KilonovaSCORER Ranking Framework

• KilonovaSCORER is a quantitative framework that scores and ranks kilonova candidates using sparse early-time multi-band photometry and gravitational-wave context.
• It integrates diverse methodologies—analytic detectability, GW forward modeling, heuristic ranking, and machine-learning TCN classification—to prioritize transients under real-time constraints.
• The framework employs prior-predictive scoring and sequential ABC diagnostics, enabling rapid candidate re-evaluation as new observations become available.

Searching arXiv for KilonovaSCORER and closely related kilonova scoring/ranking methods. KilonovaSCORER is a quantitative framework for scoring and ranking candidate kilonovae during gravitational-wave and multimessenger follow-up. In its explicit 2026 formulation, it is an open-source system for sparse early-time, multi-band photometry that compares observations in absolute-magnitude space against a physically motivated kilonova prior-predictive grid by means of two per-observation metrics and a sequential Approximate Bayesian Computation (ABC) diagnostic (Darc et al., 24 Apr 2026). In related literature, closely allied “KilonovaSCORER”-style workflows also denote analytic detectability calculations, GW-conditioned forward light-curve synthesis, heuristic multiplicative ranking, and temporal-convolutional classification, all aimed at the same operational problem: prioritizing the small subset of transients most consistent with kilonova expectations under severe real-time constraints (Guessoum et al., 2019).

1. Scope, lineage, and methodological variants

The literature uses KilonovaSCORER in more than one technical sense. Some formulations are analytic and physics-first, asking when a kilonova should outshine a gamma-ray-burst afterglow. Others are GW-conditioned forward models that propagate posterior samples in binary and equation-of-state space into ejecta properties and expected light curves. More recent formulations are explicit ranking systems for transient streams, either as interpretable multiplicative scores or as prior-predictive photometric consistency scores. Survey-oriented work also includes neural classifiers trained on simulated light curves plus GW contextual information (Nicholl et al., 2021, Franz et al., 20 Oct 2025, Liang et al., 2023, Darc et al., 24 Apr 2026).

Variant	Core quantity	Primary inputs
Analytic detectability	$$F_{\nu,\mathrm{KN}}(t_{\rm peak}) > F_{\nu,\mathrm{AG}}(t_{\rm peak})$$	$E_{52}$, $n$ or $A_*$, $M_{\rm ej}$, $v$, $\kappa$
GW forward model	fraction of samples with $S>$ threshold or mean detection probability	$\mathcal{M}$, $q$, $E_{52}$0, $E_{52}$1, $E_{52}$2, distance
Heuristic ranking	$E_{52}$3	sky map, host redshift, catalogs, light curve
TCN classification	$E_{52}$4	5-day multi-band photometry plus GW context
Prior-predictive scoring	cumulative $E_{52}$5, $E_{52}$6, ABC $E_{52}$7	absolute magnitudes, uncertainties, model grid

Earlier survey practice already established many of the operational ingredients later absorbed into KilonovaSCORER-style pipelines: Monte Carlo transient simulation, selection cuts, host-dependent efficiency corrections, and explicit background estimation. In the Dark Energy Survey search for kilonovae, SNANA simulations were used to optimize 14 selection requirements, model supernova backgrounds, and derive upper limits from an untriggered optical search, thereby providing a survey-engineering precursor to later ranking systems (Doctor et al., 2016).

A common misconception is that KilonovaSCORER refers to one fixed algorithm. The published record instead shows a family of scoring and detectability methods, linked by their use of physically motivated kilonova expectations, GW context, and rapid candidate triage.

2. Physical basis: ejecta models, afterglow competition, and forward synthesis

The simplest KilonovaSCORER formulation is the detectability analysis of kilonova or supernova imprints in short-GRB afterglows. In that framework, the kilonova peak time and peak luminosity follow power-law scalings with ejecta mass $E_{52}$8, expansion velocity $E_{52}$9, and opacity $n$0. A representative source-frame peak-time relation is

$n$1

with a representative peak luminosity

$n$2

The competing afterglow flux is evaluated in the slow-cooling regime $n$3, with distinct scalings before and after the jet break in both a uniform interstellar medium and a stellar-wind medium. Detectability is encoded by the inequality $n$4, which yields boundary curves in the $n$5 or $n$6 plane. In the pre-jet-break ISM case with $n$7, the resulting boundary has the scaling $n$8 (Guessoum et al., 2019).

Later GW-conditioned formulations moved from visibility boundaries to light-curve synthesis. In the Nicholl et al. framework, the inputs are GW observables $n$9, $A_*$0, and $A_*$1, together with EOS parameters $A_*$2 and $A_*$3. Quasi-universal relations are used to derive $A_*$4, compactness $A_*$5, and neutron-star radii $A_*$6; ejecta are decomposed into dynamical and viscous-wind components, with optional cocoon emission. The diffusion time for each component is

$A_*$7

and the component luminosity is

$A_*$8

with $A_*$9 over blue, red, wind, and optional cocoon components. That framework was implemented in the public MOSFiT package and used for low-latency synthesis of kilonova samples from GW source parameters (Nicholl et al., 2021).

Related physically motivated grids further widened the modeling space available to scoring systems. The semi-analytic model applied to AT2017gfo uses three axisymmetric ejecta components—dynamic, wind, and secular outflows—discretized into $M_{\rm ej}$0 angular bins and evolved with homologous expansion, diffusion, and blackbody photospheres. It constrained the total ejected mass of AT2017gfo to $M_{\rm ej}$1–$M_{\rm ej}$2, the observation angle to between $M_{\rm ej}$3 and $M_{\rm ej}$4, and the disk mass to $M_{\rm ej}$5 (Perego et al., 2017). For BH–NS mergers, POSSIS-based modeling supplies an empirical inversion between 1-day $M_{\rm ej}$6-band absolute magnitude and total unbound mass,

$M_{\rm ej}$7

calibrated over $M_{\rm ej}$8 and $M_{\rm ej}$9, which enables rapid ejecta-mass inference without rerunning radiative transfer (Mathias et al., 2023).

This physical layer is foundational. KilonovaSCORER does not operate on photometry alone; its ranking behavior is determined by the kilonova family it assumes, the ejecta decomposition it permits, and the way it couples that family to distance and observing cadence.

3. Scoring formulations

One explicit ranking formulation is the multiplicative algorithm introduced in the S250818k case study. Its total score is

$v$0

Here $v$1 is a sky-localization score obtained by integrating the GW probability over all pixels with probability density at least as high as the candidate’s pixel; $v$2 is the maximum overlap integral between the GW distance posterior and Gaussian distance kernels derived from candidate-host redshifts within $v$3 and $v$4; $v$5 penalizes matches to stellar-variability catalogs; and $v$6 penalizes known minor planets within $v$7. The photometric term factorizes as

$v$8

with soft penalties of $v$9 rather than hard zeros. The four photometric tests are pre-merger detections in forced ATLAS photometry over 180 days, decline rates relative to the threshold $\kappa$0, rise times relative to $\kappa$1 days, and peak specific luminosity relative to the conservative upper bound $\kappa$2. A practical follow-up threshold is $\kappa$3 (Franz et al., 20 Oct 2025).

The 2026 framework replaces binary or near-binary photometric penalties with prior-predictive probabilities. For an observed absolute magnitude $\kappa$4 with uncertainty $\kappa$5, the model grid defines a noise-convolved prior-predictive distribution $\kappa$6. Two per-observation metrics are then computed. The first is a two-sided tail probability,

$\kappa$7

where $\kappa$8 is the cumulative distribution function of $\kappa$9. The second is a local “near” probability,

$S>$0

with a Region of Practical Equivalence

$S>$1

and fiducial $S>$2. Scores from different epochs and bands are aggregated in logit space through inverse-variance weighting: $S>$3 followed by

$S>$4

A sequential ABC diagnostic monitors whether any single model in the prior grid remains consistent with all epochs,

$S>$5

If $S>$6 at any epoch, the cumulative $S>$7 is set to zero thereafter (Darc et al., 24 Apr 2026).

A third formulation is posterior-sampling based rather than deterministic ranking. In the Nicholl et al. implementation, one draws $S>$8 samples from GW posteriors for $S>$9, computes ejecta properties and synthetic light curves for each draw, converts $\mathcal{M}$0 to filter magnitudes, and defines a detectability metric

$\mathcal{M}$1

or a probability of $\mathcal{M}$2. The kilonova score is then the fraction of samples with $\mathcal{M}$3 threshold or the mean detection probability over the posterior (Nicholl et al., 2021).

These formulations differ in mathematical form, but all are model-relative consistency measures rather than generic anomaly scores.

4. Machine-learning classification and survey triage

The survey-classification branch of KilonovaSCORER uses a causal Temporal-Convolutional Network (TCN) with residual blocks, based on Bai et al. and modified in the style of RAPID and El-CID for short-timescale transients. The input is a time-series matrix $\mathcal{M}$4 with $\mathcal{M}$5 time steps over 0–5 days at $\mathcal{M}$6 day, $\mathcal{M}$7 photometric bands $\mathcal{M}$8, and $\mathcal{M}$9 contextual features injected as constant channels at each time step. The contextual features tested are the GW line-of-sight localization probability $q$0 and the luminosity-distance posterior mean and width $q$1. The network uses two residual blocks with dilation $q$2 and $q$3, kernel size $q$4, 64 filters, ReLU activation, weight normalization, optional Dropout(0.1), and skip connections; the two-block sequence is repeated twice, then global average pooling feeds a Dense(2) and Softmax layer returning $q$5 (Liang et al., 2023).

The training set in the WFST study contains 77,005 simulated objects. Kilonovae were drawn from two-component POSSIS/Bulla and grey-opacity MOSFiT models; contaminants included SNIa, SNIbc, SNIIn, SNIIP, SLSN-I, and SNIa-91bg populations. Training used categorical cross-entropy, Adam with learning rate $q$6, batch size 128, and 50 epochs. At threshold $q$7, the best PMD model achieved precision $q$8 and recall $q$9 for the kilonova class, with $E_{52}$00. Time-dependent accuracy reached KN $E_{52}$01 and Other $E_{52}$02 by 3 days, and the estimated probability of inclusion for a true kilonova was $E_{52}$03 when selecting 20 candidates among $E_{52}$04 survivors (Liang et al., 2023).

This classifier sits downstream of standard survey vetting. In the same WFST pipeline, real-bogus filtering and catalog cross-matching reduce the nightly transient stream to $E_{52}$05 candidates before the TCN ranks them by $E_{52}$06. The design therefore complements rather than replaces hard vetoes and image-domain quality control.

The survey-search precursor is the Dark Energy Survey kilonova analysis. There, a theoretically predicted r-process optical transient was searched for using griz broadband data, with KN and SN simulations generated in SNANA to optimize selection requirements and predict backgrounds. Operational cuts included a simultaneous $E_{52}$07- and $E_{52}$08-band trigger, red-color requirements, pre-trigger non-detections, post-trigger fading, and an asteroid veto via centroid separation. That analysis found 0 events, consistent with a predicted 1.1 background events, and set 90 percent upper limits on the volumetric rate ranging from $E_{52}$09 for the dimmest model considered to $E_{52}$10 for the brightest, with host-galaxy subtraction effects degrading efficiency (Doctor et al., 2016).

5. Empirical behavior on real events and simulations

AT2017gfo is the principal positive control across multiple KilonovaSCORER variants. In the 2026 prior-predictive framework, when early follow-up is emulated as one detection per band per night in $E_{52}$11, $E_{52}$12 in each band for $E_{52}$13 days. The cumulative $E_{52}$14 is $E_{52}$15 on night 1, $E_{52}$16 on night 2, and stabilizes to $E_{52}$17 by day 5; the ABC survival fraction declines gently but never reaches zero. In the S250818k multiplicative ranking scheme, AT2017gfo obtains $E_{52}$18, illustrating that a confirmed kilonova need not score near unity (Darc et al., 24 Apr 2026, Franz et al., 20 Oct 2025).

Negative controls are equally informative. SN 2025ulz initially resembled a plausible kilonova candidate after S250818k: in the multiplicative framework it began at $E_{52}$19, with $E_{52}$20 and $E_{52}$21, but after spectroscopic redshift acquisition at $E_{52}$22 days its distance overlap fell to $E_{52}$23; once its light curve re-brightened at $E_{52}$24 days, the photometric sub-scores dropped to $E_{52}$25 and the total score fell to $E_{52}$26. In the prior-predictive framework, its early behavior likewise gave $E_{52}$27 and cumulative $E_{52}$28, but the ABC survival fraction collapsed to zero at $E_{52}$29 days, forcing the cumulative score to zero thereafter. Among the 121 TNS transients within the 95% contour, there were already $E_{52}$30 higher-scoring candidates at $E_{52}$31 days, $E_{52}$32 at $E_{52}$33 days, and $E_{52}$34 by $E_{52}$35 days (Franz et al., 20 Oct 2025, Darc et al., 24 Apr 2026).

The WFST classifier exhibits the same pattern. AT2017gfo reaches $E_{52}$36 by day 2 in the PMD model, whereas AT2019npv, a SN Ibc near GW190814, has early $E_{52}$37 because of its fast decline but falls to $E_{52}$38 after 3 days, correctly reverting to the non-kilonova class. The stated lesson is that sparse early photometry can yield high $E_{52}$39 for non-KN sources and that multi-epoch coverage is therefore critical (Liang et al., 2023).

Rubin/LSST Target-of-Opportunity simulations quantify the same separation statistically. Under a “silver” cadence of $E_{52}$40 each night for 4 nights, median cumulative $E_{52}$41 for BNS kilonovae is $E_{52}$42 at day 1 and $E_{52}$43 at day 4, while NSBH kilonovae start at $E_{52}$44 and decline to $E_{52}$45. By contrast, Type Ia supernovae have median $E_{52}$46 at day 2 and collapse to zero by day 4; shock-cooling core-collapse supernovae are zero by day 3–4; and CSM-interacting supernovae are zero by day 2. The framework thus recovers kilonova candidates with high confidence while ruling out supernova contaminants within five days of the GW trigger (Darc et al., 24 Apr 2026).

6. Interpretation, limitations, and extensions

KilonovaSCORER is deliberately interpretable, but its outputs are conditioned on modeling choices. In the S250818k ranking algorithm, transparency comes from the fact that each term has an explicit astrophysical meaning—sky localization, distance overlap, catalog vetting, or photometric behavior—but the same paper identifies a limitation: all factors are multiplicative and binary $E_{52}$47 versus $E_{52}$48 except the continuous $E_{52}$49 and $E_{52}$50. Future versions were explicitly suggested to replace the decline-rate, rise-time, and peak-luminosity penalties with smoothly graded scores and to add color-evolution terms (Franz et al., 20 Oct 2025).

The 2026 framework addresses some of these issues by replacing binary photometric tests with prior-predictive probabilities and inverse-variance aggregation in logit space. This naturally down-weights uncertain epochs and supports sequential updates. Its hard ABC penalization, however, is still grid-dependent: a score of zero means that no single prior-sampled model in the adopted kilonova family explains all epochs, not that the transient is uninteresting in a broader astrophysical sense. This suggests that model breadth is operationally as important as statistical machinery (Darc et al., 24 Apr 2026).

Model dependence also enters through the forward physics. GW-conditioned synthesis depends on quasi-universal relations, ejecta-mass fits, opacity prescriptions, and priors on $E_{52}$51, $E_{52}$52, $E_{52}$53, and $E_{52}$54. In the Nicholl et al. framework, these ingredients enabled not only detectability forecasts but also EOS inference, including $E_{52}$55 and $E_{52}$56 km after re-weighting with an EOS prior that supports the fitted $E_{52}$57 range (Nicholl et al., 2021). For BH–NS applications, the ejecta-mass inversion based on POSSIS carries $E_{52}$58 uncertainty in $E_{52}$59, with combined photometric, opacity, and modeling systematics reaching $E_{52}$60 mag, and the underlying fits assume aligned spin and fixed $E_{52}$61 values (Mathias et al., 2023).

A further misconception is that high scores alone certify merger association. The case studies show the opposite. Confirmed kilonovae need not achieve values near one, and some supernovae can score highly during the first few days if only sparse photometry is available. What separates the methods is therefore not only their initial ranking power but their capacity for rapid score revision as new epochs arrive.

Operationally, the framework is designed for integration rather than isolation. The 2026 implementation provides a public repository, pre-binned prior-predictive grids, a CLI and API, and direct integration paths to the Tool for Rapid Object Vetting and Examination, LSST alert brokers such as Fink, ALeRCE, and ANTARES, and Target and Observation Managers. In that setting, KilonovaSCORER functions as a bridge between physically motivated ejecta modeling, GW localization information, and real-time follow-up coordination (Darc et al., 24 Apr 2026).