the star, we could inter­pret the obser­va­tions either as a wide or a close orbit for the plan­et — an ambi­gu­i­ty astronomers can often resolve with oth­er data.

Accord­ing to Gau­di, a sec­ond type of degen­er­a­cy occurs when the back­ground starlight pass­es close to the plan­et. In this case, the two dif­fer­ent solu­tions for the plan­e­tary orbit are gen­er­al­ly only slight­ly different.

The researchers said that these two sim­pli­fi­ca­tions of two-body grav­i­ta­tion­al microlens­ing are usu­al­ly suf­fi­cient to deter­mine the true mass­es and orbital distances.

What’s in the new paper based on general relativity?


Zhang and Gau­di have sub­mit­ted a new paper that rig­or­ous­ly describes the new math­e­mat­ics based on gen­er­al rel­a­tiv­i­ty. And it 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. It’s because there are more degen­er­ate solu­tions to describe the obser­va­tions. How­ev­er, the the­o­ry also clear­ly demon­strates that observ­ing the same microlens­ing event from two per­spec­tives; it’s from Earth and from the orbit of the Roman Space Tele­scope, for exam­ple. It will make it eas­i­er to set­tle on the cor­rect orbits and mass­es. Gau­di also clar­i­fied that that is what astronomers cur­rent­ly have planned to do.

Like­wise, Bloom said that 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.

So, for now AI researchers, astronomers and cos­mol­o­gists are con­fi­dent that machine learn­ing is use­ful in under­stand­ing microlens­ing. They say that the new method has led to the dis­cov­ery of a new math­e­mat­i­cal prop­er­ty of gen­er­al rel­a­tiv­i­ty. It could be use­ful for find­ing exo­plan­ets with NASA’s Roman Space Telescope.

The team also says they may use their method to solve oth­er issues in astro­physics. They have already found an inter­est­ing appli­ca­tion in a sep­a­rate field of stel­lar physics. There, researchers are try­ing to deter­mine the aver­age tem­per­a­ture and den­si­ty of stars more accu­rate­ly than they can now. These quan­ti­ties are impor­tant for under­stand­ing how stars evolve over cos­mic time and how they explode as supernovas.

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