Filling in the gaps:
Imputing exoplanet properties with machine learning

Elizabeth Tasker

Nicholas Guttenberg

Matthieu Laneuville

Tasker, Laneuville & Guttenberg, AJ 2020.
ArXiv: 1911.11035

SaturnEarthMercury

UranusMarsVenus

Jupiter

Neptune4000+ exoplanets
Statistics

Understanding
formation… and habitability

BUT….

2016
2017
1999
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2000

2014
2015

3000

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https://exoplanetarchive.ipac.caltech.edu

Transit
Radial velocity
Other

96% exoplanets found byeither the radial velocity
or transit technique
Give different planetproperties.

Star “wobbles”due tothe planet’s gravity.

Radial velocity
orDoppler wobble

Periodic shift inwavelength+

Gives a minimum mass for theplanet+m sin (i) = mass

m sin (i) << massTransit

Dip in light as planetcrosses our line ofsight to the star

Gives a radius for theplanet

RadiusaTransit required
TransitNo transit

R*pT =a0.47%
Earth analogue

Low probability far
from star.

Mass+

Detection by 2
methods required(often impossible)

Planet characterisation needs mass & radius.

GasRocky?

HybridIceProxima Centauri b(Nearest star)(Radial velocity)(min. mass)

Period = 11.2 days

Red dwarf(small, dim star)

Habitable Zone

Earth could support liquid water(assumes our surface pressure & atmosphere)Proxima Centauri b

0.0485 au

0.04 au

0.08 au

Proxima Centauri b :M sin(i = 90∘) = M

M sin(i < 90∘) < M

Planet Neptune-like(not habitable!)

empirical rocky
planet limit(Rogers, 2015, ApJ 801)

(Transit detection)

Kepler-186f
Period = 130 days

Habitable Zone

(Transit detection)

Kepler-186f
Period = 130 days

Degenerate compositionsgives x10 spread in mass

Lopez-Morales et al, ApJ 152:204, 2016

4000+ exoplanet discoveries

Many potential
planet properties… sparse table

https://exoplanetarchive.ipac.caltech.edu

When telescopes cannot help…
What can we do?

Can we impute missing values, basedon known properties?

But…

BA

Multi-dimensional dataneural network:

Incomplete planet formation theories

planet property generator

NEURAL NETWORKType of machine learning, inspired by the brain.
Given examples, a neural network finds trends between variables.

Excellent for multi-dimensional data

Red

Four wheels

Two floors London
Carry people

Carry many people
Fixed route
Involves a fee

Red
Fixed route

W2

Carry people
INPUT

FEATURES

W1 = W2 = W3

W1

W3

WEIGHTSACTIVATIONRESULT

Red
Fixed route

W2

Carry people
INPUT

FEATURES

W1

W3

WEIGHTSACTIVATIONOPTIMISER

W1 = W2 = W3

RESULT

Red
Fixed route

W2

Carry people
INPUT

FEATURES

W1W3

WEIGHTSACTIVATIONOPTIMISER

W1 < W2 < W3

RESULT

You can choose the number of features (nodes)

*+#,%)&'(()!"##$%."#"&
You can choose the number of features (nodes)
But the network selects what each node
represents and its weight

*+#,%)&'(()!"##$%ORBITALPERIOD."#"&EQUILIBRIUM
TEMPERATURE

Can a neural network find the relation between
orbital period and equilibrium temperature?

Not very difficult…

Short period
planets are hot

Long period
planets are coldlog Tlog P*+#,%)&'(()!"##$%PERIOD."#"&

EQ. TEMP.

blue = data
Eq. T [K]orange = network prediction
But how do we train the network ifwe don’t know the right answer?
Period [days]

Feed the network
a set of properties
for many planets
Network finds astatisticalrepresentation of
those properties

PLANETNEURAL NETWORK6 parameter
density space

PLANETNEURAL NETWORKNetwork can create
a “new” planets
whose properties fit
the statisticaldistribution.

NEURAL NETWORK#ALTPLANET

… or generate justone missing property.

NEURAL NETWORKDETAILS(feel free to sleep for the next few slides)

This will all end in tears.
I just know it.

Small print

Require complete property set for a group ofplanets for network training:radius, mass, period, equilibrium temperature,
number of planets in system, stellar mass

Modified
Create statistical distribution by representing
boltzmann each planet’s properties as an energy.
machine

TRAINING

Network adjusts
features / weights
to find a
distribution thatfits the training set.

+"-//"(,.)0
1&,(,1(,2,Small print

Require complete property set for a group ofplanets for network training:radius, mass, period, equilibrium temperature,
number of planets in system, stellar mass

Modified
Create statistical distribution by representing
boltzmann each planet’s properties as an energy.
machine

TRAINING

Network adjusts
features / weights
to find a
distribution thatfits the training set.

+"-//"(,.)01&,(,1(,2,Small print

Require complete property set for a group ofplanets for network training:radius, mass, period, equilibrium temperature,
number of planets in system, stellar mass

Modified
Create statistical distribution by representing
boltzmann each planet’s properties as an energy.
machine

TRAINING

Network adjusts
features / weights
to find a
distribution thatfits the training set.

+"-//"(,.)01&,(,1(,2,Small print

Require complete property set for a group ofplanets for network training:radius, mass, period, equilibrium temperature,
number of planets in system, stellar mass

Modified
Create statistical distribution by representing
boltzmann each planet’s properties as an energy.
machine
Monte
Carlo

Energy of trained system

New planet (or planet property) accepted
based on the energy difference from adding
the planet to the distribution:

Generated planet

Energy of system +generated planet

RejectSmall print

Require complete property set for a group ofplanets for network training:radius, mass, period, equilibrium temperature,
number of planets in system, stellar mass

Modified
Create statistical distribution by representing
boltzmann each planet’s properties as an energy.
machineMonteCarlo

Energy of trained system

New planet (or planet property) accepted
based on the energy difference from adding
the planet to the distribution:

Generated planet

Energy of system +generated planet

AcceptSmall print

Require complete property set for a group ofplanets for network training:radius, mass, period, equilibrium temperature,
number of planets in system, stellar massModified
Create statistical distribution by representing
boltzmann each planet’s properties as an energy.
machineMonteCarlo

New planet (or planet property) accepted
based on the energy difference from adding
the planet to the distribution:

Property
distribution

Create multiple (1000) values per planet
and take the mean.

Assume you found atransiting planet(Radius, no minimum mass)

Give the (trained) neural network
5 measured properties

Outputs a distributionof possible mass values+Assume you found a RV planet(minimum mass, no radius)sin(i)iCombine withpossible masses
based on m sin(i)(Assuming random i)

Give the (trained)neural network 4
measured properties

Outputs distributionof possible mass &radius values

RESULTS(wake up!)

Incredible… it’s even worse
than I thought it would be.

sin(i)++i

Test results! RV planets(pretend we only know
m sin(i) and look at network
generated masses)(secretly do know themass of these planets)sin(i)+
Test results! RV planets+isin(i)++i

Test results! RV planets
What can we compare this to?

Switch network distribution
for the distribution of known
planet massesNMsin(i)++i

Test results! RV planets
What can we compare this to?
What if we didn’t use thenetwork, and just comparedm sin(i) to the distribution ofknown planet masses?
NMsin(i)++i

Test results! RV planets

ϵ = ln(Mobs /Mimputed)
Network error = 0.39
Obs. error = 0.41

On average, network finds aplanet mass ~1.5 x true masssin(i)++i

Test results! RV planets
Where do we do well?
WASP-68b has a very lowerror
What kind of planet isthis?

Best Worlds

Inflated hot JupiterM = 1.1MJup
P = 5 days

R = 1.32RJupsin(i)++i

Test results! RV planets
How about the badplanets?
K2-66 b has a high error

What’s its problem?!

Bad WorldsDanger!
If your m sin(i) value lies in the low probability tail of the network
distribution, it may indicate a high error.

Bad Worlds

Hot sub-Neptune

M = 21.3M⊕
P = 5 days

R = 2.5R⊕“Photoevaporation dessert”

Curious worlds

superEarthhotJupiterSuper-size hot JupiterM = 2.5MJup

R = 1.1RJup

P = 8 days
2 statistically consistent options

sin(i)+

Proxima Centauri-b+
i

~ 1.3

sin(i)++i

Proxima Centauri-b
M sin(i) ≃ 1.3

M ≃ 1.6+0.46−0.36
R ≃ 1.3+1.2−0.65

Test results! Transit planets(pretend we only know
radius and look at network
generated masses)

Test results! Transit planets
How does this comparewith other methods?

Test results! Transit planets

MR Forecaster(Chen & Kipping, 2017)

Test results! Transit planets

MR Forecaster(Chen & Kipping, 2017)

Weiss & Marcy, 2014
(Empirical < 4RP < 1.5R)⇢P = 2.43 + 3.39

1.5  RP /R < 4✓

MP= 2.69
MRPR✓◆

RPRgcm 3◆0.93

Test results! Transit planets

Errors:Network = 0.98
Forecaster = 1.6
WM2014 (< 4 RE) = 1.02

On average, network finds aplanet mass ~2.7 x true mass
But why more scatter?

Test results! Transit planets
Higher error than RV as….
1. No minimum mass guide
2. Stellar degeneracy in radiusTest results! Transit planets
How about the bad planets?

Kepler-145 b has a high errorWhy?!

Bad Worlds

Unusually large rocky planet

M = 37.1M⊕ R = 2.65R⊕
ρ = 11.0 g/cm3

Network thinks thisplanet should havea thick atmosphere(and lower mass)

Test results! Transit planets
How about the REALLY badplanets?
Kepler-415b
2MASS J2140+16A b

Really Bad Worlds

M = 120 M⊕
R = 1.2 R⊕
ρ = 373.1 g/cm3!!!

Really Bad Worlds+102.1
M = 120−87.4 M⊕
Network estimate: M = 1.7 M⊕

Really Bad Worlds

M = 21 MJup

Possible brown dwarf

R = 0.9 RJup
P = 20 years

Very little data here!

Really Bad Worlds

Training data

M = 21 MJup
R = 0.9 RJup
P = 20 years

Very little data here!

Really Bad Worlds

M = 21 MJup
R = 0.9 RJup
P = 20 years

Flat distributionEhhh??

Kepler-186f~ 1.1

Neural networks can identify trends between planet properties… to interpolate between known data and estimate missing values

Best
accuracyPoor
accuracy

Neural networks can identify trends between planet properties… to interpolate between known data and estimate missing values
Best performance in densely populated parameter space

High certainty

2 consistent values…. not a clue!

Neural networks can identify trends between planet properties… to interpolate between known data and estimate missing values
Best performance in densely populated parameter space
Distribution contains important information.

All new data will improve the method

Neural networks can identify trends between planet properties… to interpolate between known data and estimate missing values
Best performance in densely populated parameter space
Distribution contains important information.

Outreach:https://www.youtube.com/watch?v=cQygpmYwKw4