Identifying Earth-impacting asteroids using an artificial neural network
AAstronomy & Astrophysics manuscript no. main c (cid:13)
ESO 2020January 14, 2020
Identifying Earth-impacting asteroids using an artificial neuralnetwork
John D. Hefele , Francesco Bortolussi , and Simon Portegies Zwart Sterrewacht, Leiden University, Leiden, NL LIACS, Leiden University, Leiden, NLReceived 29 May 2019 / Accepted 9 December 2019
ABSTRACT
By means of a fully connected artificial neural network, we identified asteroids with the potential to impact Earth. The resultinginstrument, named the Hazardous Object Identifier (HOI), was trained on the basis of an artificial set of known impactors which weregenerated by launching objects from Earth’s surface and integrating them backward in time. HOI was able to identify 95.25% of theknown impactors simulated that were present in the test set as potential impactors. In addition, HOI was able to identify 90.99% ofthe potentially hazardous objects identified by NASA, without being trained on them directly.
Key words.
Comets: general - Minor planets, asteroids: general - Methods: data analysis - Methods: statistical
1. Introduction
In 1990 the US Congress requested for NASA to establish twoworkshops to focus on the identification of potentially hazardoussmall bodies and on methods of altering their orbits to preventimpact (Milani et al. 2002). The workshops led to the estab-lishment of the
Sentry earth impact monitoring system (NASA2018c). If a hazardous asteroid is identified early enough prior toimpact, it would be possible to mitigate the impact by means ofan appropriate space mission to alter the asteroid’s orbit througha gravitational tugboat (Schweickart & et al. 2003) or by obliter-ating it with a nuclear warhead (Barbee et al. 2018). Both mitiga-tion strategies require many years of preparation, which makesthe early detection of hazardous objects vital for allowing ampletime to prepare such missions.The Sentry system adopts a Monte Carlo approach in whichmillions of virtual objects are launched with orbital parametersthat are statistically sampled from within the error ellipse of theobserved asteroids. The impact probability is subsequently deter-mined based on the fraction of virtual asteroids that reach Earthwithin some predetermined striking distance (Milani et al. 2002).In this approach, the orbits of many asteroids are integrated nu-merically and the final parameter space is considered to representthe probability-density distribution of the respective objects. Thecalculation of this probability density distribution relies on thealgorithm and implementation used to integrate the orbits of theasteroids. The time scale over which such integrations remainreliable depends on the degree to which the asteroid’s orbit ischaotic, that is, it depends on the value of the largest positiveLyapunov exponent. Additionally, the reliability of such integra-tions depends on the ability of the integrator to obtain a solution,such that the integration complies to the concept of nagh Hoch (Portegies Zwart & Boekholt 2018). Nagh Hoch is a concept stating that an ensemble of random initialrealizations in a wide range of parameters gives statistically the sameresult as the converged solutions of the same ensemble of realizations.
Both of these concepts are not guaranteed with regard tothe adopted numerical schemes and the results reach question-able proportions as soon as the asteroid experiences a close en-counter with any object other than the Earth. In the latter case,the phase space of possible solutions grows exponentially due tothe chaotic nature of the equations of motion. Establishing thechaotic nature of an asteroid is limited by the accuracy of its or-bital determination. This is generally realized by observing anyparticular asteroid a number of times. These observations resultin a data arc, the fraction of the orbit over which the object hasbeen observed. The adopted Monte-Carlo method used in theSentry system is expected to be reliable for at most a few dozenyears (NASA 2018a) for asteroids whose observed data arc isshorter than a month, which comprises 12.9% of all smallbodies(Giorgini & Chamberlin 2014).Considering the high degree of chaotic motion (small Lya-punov time scale) in asteroids and the consequential exponentialdivergence of its orbit, one might wonder if it is worth the ef-fort to perform extensive computer simulations to track the or-bital trajectories of a large number of particles so long as theveracity of the orbital integration cannot be guaranteed. For themost chaotic asteroids, the impact probability depends acutelyon the statistics of the adopted method and a more coarse grainedapproach to identify potentially hazardous objects may su ffi ce.This approach would free up computer time to provide a morereliable impact probability for the most promising candidate im-postors.We explore the population of asteroids and, in particular,the potentially dangerous ones by means of automatic machinerecognition through a combination of numerical integrations anda trained neural network similar to the architectures describedin Misra & Bus (2008) and Song & Gong (2019), which wereused for classifying hazardous taxonomy and solar sail trans-fer time estimation respectively. It is a statistical approach inwhich we determine the prospect for impact of the known popu-lation of asteroids gathered from the dastcom5 o ff -line database(Giorgini & Chamberlin 2014). Our analysis is mediated by Article number, page 1 of 6 a r X i v : . [ a s t r o - ph . E P ] J a n & A proofs: manuscript no. main an artificial neural-network dubbed HOI for Hazardous Ob-ject Identifier, which was trained on a population of known im-pactors (KI) and a random sample from the observed databaseusing the TensorFlow framework (Abadi et al. 2016). The KIsare machine-generated from an integrated population of aster-oids that start their orbit on a random position of Earth’s surfaceand are launched radially away with the varying speeds. Theseobjects are subsequently integrated backward in time togetherwith the planets in the Solar System for up to 20,000 years. Totrain HOI, these computer generated KIs are then mixed witha subset of observed asteroids, which we assume to be knownnon-impacting objects. The trained network is then used on an-other random selection of observed asteroids in order to identifypotential impactors (PIs). All the objects that were not identifiedby the model as PIs, which were not initially labeled as KIs, arereferred to as unidentified objects (UOs).We begin by describing HOI’s architecture in Section 2,followed by a discussion of the generation of the small-bodydatasets in Section 3. The results are examined in Section 4 andconclusions are drawn in Section 5. All the code used to trainthe neural network, generate data, and evaluate the results arepublicly available on GitHub .
2. Hazardous Object Identifier (HOI)
In general, neural networks are particularly well-suited for rec-ognizing complex patterns hidden in multidimensional datasets.In our particular case, we strive to identify observed objects thathave topologically similar trajectories to the trajectories of thepopulation of KIs. Because we are no longer reliant on calcula-tions that attempt to estimate the asteroids position at a particularpoint in time, the network is more resilient to perturbations of theinitial conditions, that is, chaotic motion.The problem at hand is a discrete binary classification task,where the two mutually exclusive classes for the observed ob-jects are either potential impactors (PIs) or unidentified objects(UOs). For the purpose of our experiments, the UOs are what wewould consider “benign objects”, meaning objects that are iden-tified as having a negligible chance of colliding with the Earth.To quantify the network’s accuracy, the standard cross-entropycost function is used. This is defined as: H ( y, ˆ y ) = − N (cid:88) i y i ln(ˆ y i ) + (1 − y i )ln(1 − ˆ y i ) . (1)Here y is the actual value, or label, ˆ y is the predicted value, and N is the total amount of predictions. This cost function has theconvenient property that its derivative with respect to some inputweight, w , scales linearly with the di ff erence between the labeland predicted value (Nielsen 2015): ∂ C ∂w = N N (cid:88) i x (ˆ y i − y i ) (2)Here x is the input value by which w is multiplied. To mini-mize (1), the Adam Optimizer is used, which expands upon naïvestochastic gradient descent by adapting its learning rate based onboth the average of the first and second moments of the gradi-ents (Kingma & Ba 2015). Empirically, it is observed that thisoptimizer reduces the cost function to the lowest value with the This also means “Hello” in the Dutch language. https://github.com/mrteetoe/HOI Fig. 1.
HOI network architecture. The input layer is comprised of fivenodes, which is followed by two hidden layers of seven and three nodes,and an output layer of a single node. fewest number of iterations relative to the other algorithms avail-able in TensorFlow.Each object fed into the HOI is represented by a five-elementvector where each vector is the Keplerian elements of the as-teroid around the sun including the semi-major axis ( a ), eccen-tricity ( e ), inclination ( i ), the mean speed ( N ), and the specificangular momentum ( H ). These five orbital elements fully char-acterize the shape of an asteroid trajectory around the sun, butnot its orientation as the longitude of the ascending node Ω andargument of periapsis ω are omitted.A diagram showing the HOI architecture is presented in Fig.1. The input layer is a vector of f i v e neurons that matches the di-mensionality of the input, which is followed by two hidden lay-ers that are composed of seven and three neurons, respectively,from the input layer. The output layer is composed of a singleneuron whose values are restrained between 0 and 1 by virtue ofthe sigmoid function. Here, objects with a rating of 0.5 or aboveare classified as PI while those below the threshold are classi-fied as UO. This neural network architecture was arrived at by acombination of empirical experimentation and the incorporationof domain knowledge. We wanted to provide the network withenough degrees of freedom to properly generalize the orbital el-emental profiles of KI but to avoid giving it so many degrees offreedom that the network would overfit to the training datasets.The described architecture results in 69 free parameters: 59weights and ten biases . To optimize these parameters, the net-work is trained on five randomly selected sub-sets of 100,000observed and KI objects over 20 epochs, which took less thanfive minutes on a CPU-type laptop without a GPU. The trainingwas halted when the relative loss decrease per epoch was lessthan 1% to prevent overfitting. At the end of the training pro-cess, the network’s performance was validated with a subset of20,000 KI and 20,000 observed objects that had been held out ofthe training process. Furthermore, all potentially hazardous ob-jects (PHOs) were held out of the training process and used ex- Following the architecture described, the number of free parame-ters can be calculated as follows: the input is fed through layers whichare comprised of 7, 3, and 1 neuron(s). This results in 5 × + × + × + All objects with a minimum orbit intersection distance of 0.05 AU orless and an absolute magnitude (H) of 22.0 or less are considered PHOs(NASA 2018b).Article number, page 2 of 6. D. Hefele et al.: On the identification of Earth-impacting asteroids using an artificial neural network
Fig. 2.
Normalized training and validation losses plotted against thetraining epoch number, along with the fraction of PHOs identified bythe network. clusively for testing purposes. Fig. 2 shows how the training andvalidation loss decreased per training epoch, while the fractionof PHO hazardous objects identified simultaneously increased.We gave the observed objects and KIs labels of 0.1 and0.9, respectively. Here, higher numbers correspond with a largerprobability of colliding with Earth. The label of 0.9 was chosenfor the KIs to represent calculations of the KI trajectories whichare not converged solutions (Portegies Zwart & Boekholt 2014)and to show that several perturbing e ff ects in the Solar Systemwere neglected during the simulations, implying that all of theKIs will, in fact, not collide with Earth when their respective ve-locities are negated.To arrive at the label of 0.1 for the observed objects, we as-sumed that any individual observed object is very likely to bebenign by the following logic: first, all of the PHOs which haveconsiderably larger probability to collide with the Earth com-pared with the rest of the observed population are not used inHOI training. As a result, their labeling does not degrade thenetwork’s ultimate performance. Second, impacts from large ob-jects are rare (Chapman & Morrison 1994) as the impact fre-quency of an asteroid collision decreases with the cube of anasteroid’s diameter. Earth collisions with 5 kilometer asteroidsoccur approximately every 20 million years, while those with a100 meter asteroids occur every 500 years (Tedesco 1994). Be-cause 98.4% of the observed objects used for our experimentsare greater than 100 meters in diameter , we can use the follow-ing formula to estimate an upper-bound of the number of ex-pected Earth impacts from asteroids in our sample within thenext 20,000 years: N collisions = (cid:90) ∞ × D = , (3)Where D is the diameter of an asteroid. Given that over 700,000objects were used in HOI training, the number of 2000 misla-beled objects implies that 0.3% of the observed labels are inac-curate. As discussed further in the following sections, althoughour sample contains only a small fraction of misclassified non-impactors, they still may e ff ect the ability of HOI to accuratelyidentify an impactor.
3. Data generation and acquisition
We extracted 736 ,
496 minor bodies from NASA’s dastcom5 database (Giorgini & Chamberlin 2014). A percentage of 95.5% This assumes an albedo of 0.15 for all small bodies. of the extracted objects are main-belt asteroids, 3.2% are aster-oids that are not in the main belt (such as Apollo or Trojan as-teroids), 0.7% are comets, 0.2% are Kuiper-belt objects, and theremaining 0.4% is composed of a plethora of miscellaneous ob-jects, such as planetary satellites and centaurs (Johnston 2018).These proportions, however, are not representative of the actualsmall-body populations because there is considerable observa-tional bias towards the closer main-belt asteroids in comparisonwith more distant objects (Stern 2012).
We generated an ensemble of 330,000 KIs according to Algo-rithm 1 to act as examples of hazardous objects. Here virtualobjects are launched from future positions of Earth’s surface andthen integrated backward in time to the present era. The idea isthat the virtual objects’ trajectories would be similar to that ofan asteroid observed in the present that would strike the Earth orcome very close to it at some point in the future. Algorithm 1
KI generation algorithm. Here, T is the earliestSolar System orientation, T is the latest orientation, n is thenumber of KIs, and ∆ T = ( T − T − / n T = [ T , T + ∆ t , T + ∆ t , ..., T + ( n − ∆ t , T ] for each τ in T do Initialize the Solar System’s planets’ velocities andpositions with values corresponding to epoch τ . Launch a virtual object perpendicularly from Earth’ssurface with a velocity magnitude randomly drawnfrom an even distribution between 15 and 45km / s. Integrate the object backward in time along with allother Solar System objects until the present epoch. If the object has left the Solar System or spun into thesun, discard it and rerun the simulation.The future launch dates, defined by the orientation of the So-lar System, are evenly distributed between 300 and 20,000 yearsin the future, which correspond to T and T values of 2318and 22018, respectively. The launching velocities are selected tobracket the Earth’s and Solar System’s escape speeds of 11.2 and42.5km / s, respectively. We deliberately did not attempt to mimicthe observed asteroid impact velocities to allow the neural net-work to learn from the full range of parameters, rather than justbased on a hand-selected subsample.
4. Results
The training of the network led to the positive identification of95.25% of the KIs that were not part of the training and 90.99%of the PHOs as PIs. Additionally, 1.94% of the observed objectsthat were not classified as PHOs were identified as PIs. The highfraction of correctly identified KIs indicates that HOI positivelyrecognizes most objects that are constructed to strike Earth. Thisresult is not unexpected because HOI was specifically tuned toidentify artificial KI objects. A more meaningful metric of per-formance is the percentage of PHOs identified. Although 9.01% An object, for example, that is launched from the Solar System at theyear 2318, and is then integrated backwards in time 300 years, wouldcreate an example of a present day asteroid that would strike the Earth in300 years after the velocity vectors are negated to account for the timereversal. As explained in Section 2, the asteroids are not guaranteed tocollide with Earth due to the finite precision of the integrations.Article number, page 3 of 6 & A proofs: manuscript no. main
PHOs were not classified as potential impactors, HOI is approx-imately 47 (90.99 / ff ectiveness of HOI, we performedsimulations to compare the closest Earth approaches of PIs andUOs. To run these simulations, we began by loading the posi-tions and velocities of the asteroids and other Solar System ob-jects corresponding to January 1, 2018. We then integrated all ofthe bodies forward in time for a thousand years while saving theclosest approach that the asteroids made relative to Earth. Thetrajectories of all the 14,680 observed PIs and an equal numberof randomly selected UO asteroids were computed. The distri-butions of the closest Earth approaches achieved during thesesimulations are plotted in Fig. 3. o f o b j e c t s Potential impactorsUnidentified objects
Fig. 3.
Closest approaches to Earth achieved in the next 1000 years forall the observed PIs and an equal number of randomly selected UOs.108 PIs and 884 UOs are not plotted because their closest approachesexceeded the x-axis limits of 2 au. Every object that reach Earth within0.01 au and 99.9% of objects within 0.05 au are identified by HOI asPIs.
To investigate why HOI only identified approximately nine-tenths of PHOs as PIs, the thousand-year integrations describedabove were additionally performed for all PHOs. We present inFig. 4 the distributions of these closest approaches. The distri-butions of identified PHOs and unidentified PHOs are similar,therefore the fraction of PHOs identified as PIs could be used asa measure of the network’s performance. Additionally, all ob-jects that did not approach Earth within at least 0.5 au couldbe considered misclassified PIs. This cut-o ff is not arbitrary butbased, rather, on the minimum distance achieved by approxi-mately 99.7%, or 3 σ , of PHOs. In the case of HOI, 12.2% ofthe PIs are outside of this threshold and are therefore consid-ered misclassified. The root of this misclassification likely stemsfrom the approximations made in the labeling schemes describedin Section 2.A total of 13 ,
258 asteroids identified by HOI as KIs arenot listed by NASA as PHOs. In our thousand-year integrations,4472 of these objects approached within 0.05 au of Earth while2015 approached within 0.02 au. In Table. 4.1 we present a shortlist of 11 notable asteroids with absolute magnitudes of less than22, data arcs of less than 31 days, and closest approaches lessthan 0.02 au.The absolute magnitude threshold of 22 was chosen so thatonly asteroids that have the potential of causing regional dev-astation unprecedented in human history would make the short-list. Assuming a geometric albedo between 0.05 and 0.25 anda spherical shape, objects with an absolute magnitude of 22 areestimated to have diameters between from 100 m to 236 m. Forperspective, Tunguska object which flattened 2,000 square kilo-meters of forest in Siberia was estimated to have a diameter of
Fig. 4.
Closest approach distances to Earth reached for PHOs in thecoming 1000 years.
Designation CA t CA H arc [au] [Year] [mag] [day]2005 RV24 0.020 Feb. 2374 20.60 282008 UV99 0.013 April 2332 20.03 12011 BU10 0.006 April 2920 21.30 182011 HH1 0.012 July 2923 21.7 132011 WC44 0.018 Feb. 2679 20.5 312013 AG76 0.013 Dec. 2638 20.3 242014 GL35 0.018 July 2556 20.6 232014 TW57 0.017 Sept. 2165 20.1 242014 WD365 0.017 Sept. 2735 19.7 52017 DQ36 0.013 Dec. 2131 19.3 292017 JE3 0.016 July 2741 21.9 23
Table 1.
Potential impactor shortlist: relatively large minor bodies witha short data arcs that were identified as PIs by HOI but are not consid-ered PHOs. Along with their closest approaches (CA) in au, the monthand year that their closest approaches occurred ( t CA ), their absolutemagnitudes (H), and their data arc lengths in days (arc) are tabulated. between 50-80 m (Farinella et al. 2001). The month long data-arc limit is selected because the Monte-Carlo method adopted byNASA is particularly ill-suited for calculating the impact proba-bilities of such uncertain orbits. As a consequence, these objectsare the most likely to be overlooked as PHOs. The characteristics of the simulated KIs and the observed ob-jects are compared to better understand how HOI di ff erentiatesbetween the two populations. In Fig. 5 we present 100 trajecto-ries of observed objects and KIs.There are profound di ff erences between the orbital elementsof the two distinct populations of objects. Our artificial popu-lation of objects launched from Earth tend to have highly ec-centric and inclined orbits, whereas the observed objects tendto have circular orbits confined near the ecliptic plane. For theobserved objects, the orbital plane is essentially empty withinapproximately 2 au of the Sun, while for the KIs this is the mostdensely occupied space. This object distribution should be ex-pected considering that all the KIs were generated 1 ± .
017 au
Article number, page 4 of 6. D. Hefele et al.: On the identification of Earth-impacting asteroids using an artificial neural network x [au] y [ a u ] -7.5 -5 -2.5 0 2.5 5 7.5 10 x [au] Fig. 5.
Illustration of the di ff erence between the trajectories of observed objects (left) and KIs (right). The observed objects tend to have circularorbits which lie in the orbital plane of Earth around the Sun, whereas the KIs exhibit a much broader distribution in eccentricity and inclination.These characteristics, however, are not mutually exclusive and could be one the root causes of HOI’s imperfect classification. away from the Sun along the Earth’s orbit and that the integra-tion times were not su ffi ciently long enough to allow consider-able outward migration of the objects.The a versus e ratio is an important factor in an object’s iden-tification, as illustrated in Fig. 6. A curve is drawn to highlightan apparent “classification boundary”, which is above 95.2% ofPI and below 90.3% of unidentified observed objects. Althoughthe boundary is an indicator of an object’s potential classifica-tion, it is not definite, which is understandable considering thatHOI takes five orbital elements as input for each object insteadof just the a and e orbital elements.
5. Conclusions
We designed, constructed, and trained a fairly simple neural net-work aimed at classifying asteroids with the potential to impactthe Earth over the coming 20 ,
000 years. Our method takes theobserved orbital elements as input and provides a classifier forthe expectation value for the object’s striking Earth.The network was able pick out 95.25% of the KIs whenmixed into a set of observed asteroids which are not expected tostrike Earth. When applied to the entire population of observedasteroids, the network was able to identify approximately nine-tenths of the asteroids identified by NASA as PIs and along withvirtually every other observed asteroid that approached within0.05 au of Earth. We generated a short list of network iden-tified PIs which NASA does not label as PHOs, mainly be-cause the observed orbital elements are so uncertain that NASA’sMonte Carlo approach to determine their Earth-striking proba-bility fails. The network classifies an object as a PI or UO within0 .
25 milliseconds, which is negligible compared to the time re-quired for the Monte-Carlo method employed by NASA.Follow-up calculations over a time-span of 1000 years re-vealed that 12.2% of the PIs identified by the network did notcome within 0.5 au of Earth. This may imply that thee asteroids pose no direct threat on the time scale considered. Integratingtheir orbits for a longer time-frame, however, this is impracticalbecause of the large uncertainty in their orbital elements and therelatively small Lyapunov timescale for these objects.We look forward to improving the network’s classificationaccuracy. The network, as we show in Fig. 1, is the result ofa great deal of experimentation in network depth, width, and(sub)selection input parameters. It is possible that the struc-ture preserving mimetic architectures motivated by the underly-ing Keplerian topology of the orbits could allow us to achievea higher quality of prediction accuracy but this still requiresa considerable degree of further experimentation. Another im-provement could be carried out by considering a stricter labelingscheme in which some probability statistics for impacting theEarth could be taken into account.
Acknowledgements.
We thank the Microsoft Cooperation for access to the Azurecloud on which many of the calculations presented here are performed. John D.Hefele thanks Sander van den Hoven for his mentoring during his internship atMicrosoft Amsterdam. This work was supported by the Netherlands ResearchSchool for Astronomy (NOVA), NWO (grant
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