Deep learning model for multiwavelength emission from low-luminosity active galactic nuclei
MMNRAS , 1–9 (2021) Preprint 12 February 2021 Compiled using MNRAS L A TEX style file v3.0
Deep learning model for multiwavelength emission fromlow-luminosity active galactic nuclei
Ivan Almeida ★ , Roberta Duarte , and Rodrigo Nemmen Universidade de São Paulo, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Departamento de Astronomia,São Paulo, SP 05508-090, Brazil
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Most active supermassive black holes (SMBH) in present-day galaxies are underfed and consistof low-luminosity active galactic nuclei (LLAGN). They have multiwavelength broadbandspectral energy distributions (SED) dominated by non-thermal processes which are quitedifferent from those of the brighter, more distant quasars. Modelling the observed SEDsof LLAGNs is currently challenging, given the large computational expenses required. Inthis work, we used machine learning (ML) methods to generate model SEDs and fit sparseobservations of LLAGNs. Our ML model consisted of a neural network and reproduced withexcellent precision the radio-to-X-rays emission from a radiatively inefficient accretion flowaround a SMBH and a relativistic jet, at a small fraction of the computational cost. The MLmethod performs the fit 4 × times faster than previous semianalytic models. As a proof-of-concept, we used the ML model to reproduce the SEDs of the LLAGNs M87, NGC 315and NGC 4261. Key words: black hole physics – accretion discs – galaxies: active
Quiescent galaxies with little or no ongoing star formationdominate the local universe (Bell et al. 2004; Bundy et al. 2006;Faber et al. 2007; Ilbert et al. 2010). The observed quiescence canbe related to the activity phase of an active galactic nucleus (AGN).In neighbor galaxies with AGNs, we do not observe a relevantquasar population. Instead the observations show an active galaxypopulation mainly formed by low-luminosity AGNs (LLAGNs);some examples are SgrA* (Narayan et al. 1995; Yuan et al. 2003),NGC 3115 (Wong et al. 2014), and M87 (Event Horizon TelescopeCollaboration et al. 2019).LLAGNs present different observational signatures comparedto more luminous AGNs – i.e., quasars, blazars. All AGNs displaya broadband multiwavelength emission, but LLAGNs did not haveprominent UV continuum emission – characteristic of an opticallythick and geometrically thin accretion disc (Ho 1999, 2008; Nem-men et al. 2006; Wu et al. 2007). LLAGNs show weak and narrow FeK 𝛼 (Terashima et al. 2002) lines in their spectra, which agrees witha thin accretion disc absence. Furthermore, the observed luminosityfrom these LLAGNs is far below the expectation for a thin disc withan efficiency of 10% ( 𝐿 = . (cid:164) 𝑀𝑐 ; being 𝐿 the luminosity and (cid:164) 𝑀 the accretion rate). These characteristics suggest that LLAGNs areradiatively inefficient systems drastically different from the standardscenario. ★ E-mail: ivan.almeida003gmail.com
The AGN dynamics depends on how the supermassive blackhole (SMBH) accrete the available gas in its surroundings. Theseprocesses rely strongly on whether the viscously generated ther-mal energy is radiated away (Abramowicz & Fragile 2013). TheLLAGNs in our nearby vicinity are underfed SMBHs with accre-tion rate (cid:164)
𝑀 < − (cid:164) 𝑀 Edd ( (cid:164) 𝑀 Edd is the Eddington accretion rate),these objects are classified as radiatively inefficient accretion flows(RIAF). RIAFs are extremely hot, optically thin, and geometricallythick accretion discs; for more details, see Yuan & Narayan (2014).RIAFs have characteristic emission in two primary wave-lengths: radio and X-ray. The radio component of the spectral energydensity (SED) is related to synchrotron emission in the accretiondisc. The elevated temperatures in RIAFs (Yuan & Narayan 2014)indicate an electronic population with very high average energy.These electrons can interact with available photons and transfer en-ergy via inverse Compton scattering (IC). IC is one of the primarysources of X-ray emission. RIAFs can emit bremsstrahlung radiationalso, via electron-ion scattering inside the accretion flow. Howeverthe radiation field in RIAFs is very faint, and it has negligible effectsin the optically thin accretion flow dynamics.An astrophysical object’s emitted light carries informationabout the physical processes occurring in the source. With the ob-served SED, one can model the emitting source. LLAGNs have abroadband emission, and modeling their multiwavelength emissiongives us valuable knowledge about the system – e.g., the accretionrate or electronic and ionic distributions in the accretion flow. Sev-eral works (Yuan et al. 2003; Nemmen et al. 2006, 2014; Almeida © a r X i v : . [ a s t r o - ph . GA ] F e b Almeida et al. et al. 2018; Bandyopadhyay et al. 2019) performed similar analy-ses. Traditional methods to fit LLAGN SEDs (e.g. Nemmen et al.(2014)) are computationally intensive and require the user to ac-tively monitor and participate in the modelling process.In the last few years, machine learning (ML) methods havebecome extremely common in science, especially in dealing withbig data problems, like Astronomy. The development of better tele-scopes gives us a massive amount of data, which is a favorablescenario to implement ML algorithms (George & Huerta 2018).Many authors published works using ML methods in astronomicaldata, doing object classification (Rohde et al. 2005; Banerji et al.2010), and spectra analysis and modeling (Firth et al. 2003; Valdés& Bonham-Carter 2006; Ball et al. 2007; Marulanda et al. 2020;Liew-Cain et al. 2020), for example.Neural Network (NN) is a ML method based on biological neu-rons and how they pass through the information (McCulloch & Pitts1943). It is widely used in the scientific community since they showresults when it comes to classification (Wan 1990; Storrie-Lombardiet al. 1992; Odewahn 1995) and regression (Specht 1991; Comrie1997). NNs consist of neurons and connections between them. Withweights ( 𝑤 𝑖 ) associated with each connection. Each neuron has aactivation function 𝑓 ( (cid:205) ( 𝑤 𝑖 𝑥 𝑖 )) that is a relation between the inputs( 𝑥 𝑖 ) and weights (Leshno et al. 1993). Deep learning (DL) is a verypowerful tool, for more details see (Breen et al. 2020; Rodriguezet al. 2018; LeCun et al. 2015).Other works used NNs to fit observational data (Asen-sio Ramos & Ramos Almeida 2009; Pacheco-Sanchez et al. 2019;Fathivavsari 2020). For instance, Asensio Ramos & Ramos Almeida(2009) shows a technique based on the combination of two MLmethods: principal analysis component (PCA) and NNs. It uses aPCA for dimensionality reduction, and the NNs are used to interpo-lation. The PCA is useful to get faster results since it can shrink thesize of the data. In our work, we do not perform a dimensionality re-duction, but the speed-up is adequate. Fathivavsari (2020) proposedthe use of NNs as a new technique to predict the flux and the shapeof Ly 𝛼 emission lines in the spectra from quasars. The architec-ture proposed in Fathivavsari (2020) is a deep NNs with five layerswith the input being 𝑆𝑖 𝐼 𝑉 , 𝐶 𝐼 𝑉 , and 𝐶 𝐼 𝐼 𝐼 ] emission lines, and theoutput is the Ly 𝛼 emission line. Similarly to our work, they usedhyperparameter tuning methods to find the best architecture. Theyobtained a NN able to predict Ly 𝛼 emission lines with a precision6% − ∼ ∼ AGNNES ( A ctive G alactic N uclei Ne ural network S ED generator).In section 2, we presented the details of the model, details aboutthe NN construction and training are in section 2.2. In section 3 wepresented our results. We compared our results to other similarworks in literature in section 4. The summary of the work is insection 5.
We assumed sub-Eddington LLAGNs are accreting as radia-tively inefficient accretion flow (RIAF). We used a semi-analyticalapproach to treat the RIAF emitted radiation (Nemmen et al. 2014).Normally LLAGN SEDs are radio-loud (Ho 1999; Sikora et al.2007). In our model, we also included the synchrotron emissionfrom a relativistic jet, either. Here in this work, we followed thesame approach as Nemmen et al. (2014) to generate our SED sam-ple. . Henceforth we will call this model as the “fiducial” one. We considered the calculation of an optically thin and geo-metrically thick two-temperature accretion flow with outer radius 𝑟 = 𝑅 𝑆 ( 𝑅 𝑆 is the Schwarzschild radius), which presents verylow radiative efficiency (Narayan et al. 1998). Our assumptions tocalculate the system SED were:(i) The accretion flow is stationary.(ii) Viscosity is parameterized as Shakura & Sunyaev (1973) 𝛼 -viscosity.(iii) The gravity is described with a pseudo-Newtonian potential(Paczyńsky & Wiita 1980).The radiative transfer is treated carefully in more detail. We tookinto account radiation emission from synchrotron, inverse Comptonscattering (IC), and bremsstrahlung processes occurring inside theaccretion flow. (Nemmen et al. 2006; Yu et al. 2011; Nemmen et al.2014).Outflows, or winds, are an intrinsic feature of RIAF’s model,e.g. Yuan et al. (2012, 2015); Almeida & Nemmen (2020). In thiswork, we considered the parameterization proposed by Blandford& Begelman (1999) for the accretion rate as a function of radiusfollowing a power-law relation: (cid:164) 𝑀 = (cid:164) 𝑀 (cid:18) 𝑟𝑟 (cid:19) 𝑠 (1)the parameter 𝑠 is related to the “intensity” of winds, higher valuesof 𝑠 mean stronger winds. (cid:164) 𝑀 is the accretion rate at the definedradius value 𝑟 in units of (cid:164) 𝑀 Edd . In this work, we used 𝑟 as theouter radius of the accretion disc, 𝑟 = 𝑅 𝑆 . Following Nemmenet al. (2014) we assumed that 𝑠 is limited to the range 0 (cid:46) 𝑠 (cid:46)
1. For (cid:164) 𝑀 , we considered a sub-Eddington system and limited the possiblevalues to (cid:164) 𝑀 < . (cid:164) 𝑀 Edd .The RIAF solution depends on the system’s physical param-eters: the black hole mass 𝑀 , the viscosity parameter 𝛼 , the adia-batic index 𝛾 , the parameter 𝛽 – called modified plasma parame-ter – defined as the ratio between gas pressure and total pressure( 𝛽 = 𝑃 gas / 𝑃 total ), and the fraction of turbulence energy dissipatedthat heats the electronic population of the plasma 𝛿 . Here we fol-lowed Nemmen et al. (2006) and adopted 𝛼 = . 𝛽 = . 𝛾 = .
5. For 𝛿 values, normally they were considered small (0 . 𝛿 to vary between 0 . ≤ 𝛿 ≤ . Fiducial model source code can be found in: https://bitbucket.org/nemmen/adaf-code/src/master/
MNRAS , 1–9 (2021) eep Learning model for LLAGNs emission In the RIAF model, we varied three free parameters: 𝛿 , 𝑠 and (cid:164) 𝑀 . We generated ∼ . ≤ 𝛿 ≤ .
3; 0 ≤ 𝑠 ≤ − ≤ log (cid:0) (cid:164) 𝑀 / (cid:164) 𝑀 Edd (cid:1) ≤ − The RIAF component does not produce enough radio emissionto match the radio observations of LLAGN (Ulvestad & Ho 2001;Nemmen et al. 2006; Liu & Wu 2013). We included in our modelthe contribution of a jet component modeled based on the scenarioof internal shocks (Spada et al. 2001). Following this model inthe SMBH surroundings, a portion of the accretion flow gas istransferred to the jet generating a mass outflow rate (cid:164) 𝑀 𝑗 and a shockwave. The shock wave makes the jet emission dominated by a non-thermal leptonic population.Our modeled jet has a conical geometry with a half-openingangle of 0.1 rad ( ∼ ◦ ) and a constant bulk Lorentz factor of 2.9,independent of the distance to the central SMBH. The jet is perpen-dicular to the accretion disc with an angle with the line of sight of30 ◦ . The shocks accelerate the electrons to a power-law with index 𝑝 . The parameters 𝜖 𝑒 and 𝜖 𝐵 describe respectively the fraction ofenergy density from the electrons and the magnetic field.The jet modelling free parameters were: (cid:164) 𝑀 𝑗 , 𝑝 , 𝜖 𝑒 and 𝜖 𝐵 . Weallow 𝑝 to be in the range [ , ] , as the shock theory predicted it.We expect that (cid:164) 𝑀 𝑗 < (cid:164) 𝑀 , here (cid:164) 𝑀 is from RIAF modeling, themass outflow in the jet should not be higher than the mass inflowin the accretion disc. By definition, both 𝜖 <
1, since they arefractions of the total energy. We generated ∼ ≤ 𝑝 ≤ − ≤ log (cid:0) (cid:164) 𝑀 𝑗 / (cid:164) 𝑀 Edd (cid:1) ≤ − − ≤ log 𝜖 𝑒 ≤ − − ≤ log 𝜖 𝐵 ≤− Our model is a deep neural network composed of neurons withseveral layers and weights. In the output layer, we have a functioncalled loss function L which is any error function that gives us howmuch the prediction and target are different. The learning procedureis given by the backpropagation method that consists of derivativesof L concerning the weight we want to learn (Kelley 1960). In otherwords, the backpropagation uses gradient descent (Ruder 2016) tofind the minimum value in a space given by L( 𝑤 𝑖 𝑗 ) , i.e., find whichweights 𝑤 𝑖 𝑗 gives the minimum of L .The learning part starts when we feed the neural network withdata from the training set. We can give the data in batches, whichis giving data by parts; this corresponds with faster training. Epochis passing all batches once. The batch size and epoch are calledhyperparameters. They are changed to find which combination ofhyperparameters gives better results. In our work, we considered thenumber of neurons and the number of layers as hyperparameters. Inthis way, our goal was to find the best architecture for our model. Wecreated a GridSearch to find the best values of our hyperparameters.The
GridSearch is a hyperparameter tuning method (Bergstra &Bengio 2012) that consists of train the NN with several combinationsof hyperparameters. In our case, our hyperparameter is the numberof neurons in each layer. We created a shell script that runs all thecombinations possible and saves the chosen metric. The trainingswith the better metrics are the one we use to further analyze. Ourbest model is composed of two architectures, one is to analyze theRIAF and the other to analyze the jet region. The RIAF model is composed of 4 layers with 56, 60, 99, and 99 neurons, respectively.The jet model is composed of 5 layers with 10, 44, 66, 99, and 130neurons. Each layer has a ReLU activation except for the last layerwhich is a linear function. The mean absolute error as L and theoptimizer is Adam (Kingma & Ba 2014).To summarize, we build our neural network from scratch usingthe GridSearch technique. Our architecture is composed of hiddenlayers meaning that it is a deep neural network. We tested otherarchitectures with different hyperparameters, but this is the bestmodel.
SED calculations for LLAGN are time expensive. The fiducialcode which we generated our training RIAF SED’s sample took aminute per spectrum . The trained NN, AGNNES, calculates thesame component in approximately 0 . ∼ ∼ . . ∼
500 times.AGNNES results are an approximation from the original cal-culation. We had an extremely high speed-up in calculations, butthe NN introduces inherently small errors when compared to thefiducial code. AGNNES, on average, can reproduce very well thevalidation data – see appendix C. Comparing the AGNNES pre-dictions with the validation data sample, we defined Δ SED as the“distance” between the model and AGNNES prediction: Δ SED ( 𝜈 ) ≡ log ( 𝜈𝐿 𝜈 ) original − log ( 𝜈𝐿 𝜈 ) AGNNES (2)Considering the validation sample and comparing original dataagainst AGNNES predicted one, for every point (i.e. frequency). Wefound the averaged value of Δ SED = 0 . ± .
05 (see (2)), we plot-ted in figure 1. For the RIAF component the NN predicted slightlysmaller emission values. The jet component presented Δ SED =0 . ± .
01. These Δ SED values are AGNNES’s uncertainty.The original data is not perfect. Sometimes the original coderandomly fails while calculates the inverse Compton emission, re-turning a lower value for the emission. We automatically generatedthe data, and we identified the code failures and discarded the wrongdata automatically, but it was not 100% efficient. The data set havefew“bad” SEDs mixed in the whole set; this can affect the NNtraining and be responsible for the slightly systematic deviationof 0.02 dex in 𝑙𝑜𝑔 ( 𝜈𝐿 𝜈 ) . However, LLAGNs are very difficult toobserve, and the observations typically have considerable uncertain-ties, higher than 0.02 dex. The theoretical models for the LLAGNemission have their uncertainties. The NN averaged deviation fromthe original model is negligible if compared with the usual errorbars in measurements and model uncertainties. The current approach for LLAGN SED fitting in literatureis an iterative method in which one changes all the parameters Depends on the hardware and parameters set. For our available computers,it took 0.5-2minMNRAS000
01. These Δ SED values are AGNNES’s uncertainty.The original data is not perfect. Sometimes the original coderandomly fails while calculates the inverse Compton emission, re-turning a lower value for the emission. We automatically generatedthe data, and we identified the code failures and discarded the wrongdata automatically, but it was not 100% efficient. The data set havefew“bad” SEDs mixed in the whole set; this can affect the NNtraining and be responsible for the slightly systematic deviationof 0.02 dex in 𝑙𝑜𝑔 ( 𝜈𝐿 𝜈 ) . However, LLAGNs are very difficult toobserve, and the observations typically have considerable uncertain-ties, higher than 0.02 dex. The theoretical models for the LLAGNemission have their uncertainties. The NN averaged deviation fromthe original model is negligible if compared with the usual errorbars in measurements and model uncertainties. The current approach for LLAGN SED fitting in literatureis an iterative method in which one changes all the parameters Depends on the hardware and parameters set. For our available computers,it took 0.5-2minMNRAS000 , 1–9 (2021)
Almeida et al. (a) RIAF(b) Jet
Figure 1.
From the validation set, we calculated the difference betweenlog 𝜈𝐿 𝜈 from the original data and the calculated by AGNNES and plottedthese values as a histogram. We obtained Δ SED ≈ . ± .
05 for RIAFmodel and Δ SED ≈ . ± .
01 for jet model, respectively top and bottompanels. individually while the others remain unchanged. The best fit isdetermined visually after a certain number of attempts with noestimated uncertainties on the results (Nemmen et al. 2014; Almeidaet al. 2018). The SED calculation is computationally expensive. Thebottleneck of LLAGN SED calculation is in the Comptonization.The fiducial code takes ∼ SEDs, we would need approximatelytwo months without pause. With a faster method to calculate SEDs,we could explore a broader range of parameters and apply morerobust fitting methods.Time performance is the strongest point of AGNNES whenwe compare it with the iterative method. A well trained NN can dothe IC step smoothly without high time spending. The NN is not aperfect copy of the original model. During the training, there is errorpropagation, and the NN final result is an approximation of the realvalue; for simplicity, we assumed the original code gives the perfectSED value, and we compared AGNNES with it. We discussed theNN performance in section 2.3.We implemented the fitting procedure using Markov-chainMonte Carlo method. We performed the chain calculation with the
Python package emcee (Foreman-Mackey et al. 2013). We used emcee to estimate the posterior distributions for the parameters – 𝛿 , 𝑠 , (cid:164) 𝑀 , 𝑝 , (cid:164) 𝑀 𝑗 , 𝜖 𝑒 , 𝜖 𝐵 – that better describe the data. We defined thelikelihood function as a pure Gaussian likelihood. The final likeli-hood is the sum of all seven parameters’ likelihoods. The priors ofparameters have initially been the limits of the data set presented insections 2.1.1 and 2.1.2.We started the MCMC with a flat distribution ball around ran-dom initial values with small radius, considering all parameters asadimensional. Our MCMC chain ran with 300 walkers for the num-ber of steps N: 𝑁 > 𝜏 ) implemented in emcee following Goodman & Weare(2010) method; it should be 𝑁 / (cid:38) 𝜏 . We chose some objects with available SED data in the literatureto fit. We aimed to find the best constraints for the accretion flowparameters that reproduce sources’ SED. Our chosen objects were:M87, NGC 4261, and NGC 315. The data points of all SEDs areavailable in appendix A.To obtain the fit, we used existing independent measurementsand theoretical models as priors . In our work, we considered allour priors as flat distributions, for simplicity. For the SEDs plots,we adopted the following convention: The red dashed line is theRIAF contribution, the blue dash-dotted line is the jet contribution,and the solid black line is the sum of them. The grey shaded areais a set of one hundred curves generated by the MCMC methodand represents the uncertainties in the total sum. We showed theposterior distribution of the free parameters in appendix B.We showed the fitting results in table 1. The columns show theseven free parameters for RIAF and jet models, and the last one isthe reduced 𝜒 calculated between the best fit and the observationaldata points. For observational points without uncertainty, we assumean uncertainty of 0.05 dex.In this work, we favored the scenario in which the RIAF dom-inates the high energy emission. We did not consider IC emis-sion from jet photons. The jet contribution was considered relevantmainly for low frequencies– up to near-infrared –but neglected inhigher frequencies for the galaxies NGC 4261 and NGC 315. In ourjet fitting, we considered data points above infrared as upper limitsfor the jet emission. For M87 we modeled the whole emission fa-voring the jet model due to known observational priors (Doelemanet al. 2012; Kuo et al. 2014). The elliptical galaxy M87 harbors a supermassive black holeof 6 . × 𝑀 (cid:12) at 16 Mpc of distance from us (Event HorizonTelescope Collaboration et al. 2019). The source presents strongradio emission due to a prominent relativistic jet. We showed theSED data points and the best fit in figure 2.For this source, we used as data points the high-resolutionobservations presented in Prieto et al. (2016) (c.f. Table 4). Wetreated observations with the lower spatial resolution– presented inthe same paper for different wavelengths –as upper limits.The jet emission is a known feature of M87 (Doeleman et al.2012). We tested models considering RIAF and Jet emission, wefound the best result considering only the jet emission. Our fit MNRAS , 1–9 (2021) eep Learning model for LLAGNs emission Object 𝛿 (cid:164) 𝑀 ( (cid:164) 𝑀 Edd ) 𝑠 (cid:164) 𝑀 𝑗 ( (cid:164) 𝑀 Edd ) 𝑝 𝜖 𝑒 𝜖 𝑒 𝜒 𝑟𝑒𝑑 M87 – – – 6 . + . − . × − . + . − . . + . − . × − . + . − . × − . . + × − − × − . + . − . × − . + . − . . + . − . × − . + . − . . + . − . × − . + . − . × − . . + × − − × − . + . − . × − . + . − . . + . − . × − . + . − . . + . − . × − . + . − . × − . Table 1.
The final results of AGNNES’s fit to our galaxy sample.
Figure 2.
M87 SED best fit. suggested jet dominance over the inner RIAF for all wavelengths.It was not possible to produce a good fit for the observational SEDusing the RIAF model for this source. Our result considered onlyjet synchrotron emission and did not reproduce the bump around100GHz and the most energetic data point is consistent with thebest fit with 3 𝜎 .A thermal population of electrons in the accretion flow cannotreproduce the SED of M87 with such accretion rate. It is necessaryto change the electronic distribution or assume the jet dominatesthe observed energy output entirely. The results for M87 fittingparameters are in table 1, and we only considered the synchrotronjet in our model. NGC 4261 is an elliptic galaxy at ∼ . × 𝑀 (cid:12) (Tremaineet al. 2002). The SED data is available in table A2. de Menezes et al.(2020) presented data points and similar modeling for the samegalaxy. We showed the SED data points and our best fit in figure 3.NGC 315 is another elliptical galaxy at ∼ . × 𝑀 (cid:12) (Woo & Urry 2002). The SED data is available in table A3.de Menezes et al. (2020) presented data points and similar mod-eling for the same galaxy. NGC 315’s SED data points and the bestfit are in figure 4.For these sources, we considered the optical data as upperlimits. In the optical frequency range, there is a high possibilityof stellar contamination. Stellar clusters typically inhabit the centerof galaxies, and these populations emit a considerable amount of Figure 3.
NGC 4261 SED best fit.
Figure 4.
NGC 315 SED best fit. light in the optical band (Lauer et al. 2005). Since our primaryinterest here is the AGN emission, we neglected the potentiallycontaminated points by stars.For NGC 4261 and NGC 315, our models were more focusedon the RIAF component, especially for higher frequencies. In ourmodel, the innermost regions of the RIAF produce most of the X-rayemission. We used the jet component to explain mostly the radioregion of the SED. We did not consider the jet emission to explainthe observed high energy emission (optical, UV, or X-ray bands).If we try to explain the whole SED only with a synchrotron jet, wewill get different results and higher values of 𝜒 . MNRAS000
NGC 315 SED best fit. light in the optical band (Lauer et al. 2005). Since our primaryinterest here is the AGN emission, we neglected the potentiallycontaminated points by stars.For NGC 4261 and NGC 315, our models were more focusedon the RIAF component, especially for higher frequencies. In ourmodel, the innermost regions of the RIAF produce most of the X-rayemission. We used the jet component to explain mostly the radioregion of the SED. We did not consider the jet emission to explainthe observed high energy emission (optical, UV, or X-ray bands).If we try to explain the whole SED only with a synchrotron jet, wewill get different results and higher values of 𝜒 . MNRAS000 , 1–9 (2021)
Almeida et al.
For both NGC 4261 and NGC 315,– assuming the RIAF dom-inates high energy emission –there are no strong constraints in thehigh-frequency jet emission ( 𝜈 > Hz) –, this assumption makesthe value of 𝑝 poorly constrained. The jet model fits the radio points,and this gives us information about the accretion rate (cid:164) 𝑀 𝑗 and thedistribution of energy, represented by 𝜖 𝑒 and 𝜖 𝐵 . In our model,we restrained (cid:164) 𝑀 < − (cid:164) 𝑀 Edd . We trained AGNNES to calculateSEDs with accretion rates up to 10 − (cid:164) 𝑀 Edd , but we expect evenlower accretion rates for LLAGNs. Our assumption of the maxi-mum value for (cid:164) 𝑀 resulted in the truncated distributions for (cid:164) 𝑀 inNGC 315 and NGC 4261, respectively figures B3 and B2.If the sources have higher accretion rates, the RIAF assumptionis not valid. This truncation can be a hint that the emission couldnot come from an inner hot accretion disc. The X-ray emission forNGC 4261 could be better constrained if we allow an accretion rateof (cid:164) 𝑀 = . × − (cid:164) 𝑀 Edd .For NGC 4261 and NGC 315, the fitting was not able to fullyexplain the UV emission. Both galaxies presented much lower ob-servational value in UV than our RIAF model prediction.
AGNNES’s accuracy is an essential feature of this work. Usingthe parameters set calculated by AGNNES as the best fit, we plottedfigure 5. In the top panel of this figure, the solid black line isAGNNES SED fit, and the dashed green line is the SED calculatedwith the fiducial code – for the same parameters. For all sources,both curves are very similar. In the bottom panel, there are theresiduals between the two curves. The grey zones represent theerror of AGNNES for the uncertainty of 1 𝜎 and 3 𝜎 (see figure 1).Considering all frequencies, from radio to X-ray, the fiducial codeand AGNNES are equivalent. Astronomers have studied M87 extensively over the past sixtyyears (Felten 1968; Schreier et al. 1982; Biretta et al. 1999; Doele-man et al. 2012; Event Horizon Telescope Collaboration et al. 2019).Recently, Bandyopadhyay et al. (2019) modeled this source with acombination of RIAF and synchrotron jet. They used a populationof nonthermal electrons, which is absent in our work, and they man-age to fit the bump at ∼ (cid:164) 𝑀 (cid:38) − (cid:164) 𝑀 Edd , which is not consistent with the RIAF scenario– notwithstanding our model fits well the data. de Menezes et al.(2020) Gamma-ray observations indicate the emission comes froma jet emitting synchrotron (low-frequency) and synchrotron self-Compton (high-frequency).
The original model used to calculate the SEDs has its limita-tions, and AGNNES inherited all of them. The RIAF SED followeda straightforward model, with some strong approximations. First of all, it is a 1-dimensional calculation. It was assumed an axisymmet-ric accretion flow, and we integrated over the 𝑧 -component (con-sidering a cylindrical geometry). Furthermore, the code works onstationary accretion flow, hence it cannot account time variability.Our jet SED took account of synchrotron emission only. We didnot calculate the Inverse Compton effect in the jet photons. Some ob-servations support a scenario with synchrotron self-Compton emis-sion in the jet dominating the LLAGN emission (Nagar et al. 2005;Finke et al. 2008; Takami 2011).The SED data of every object was not simultaneously mea-sured. Many authors observed each data point at a different time,with years of separation. Moreover, we did not take into accountany variability. We assumed all data comes from the quiescent stateof the source. Such assumptions can be a problem for galaxies withfew data points and not known variability patterns. M87 has morereliable data because it is a source continuously observed.AGNNES works properly inside its training parameters range(see section 2.1). For fainter sources with very low luminosity, likeSgrA*, AGNNES can not fit the SED reliably. For the SgrA* case,the accretion is too small to be inside our training specifications.The fiducial code can calculate SEDs for objects with such lowaccretion rates. However, numerical errors increase considerablyas the accretion rate decreases. To generate data for low accretionrates are harder than for mildly higher accretion rates. The difficultyin creating SEDs with (cid:164) 𝑀 (cid:38) − impacted on AGNNES results.Below this (cid:164) 𝑀 value, our NN can not calculate a correct SED.AGNNES best reproduces LLAGN SEDs with ( 𝜈𝐿 𝜈 ) peak > erg/s. The primary objective of this work was to optimize the calcu-lations of LLAGN SEDs, and the modelling of observed broadbandspectra. Several previoues works used the iterative method to cal-culate the radiative emission from RIAF and jet for LLAGNs. Thefiducial code spent few minutes to generate one
SED with two com-ponents. To implement a more robust statistical analysis, we need afaster approach to calculate a single SED. AGNNES performs thiscalculation much faster than the original code: it is ∼ × fasterfor the RIAF and ∼ × faster for the jet. We achieved a substantialspeed-up allowing us to fit some sources (M87, NGC 4261, NGC315). We constrained the better distribution of the parameters (seesection 2) to fit the SED for each object using the MCMC method.AGNNES is very accurate with respect to the fiducial method.We built AGNNES for physical systems with fitting param-eters inside its training range (see section 2.1). A possible futureimprovement is to generate more data for smaller BH masses andlower accretion rates to enhance the AGNNES training dataset. Ouroriginal code did not take into account a nonthermal leptonic pop-ulation, and this can be an improvement in the future.SED calculations are very time expensive if you need to takeinto account some iterative procedures as calculating Inverse Comp-ton emission. Our work achieved a vast speed-up of some thousandtimes in the calculation of a single SED. This is a demonstration ofthe power of deep learning algorithms for astrophysical problems. ACKNOWLEDGEMENTS
We used
Python (Oliphant 2007; Millman & Aivazis 2011) toorganise all SED data and to make all figures. In this work we used
MNRAS , 1–9 (2021) eep Learning model for LLAGNs emission (a) NGC 4261 (b) NGC 315(c) M87 Figure 5.
Top panel: Comparison between SED calculated with AGNNES (solid black line) and following the original code (dashed green line). Bottom panel:The residuals between the original code SED and AGNNES’s prediction. The darker grey region is 1 𝜎 uncertainty on the AGNNES result; the lighter greyregion is 3 𝜎 region. several packages as pandas McKinney (McKinney),
NumPy (VanDer Walt et al. 2011),
SciPy (Virtanen et al. 2019) and
Matplotlib (Hunter 2007).Figure C1 was built using the software
Nn-svg (LeNail 2019).We acknowledge useful discussions with João Paulo PeçanhaNavarro, Felipe Lucas Gewers, Raniere de Menezes, Amanda Ru-bio and Stephane V. Werner. This work was supported by FAPESP(Fundação de Amparo à Pesquisa do Estado de São Paulo) undergrants 2016/24857-6, 2017/01461-2 and 2019/10054-7. We grate-fully acknowledge the support of NVIDIA Corporation with thedonation of the Quadro P6000 GPU used for this research.
SUPPORTING INFORMATION
The LLAGN SED fitting code will be made publicly availableon github upon publication of this manuscript.
REFERENCES
Abramowicz M. A., Fragile P. C., 2013, Living Reviews in Relativity, 16, 1 Agudo I., Thum C., Gómez J., Wiesemeyer H., 2014, A&A, 566, A59Almeida I., Nemmen R., 2020, Monthly Notices of the Royal AstronomicalSociety, 492, 2553Almeida I., Nemmen R., Wong K.-W., Wu Q., Irwin J. A., 2018, MNRAS,475, 5398Asensio Ramos A., Ramos Almeida C., 2009, ApJAsmus D., Hönig S., Gandhi P., Smette A., Duschl W., 2014, MNRAS, 439,1648Ball N. M., Brunner R. J., Myers A. D., Strand N. E., Alberts S. L., TchengD., Llorà X., 2007, The Astrophysical Journal, 663, 774Bandyopadhyay B., Xie F.-G., Nagar N. M., Schleicher D. R., RamakrishnanV., Arévalo P., López E., Diaz Y., 2019, Monthly Notices of the RoyalAstronomical Society, 490, 4606Banerji M., et al., 2010, Monthly Notices of the Royal Astronomical Society,406, 342Bell E. F., et al., 2004, ApJ, 608, 752Bergstra J., Bengio Y., 2012, J. Mach. Learn. Res., 13, 281–305Biretta J. A., Sparks W. B., Macchetto F., 1999, ApJ, 520, 621Blandford R. D., Begelman M. C., 1999, MNRAS, 303, L1Breen P. G., Foley C. N., Boekholt T., Zwart S. P., 2020, Monthly Noticesof the Royal Astronomical Society, 494, 2465–2470Bundy K., et al., 2006, ApJ, 651, 120Capetti A., Kleijn G. V., Chiaberge M., 2005, A&A, 439, 935Comrie A. C., 1997, Journal of the Air & Waste Management AssociationMNRAS000
Abramowicz M. A., Fragile P. C., 2013, Living Reviews in Relativity, 16, 1 Agudo I., Thum C., Gómez J., Wiesemeyer H., 2014, A&A, 566, A59Almeida I., Nemmen R., 2020, Monthly Notices of the Royal AstronomicalSociety, 492, 2553Almeida I., Nemmen R., Wong K.-W., Wu Q., Irwin J. A., 2018, MNRAS,475, 5398Asensio Ramos A., Ramos Almeida C., 2009, ApJAsmus D., Hönig S., Gandhi P., Smette A., Duschl W., 2014, MNRAS, 439,1648Ball N. M., Brunner R. J., Myers A. D., Strand N. E., Alberts S. L., TchengD., Llorà X., 2007, The Astrophysical Journal, 663, 774Bandyopadhyay B., Xie F.-G., Nagar N. M., Schleicher D. R., RamakrishnanV., Arévalo P., López E., Diaz Y., 2019, Monthly Notices of the RoyalAstronomical Society, 490, 4606Banerji M., et al., 2010, Monthly Notices of the Royal Astronomical Society,406, 342Bell E. F., et al., 2004, ApJ, 608, 752Bergstra J., Bengio Y., 2012, J. Mach. Learn. Res., 13, 281–305Biretta J. A., Sparks W. B., Macchetto F., 1999, ApJ, 520, 621Blandford R. D., Begelman M. C., 1999, MNRAS, 303, L1Breen P. G., Foley C. N., Boekholt T., Zwart S. P., 2020, Monthly Noticesof the Royal Astronomical Society, 494, 2465–2470Bundy K., et al., 2006, ApJ, 651, 120Capetti A., Kleijn G. V., Chiaberge M., 2005, A&A, 439, 935Comrie A. C., 1997, Journal of the Air & Waste Management AssociationMNRAS000 , 1–9 (2021)
Almeida et al.
Doeleman S. S., et al., 2012, Science, 338, 355Event Horizon Telescope Collaboration et al., 2019, ApJ, 875, L1Faber S. M., et al., 2007, ApJ, 665, 265Fathivavsari H., 2020, Deep Learning Prediction of Quasars Broad Ly-alphaEmission Line ( arXiv:2006.05124 )Felten J. E., 1968, The Astrophysical Journal, 151, 861Ferrarese L., Ford H. C., Jaffe W., 1996, ApJ, 470, 444Finke J. D., Dermer C. D., Böttcher M., 2008, ApJ, 686, 181Firth A. E., Lahav O., Somerville R. S., 2003, Monthly Notices of the RoyalAstronomical Society, 339, 1195Foreman-Mackey D., 2016, The Journal of Open Source Software, 24Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125,306George D., Huerta E., 2018, Physics Letters B, 778, 64–70Giovannini G., Feretti L., Comoretto G., 1990, The Astrophysical Journal,358, 159Gonzalez-Martin O., Masegosa J., Márquez I., Guerrero M. A., Dultzin-Hacyan D., 2006, A&A, 460, 45Goodman J., Weare J., 2010, Communications in applied mathematics andcomputational science, 5, 65Gu Q.-S., Huang J.-S., Wilson G., Fazio G., 2007, ApJ, 671, L105Ho L. C., 1999, ApJ, 516, 672Ho L. C., 2008, ARA&A, 46, 475Hunter J. D., 2007, Computing in science & engineering, 9, 90Ilbert O., et al., 2010, ApJ, 709, 644Jones D. L., Wehrle A. E., 1997, ApJ, 484, 186Junor W., Biretta J. A., 1995, The Astronomical Journal, 109, 500Kelley H. J., 1960, Ars Journal, 30, 947Kingma D., Ba J., 2014, International Conference on Learning Representa-tionsKuo C. Y., et al., 2014, ApJ, 783, L33Lauer T. R., et al., 2005, The Astronomical Journal, 129, 2138Lazio T. J. W., Waltman E. B., Ghigo F. D., Fiedler R. L., Foster R. S.,Johnston K. J., 2001, ApJS, 136, 265LeCun Y., Bengio Y., Hinton G., 2015, nature, 521, 436LeNail A., 2019, Journal of Open Source Software, 4, 747Lee S.-S., Lobanov A. P., Krichbaum T. P., Witzel A., Zensus A., BremerM., Greve A., Grewing M., 2008, The Astronomical Journal, 136, 159Leshno M., Lin V. Y., Pinkus A., Schocken S., 1993, Neural networksLiew-Cain C. L., Kawata D., Sanchez-Blazquez P., Ferreras I., Symeoni-dis M., 2020, Constraining stellar population parameters from nar-row band photometric surveys using convolutional neural networks( arXiv:2002.08278 )Liu H., Wu Q., 2013, ApJ, 764, 17Lonsdale C. J., Doeleman S. S., Phillips R. B., 1998, The AstronomicalJournal, 116, 8Marulanda J. P., Santa C., Romano A. E., 2020, Deep learning GravitationalWave Detection in the Frequency Domain ( arXiv:2004.01050 )McCulloch W. S., Pitts W., 1943, The bulletin of mathematical biophysics,5, 115McKinney W.,Millman K. J., Aivazis M., 2011, Computing in Science & Engineering, 13,9Morabito D., Niell A., Preston R., Linfield R., Wehrle A., Faulkner J., 1986,The Astronomical Journal, 91, 1038Nagar N. M., Falcke H., Wilson A. S., 2005, A&A, 435, 521Narayan R., Yi I., 1995, ApJ, 452, 710Narayan R., Yi I., Mahadevan R., 1995, Nature, 374, 623Narayan R., Mahadevan R., Grindlay J. E., Popham R. G., Gammie C., 1998,ApJ, 492, 554Nemmen R. S., Storchi-Bergmann T., Yuan F., Eracleous M., Terashima Y.,Wilson A. S., 2006, ApJ, 643, 652Nemmen R. S., Storchi-Bergmann T., Eracleous M., 2014, MNRAS, 438,2804Odewahn S., 1995, Publications of the Astronomical Society of the PacificOliphant T. E., 2007, Computing in Science & Engineering, 9, 10Pacheco-Sanchez J., Alejo R., Cruz-Reyes H., Álvarez Ramírez F., 2019,Fuel Paczyńsky B., Wiita P. J., 1980, A&A, 88, 23Perlman E. S., Sparks W. B., Radomski J., Packham C., Fisher R. S., PiñaR., Biretta J. A., 2001, The Astrophysical Journal Letters, 561, L51Prieto M. A., Fernández-Ontiveros J. A., Markoff S., Espada D., González-Martín O., 2016, MNRAS, 457, 3801Quataert E., Gruzinov A., 1999, ApJ, 520, 248Rodriguez A. C., Kacprzak T., Lucchi A., Amara A., Sgier R., Fluri J.,Hofmann T., Refregier A., 2018, Computational Astrophysics and Cos-mology, 5Rohde D. J., Drinkwater M. J., Gallagher M. R., Downs T., Doyle M. T.,2005, Monthly Notices of the Royal Astronomical Society, 360, 69Ruder S., 2016, arXiv preprint arXiv:1609.04747Schreier E. J., Gorenstein P., Feigelson E. D., 1982, The AstrophysicalJournal, 261, 42Shakura N. I., Sunyaev R. A., 1973, A&A, 24, 337Sharma P., Quataert E., Hammett G. W., Stone J. M., 2007, ApJ, 667, 714Sikora M., Stawarz Ł., Lasota J.-P., 2007, ApJ, 658, 815Spada M., Ghisellini G., Lazzati D., Celotti A., 2001, MNRAS, 325, 1559Specht D. F., 1991, IEEE transactions on neural networksStorrie-Lombardi M., Lahav O., Sodre Jr L., Storrie-Lombardi L., 1992,MNRASTakami H., 2011, MNRAS, 413, 1845Terashima Y., Iyomoto N., Ho L. C., Ptak A. F., 2002, ApJS, 139, 1Tremaine S., et al., 2002, ApJ, 574, 740Ulvestad J. S., Ho L. C., 2001, ApJ, 562, L133Valdés J. J., Bonham-Carter G., 2006, Neural Networks, 19, 196Van Der Walt S., Colbert S. C., Varoquaux G., 2011, Computing in Science& Engineering, 13, 22Verdoes Kleijn G. A., Baum S. A., de Zeeuw P. T., O’Dea C. P., 2002, AJ,123, 1334Virtanen P., et al., 2019, arXiv e-prints, p. arXiv:1907.10121Wan E. A., 1990, Trans. Neur. Netw.Whysong D., Antonucci R., 2004, The Astrophysical Journal, 602, 116Wong K.-W., Irwin J. A., Shcherbakov R. V., Yukita M., Million E. T.,Bregman J. N., 2014, ApJ, 780, 9Woo J.-H., Urry C. M., 2002, ApJ, 579, 530Wu Q., Yuan F., Cao X., 2007, ApJ, 669, 96Yu Z., Yuan F., Ho L. C., 2011, ApJ, 726, 87Yuan F., Narayan R., 2014, ARA&A, 52, 529Yuan F., Quataert E., Narayan R., 2003, ApJ, 598, 301Yuan F., Wu M., Bu D., 2012, ApJ, 761, 129Yuan F., Gan Z., Narayan R., Sadowski A., Bu D., Bai X.-N., 2015, ApJ,804, 101Zezas A., Birkinshaw M., Worrall D., Peters A., Fabbiano G., 2005, ApJ,627, 711de Menezes R., Nemmen R., Finke J. D., Almeida I., Rani B., 2020, MonthlyNotices of the Royal Astronomical Society
APPENDIX A: OBSERVATIONAL DATA
The observational data of the modelled galaxies are available intables A1-A3. Data for M87 were extracted from Prieto et al. (2016)and data for NGC315 and NGC4261 were the same as presented byde Menezes et al. (2020).
MNRAS , 1–9 (2021) eep Learning model for LLAGNs emission 𝜈 (Hz) 𝜈𝐿 𝜈 (erg s − ) Reference1.60E+09 1.87E+038 Giovannini et al. (1990)8.40E+09 1.41E+039 Morabito et al. (1986)2.20E+10 2.48E+039 Junor & Biretta (1995)8.60E+10 4.43E+039 Lee et al. (2008)1.00E+11 1.61E+040 Lonsdale et al. (1998)2.30E+11 7.25E+040 Doeleman et al. (2012)2.60E+13 1.09E+041 Whysong & Antonucci (2004)2.80E+13 1.51E+041 Perlman et al. (2001)2.47E+14 1.28E+041 Prieto et al. (2016)3.32E+14 1.39E+041 Prieto et al. (2016)3.70E+14 7.55E+040 Prieto et al. (2016)4.99E+14 6.81E+040 Prieto et al. (2016)6.32E+14 8.40E+040 Prieto et al. (2016)8.93E+14 5.15E+040 Prieto et al. (2016)1.10E+15 4.53E+040 Prieto et al. (2016)1.27E+15 7.40E+040 Prieto et al. (2016)1.36E+15 4.73E+040 Prieto et al. (2016)2.06E+15 2.75E+040 Prieto et al. (2016)2.42E+17 1.95E+040 Prieto et al. (2016)2.42E+18 1.79E+040 Prieto et al. (2016) Table A1.
SED data for M87. 𝜈 (Hz) 𝜈𝐿 𝜈 (erg s − ) Reference1.63E+09 2.40E+38 Jones & Wehrle (1997)5.00E+09 5.88E+38 Nagar et al. (2005)8.39E+09 1.24E+39 Jones & Wehrle (1997)1.50E+10 6.71E+39 Nagar et al. (2005)1.66E+13 (5 . ± . . ± . Table A2.
SED data for NGC 4261. 𝜈 (Hz) 𝜈𝐿 𝜈 (erg s − ) Reference1.40E+09 2.86E+39 Capetti et al. (2005)2.50E+09 5.28E+39 Lazio et al. (2001)5.00E+09 9.11E+39 Nagar et al. (2005)1.50E+10 3.68E+40 Nagar et al. (2005)8.62E+10 (2 . ± . . ± . . ± . . ± . . ± . . ± . Table A3.
SED data for NGC 315.
APPENDIX B: PARAMETER DISTRIBUTION
In figures B1-B3 we present the posterior distributions of ourfree parameters from the SED fits in figures 2-4. The plot was doneusing the
Python package corner (Foreman-Mackey 2016). Thevalues presented in table 1 are the mean of the distribution andthe uncertainties reported are correspondent to 1 𝜎 . We showed the parameters in the following order: 𝛿 , (cid:164) 𝑀 , 𝑠 , (cid:164) 𝑀 𝑗 , 𝑝 , 𝜖 𝐸 , 𝜖 𝐵 – thefirst three from the RIAF modeling, and the last four from the jetmodeling. APPENDIX C: NEURAL NETWORK DIAGNOSTICS
We built AGNNES with two different NNs: one for the RIAFcomponent, another for the jet. Figures C2-C3 show how close isAGNNES prediction to the original calculation. C2 is the RIAFcomponent and C3 is the jet component. In these plots, we are usingsome SEDs from the validation sample.For C4 and C5 we plotted the original value of SED againstAGNNES’s prediction for several frequencies, respectively theRIAF and jet components. The perfect result should be a straightline 𝑦 = 𝑥 , our results were very close to this. The further the pointis from the line 𝑥 = 𝑦 , the higher is the error in the NN predic-tion. Some of the simulations are not physically correct, so theseare underrepresented since the model learns mostly from physicallyaccurate simulations. Another possibility to improve the results ofthe 𝑥 = 𝑦 is to feed more data to the model with every emission lineshape equally represented. Finally, statistical learning is the base ofNN models, so they learn based on an error function and its deriva-tives. Even NNs with high accuracies have an error associated. NNswith accuracy equals to 1 are often overfitted and cannot generalizewell. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000
We built AGNNES with two different NNs: one for the RIAFcomponent, another for the jet. Figures C2-C3 show how close isAGNNES prediction to the original calculation. C2 is the RIAFcomponent and C3 is the jet component. In these plots, we are usingsome SEDs from the validation sample.For C4 and C5 we plotted the original value of SED againstAGNNES’s prediction for several frequencies, respectively theRIAF and jet components. The perfect result should be a straightline 𝑦 = 𝑥 , our results were very close to this. The further the pointis from the line 𝑥 = 𝑦 , the higher is the error in the NN predic-tion. Some of the simulations are not physically correct, so theseare underrepresented since the model learns mostly from physicallyaccurate simulations. Another possibility to improve the results ofthe 𝑥 = 𝑦 is to feed more data to the model with every emission lineshape equally represented. Finally, statistical learning is the base ofNN models, so they learn based on an error function and its deriva-tives. Even NNs with high accuracies have an error associated. NNswith accuracy equals to 1 are often overfitted and cannot generalizewell. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000 , 1–9 (2021) Almeida et al.
Figure B1.
Corner plot for the fit parameters of M 87. In the main diagonal were plotted the posteriori distribution of the parameters. The other plots show thecorrelation between each pair of variables. MNRAS , 1–9 (2021) eep Learning model for LLAGNs emission Figure B2.
Corner plot for the fit parameters of NGC 4261. In the main diagonal were plotted the posteriori distribution of the parameters. The other plotsshow the correlation between each pair of variables.MNRAS000
Corner plot for the fit parameters of NGC 4261. In the main diagonal were plotted the posteriori distribution of the parameters. The other plotsshow the correlation between each pair of variables.MNRAS000 , 1–9 (2021) Almeida et al.
Figure B3.
Corner plot for the fit parameters of NGC 315. In the main diagonal were plotted the posteriori distribution of the parameters. The other plots showthe correlation between each pair of variables. MNRAS , 1–9 (2021) eep Learning model for LLAGNs emission (a) NN architecture for RIAF(b) NN architecture for Jet Figure C1.
The architecture (a) is the one used to predict the emission lines from RIAF mode and (b) to predict the emission line from jets.MNRAS000
The architecture (a) is the one used to predict the emission lines from RIAF mode and (b) to predict the emission line from jets.MNRAS000 , 1–9 (2021) Almeida et al.
Figure C2.
Plots comparing AGNNES output with the expected value for the RIAF component. MNRAS , 1–9 (2021) eep Learning model for LLAGNs emission Figure C3.
Plots comparing AGNNES output with the expected value for the jet component.MNRAS000
Plots comparing AGNNES output with the expected value for the jet component.MNRAS000 , 1–9 (2021) Almeida et al.
Figure C4.
From the validation data set, we selected frequencies and plotted the SED value generated by the original code and the SED predicted by AGNNESfor the RIAF component, respectively y-axis and x-axis. The perfect fit is the thin curve 𝑦 = 𝑥 plotted in red. MNRAS , 1–9 (2021) eep Learning model for LLAGNs emission Figure C5.
From the validation data set, we selected frequencies and plotted the SED value generated by the original code and the SED predicted by AGNNESfor the jet component, respectively y-axis and x-axis. The perfect fit is the thin curve 𝑦 = 𝑥 plotted in red.MNRAS000