Radiative Transfer Modeling of Stripped-envelope Supernovae II: Neural Network Emulation of Light Curves

The paper presents the first neural-network emulator of stripped-envelope supernova (SESN) light curves, trained on a grid of 4499 light curves simulated with the radiative transfer (RT) code SEDONA. Using this emulator, the authors show that mNi, mej, the ejecta velocity profile, and the degree of 56Ni mixing can all be inferred from multiband light curves. They find that the degeneracy between ejecta mass and ejecta velocity is substantially weaker with this emulator than in traditional semianalytical models. The emulator is able to independently constrain the influence of ejecta mass and of ejecta velocity on the resulting light curve, rather than making them degenerate by design as traditional semianalytical models do. They additionally show that this inference is significantly more accurate than that done by the classical Arnett model for both simulated ZTF-like and LSST-like light curves. Finally, they present light curve fits to three well-studied SESNe: SN 1994I, SN 2007gr, and iPTF13bvn, constraining their mNi, mej, and 56Ni mixing.

The emulator has a multilayer perceptron (MLP) architecture, with five hidden layers and 2000 neurons per layer. The network was trained with a learning decay rate of 0.85, batch size of 512, and for 150 epochs. The network takes ten inputs: the nine physical parameters described above and time after explosion. The emulator is trained to predict a downsampled version of the spectrum (R≈ 30) due to substantial noise when predicting the full-resolution simulations. These downsampled spectra have only 41 log-uniformly spaced wavelengths over the same wavelength range. Training on downsampled spectra does not result in a loss in accuracy of the emulated light curve.

The emulator is least accurate at early epochs, before ∼ 18 days after explosion. These early epochs correspond to the rise phase of the light curve, when the light-curve shape evolves fastest and is most diverse across the grid. Approximately 80% of the grid light curves do not peak until later (median griz peak ≈ 25 days). The RMS of the reconstructed versus SEDONA light curve is ≈ 0.5 mag immediately at 5 days after explosion (when simulations start). The RMS value then decreases to ≈ 0.145 mag by day 18 and remains constant until day 50. Aside from time after explosion, the emulator’s performance is not dependent on any other physical parameter. Crucially, the uncertainty of the emulator presented here is comparable to the typical magnitude error in observed SESN light curves, meaning that it is important to quantify this uncertainty during inference. A significantly larger light curve grid (possibly exceeding ∼10,000 simulated light curves) would be necessary to train an emulator with sufficiently low uncertainty.

In addition to measuring the emulator’s systematic error in reproducing SEDONA light curves, the authors also estimate SEDONA’s systematic error of modeling true SESN light curves. SEDONA assumes the ejecta profile is always in local thermal equilibrium (LTE), dramatically reducing the computational cost of the radiation transfer calculation. However, a realistic RT simulation of SESN light curves needs to relax LTE assumptions to account for relevant phenomena such as the excitation of 4He by photons from 56Ni decay. Light curves generated from SEDONA will be the most realistic at phases where the LTE assumption is most accurate for the SESN ejecta. This is during light curve peak, and the LTE assumption will be least applicable both immediately after explosion and long after light curve peak. The RMS of CMFGEN versus SEDONA light curves is ∼ 0.4 mag at 5 days after explosion and decreases to ∼ 0.2 mag by 20 days post explosion. Then, the RMS again increases to ∼ 0.35 mag by ∼ 28 days and holds constant until day ∼ 50.

The authors build a new model in the Modular Open Source Fitter for Transients (MOSFiT) to perform light curve inference using this emulator. They account for both sources of systematic error in the MOSFiT fitting pipeline. They fit an analytical function to each of the empirical emulator uncertainty and SEDONA uncertainty curves. The analytical functions for the SEDONA uncertainty and emulator uncertainty in terms of the time since explosion (t) are presented in Equations 1 and 2, respectively. The resulting total uncertainty ranges from ∼ 0.6 mag at 5 days after explosion to a minimum of ∼ 0.24 mag near day 20, rising to ∼ 0.38 mag at late times.

The authors generate light curves with the emulator to match the cadence and filters of observed SESN samples, specifically those from the Bright Transient Survey (BTS) of the Zwicky Transient Facility (ZTF) and those from the LSST. ZTF observes the northern sky in the g and r filters with an average cadence of ∼ 2 days in each filter. SESN light curves from LSST are expected to be observed in ugrizy filters with typical cadences of 21, 11, 4, 6, 6, and 8 days, respectively. To generate light curves with realistic magnitude errors, they calculate the expected brightness-dependent signal-to-noise ratio (SNR) of photometric observations for both surveys. They find that the fits to the LSST-like vs ZTF-like light curves display similar degeneracies and relative constraints (i.e., He mass is poorly constrained in both surveys). They also find that fitting performance is largely similar across parameter space. The only exception to this is for models with either mNi ≥ 0.2M⊙, the resulting mNi and mej posterior distributions are much broader because the underlying light curve grid has a paucity of high-mNi models.

For a representative LSST-like light curve, the authors report which parameters are well versus poorly constrained. The top three rows show the prior and posterior distributions for the nine physical parameters that are directly inputted to the emulator. These have uniform priors, reflecting that the grid is constructed by independently and uniform-randomly sampling from these nine parameters. The bottom row shows rx,95, the “interpretable version” of the mass distribution parameters: the ratio between the velocity containing 95% of the x mass distribution and the maximum ejecta velocity. Because 4He has a negligible influence on the observed light curve, all physical parameters related to the 4He distribution (mHe, ηHe, and r95,He) are poorly constrained. Because the combination of all three of ηvel, minvel, and ∆vel produces the velocity distribution, none of these parameters independently describes the velocity distribution, and the constraints on any one of tends to be more loose than the constraint on the overall velocity distribution. Nevertheless, through the combination of constraints on ηvel, minvel, and ∆vel, the velocity profile is accurately recovered by this inference method. The parameters that describe the 56Ni and bulk mass distributions (ηNi and ηbulk, respectively) are all well recovered by this fit. The median value of the posterior distribution is within 1σ of the true value for both mass distribution parameters. Strong constraints on the interpretable values r95,Ni and r95,bulk can be placed using the inference method.

The authors also present prior and posterior distributions of ejecta profiles. Using draws from the posteriors of the training parameters, they construct distributions of velocity, 4He, 56Ni, and bulk. Because the light curve is produced by photons emitted at the photosphere, it most strongly encodes information about the ejecta layers near the photosphere. Layers deep inside the photosphere contribute little to the light curve, because photons emitted there are thermalized and reabsorbed before reaching the photosphere. Layers far outside the photosphere likewise contribute little, since they contain only a small fraction of the radiating material. The innermost and outermost velocities are poorly constrained by this fit. However, velocities closer to the center of the ejecta profile, where the photosphere lies, are better constrained. The posterior mass distribution is both considerably tighter than the prior and overlaps with the true distribution. Unsurprisingly, the 4He distribution posterior is broader than those of 56Ni and bulk. As such, though the precise numbers that parameterize the velocity and mass distributions are not directly strongly constrained, the velocity and mass distributions are well constrained.

The authors explore the parameter degeneracies via the joint posterior distributions. The joint distribution of mbulk with minvel is weakly correlated, where larger mbulk correlated with larger minvel. This correlation is reminiscent of the Arnett-like degeneracy between mej and vej, where those two parameters are positively correlated. However, they find mbulk and ∆vel are uncorrelated. In their fitting method, the degeneracy between ejecta mass and characteristic ejecta velocity that is implicit in the Arnett model is far weaker. They find instead that the values ∆vel and r95,Ni are strongly anticorrelated. This is because for samples where ∆vel is increased, a nearly identical light curve can be produced by forcing 56Ni to be less mixed into the outer layers. They find a similar anticorrelation between ∆vel and r95,bulk. The fit is able to constrain the velocity containing 95% of 56Ni mass in the ejecta and the velocity containing 95% of the bulk mass.

The authors characterize how well physical parameters can be constrained by the emulator over a range of ejecta profile parameters. In the Arnett model, the ejecta profile is assumed to be a homologously expanding sphere of uniform density. The kinetic energy of such a sphere is KE = (3/10) mej vej2, where mej is the ejecta mass, and vej is the Arnett characteristic ejecta velocity. To compare emulator-fitted velocity to the Arnett-fitted velocity, they calculate which velocity percentile in the grid of models corresponds most closely to the Arnett characteristic ejecta velocity. They find that the 66th percentile velocity of an ejecta profile most closely corresponds to the Arnett characteristic ejecta velocity across the simulation grid. They fit to each simulated light curve with the Arnett model using MOSFiT with the default constant gray opacity of κ = 0.2 cm2 g−1. With this value, the Arnett-inferred mej/vej is systematically offset below its true value by a factor of ∼ 2. Because fitting at an incorrect opacity rescales the inferred mej/vej by √(κtrue/κassumed), this offset implies an effective opacity roughly a factor of four lower. They therefore re-fit the Arnett model with κ = 0.054 cm2 g−1 (a value obtained by fitting the average offset). This new, effective opacity removes the offset.

They find that the emulator recovers mNi, mej, and vej individually more accurately than the Arnett model for both surveys. For mNi, the emulator achieves an RMS of 0.008 M⊙ (LSST) and 0.007 M⊙ (ZTF), versus 0.33 and 0.70 M⊙ for the Arnett model. The emulator error is uniform across the prior range of mNi, whereas the Arnett model systematically overpredicts mNi by ∼ 80% on average for LSST-like light curves and by nearly a factor of three for the ZTF-like light curves. The emulator recovers mej with an RMS of 0.9 M⊙ (LSST) and 1.2 M⊙ (ZTF), versus 2.6 and 3.0 M⊙ for the Arnett model. The Arnett inference is strikingly poor for mej, returning essentially draws from the prior. For vej, the emulator reaches an RMS of ∼ 1340 km s−1 (LSST) and ∼ 1450 km s−1 (ZTF), versus ∼ 3800 and ∼ 17000 km s−1 for the Arnett model. The exceptionally large ZTF Arnett vej RMS is driven by a few catastrophic fits in which the mass–velocity degeneracy drives vej toward the high-velocity edge of the prior (∼ 7×104 km s−1). Excluding these outliers lowers the RMS to ∼ 2900 km s−1. On the degenerate combination mej/vej, the emulator still outperforms Arnett. The emulator recovers it with an RMS of 0.04 and the Arnett model with an RMS of 0.10 (LSST) and 0.09 (ZTF). While by definition the Arnett model can only constrain this degenerate mass-velocity combination, the emulator additionally separates mej and the velocity profile of the ejecta. The emulator can also recover the 56Ni mixing for both surveys. It recovers r95,Ni with an RMS of 0.07 for both LSST-like and ZTF-like light curves, with uniform scatter across the range of 56Ni mixing explored here.

Fits performed to ZTF-like and LSST-like light curves result in similar accuracy in the fitted physical parameters, with ZTF-like light curves recovering mNi marginally better (RMS 0.007 versus 0.008 M⊙) and LSST-like light curves recovering mej better (RMS 0.9 versus 1.2 M⊙). The color evolution of SESN light curves encodes physical information that is well captured by the broad LSST filter set, which may aid the recovery of mej in particular. This result is encouraging for the prospect of physical inference on the upcoming sample of LSST SESN light curves.

The authors present fits to real light curves using the SEDONA emulator. They fit to the same three light curves as Y26: SN 1994I, SN 2007gr, and iPTF13bvn, obtaining photometry from Khakpash et al. (2024). In all three cases, the light curve fits match the observed light curves. Consequently they find broadly the same values for mNi, mej, and the velocity profile here, as was found by Y26. Beyond mNi, mej, and the velocity profile, the inference also constrains the degree of 56Ni mixing (r95,Ni).

For SN 1994I, a type Ic SN detected in the nearby galaxy M51, at luminosity distance of ∼ 7Mpc, the authors infer mNi of 0.048+0.002−0.002 M⊙, mej of 1.954+0.228−0.669 M⊙, and r95,Ni of 0.352+0.180−0.100. While the median of the r95,Ni posterior (0.352) lies in the upper third of the grid prior, the posterior is skewed toward high values, with a tail extending to r95,Ni ∼ 0.7 — well beyond the bulk of the prior. This indicates 56Ni mixed substantially into the outer ejecta layers, consistent with the heavy outward mixing inferred by Sauer et al. (2006) and Yoon et al. (2019). The estimate of mNi is lower than the ∼ 0.07M⊙ that is consistently found by previous light curve studies. Recently, however, Afsariardchi et al. (2021) measured the mNi using the tail of the light curve, finding a mass of ≃ 0.048 M⊙ – identical to the inferred value. The mej posterior for SN 1994I is bimodal, with a dominant family of solutions near mej ≈ 2M⊙ and a secondary family near mej ≈ 1.2M⊙. The two families share a nearly identical mNi but differ in their velocity profiles, with a narrower ∆vel for the lower-mass solution, and both families reproduce the observed light curve comparably well (∆ ln L ≈ 0.8), a manifestation of the residual ejecta mass–velocity degeneracy discussed in Section 3. Furthermore, within the mej posterior distribution, mbulk is constrained to 1.00+0.23−0.33 M⊙ with a single peak. The bimodality in the mej posterior comes from bimodality in the mHe posterior distribution, which is more loosely constrained to be 0.56+0.33−0.37 M⊙.

For SN 2007gr, a Type Ic SN in the nearby galaxy NGC 1058 (dL ≃ 9.3 Mpc), the authors find a posterior distribution of 0.075+0.005−0.006 M⊙ for mNi, of 3.787+0.833−1.157 M⊙ for mej, and a r95,Ni posterior range of 0.377+0.134−0.096, indicating an ejecta profile with 56Ni moderately mixed into the outer layers. They also find that the bulk of the ejecta (the middle ∼90% of the mass) travels between ∼ 103.5 and ∼ 103.9 km s−1, with the outermost layers exceeding 104 km s−1. As before, the mbulk is well constrained to a range of 3.14+0.84−1.00 M⊙, whereas the posterior distribution of mHe reproduces the prior distribution (i.e. is totally unconstrained). All values are consistent with the literature, and the measurable mixing is consistent with the findings of Yoon et al. (2019). Interestingly, in contrast to SN 1994I, Afsariardchi et al. (2021) measured a tail mNi ≃ 0.047, but do not require an additional heating source to account for the discrepancy between the peak and tail (i.e., their β > 0).

For iPTF13bvn, a nearby (dL ≃ 22.5 Mpc) and the first SN Ib with a progenitor detection, the authors infer mNi of 0.05 M⊙, consistent with the Fremling et al. (2014) range [0.037, 0.07] M⊙, and an mej range of [2.5, 3.8] M⊙, somewhat higher than their [1.36, 2.44] M⊙. However, the fit finds ∼ 1M⊙ of the fitted mej is 4He, which is poorly constrained, whereas the fit finds an mbulk range of [1.86, 2.49], which is potentially more consistent with Fremling et al. (2014). iPTF13bvn is the only Type Ib among the three real light curves, and its velocity profile is notably flatter and the 56Ni is less mixed than those of the Type Ic SNe 1994I and 2007gr. The middle ∼90% of the ejecta mass sits near ∼ 103.5 km s−1, rising to ∼ 104.5 km s−1 in the fastest layers. The fit supports weak mixing: they find r95,Ni of [0.1, 0.2], weakly mixed and well below that of SN 1994I, in agreement with Y26 and Yoon et al. (2019).

The key conclusions are:

1. The emulator provides notably more accurate physical parameter recovery than the Arnett model. For simulated LSST-like light curves, the emulator recovers mNi with an RMS error of 0.008 M⊙, compared to 0.33 M⊙ for the Arnett model. Similarly, the emulator recovers mej with an RMS error of 0.9 M⊙, compared to 2.6 M⊙ for the Arnett model.

2. Despite having a lower cadence in each filter than ZTF, LSST-like light curves yield similar recovery of mej and vej across the full parameter space explored here, while 56Ni mixing is recovered comparably well for the two surveys.

3. The Arnett model’s constraining capability lies in the degenerate combination mej/vej rather than in constraining mej and vej separately because of the mass-velocity degeneracy that is implicit in the Arnett model. This degeneracy is weakened with the emulator. The joint posterior distributions of mass parameters and velocity parameters are weakly correlated for every fit performed, suggesting that the emulator is able to largely independently constrain the ejecta mass and the ejecta velocity profile. Reproducing the true mej/vej with the Arnett model further requires an effective gray opacity of κ = 0.054 cm2 g−1, below the commonly assumed 0.1 − 0.2 cm2 g−1.

4. The inference pipeline is applied to three well-studied SESNe: SN 1994I, SN 2007gr, and iPTF13bvn. The inferred mNi for SN 2007gr and iPTF13bvn is, broadly, consistent with literature values. For SN 1994I the inferred mNi (0.048M⊙) falls below the peak-based estimate of ∼ 0.07M⊙ but matches the tail-based measurement of Afsariardchi et al. (2021). The inferred mej is consistent with the literature for SN 2007gr, somewhat higher for iPTF13bvn, and roughly a factor of two above the literature value of ∼ 1M⊙ for SN 1994I. The degree of 56Ni mixing in each event is additionally constrained. The Type Ic SN 1994I and SN 2007gr are both moderately-to-strongly mixed, and the Type Ib iPTF13bvn is weakly mixed.

Improvements to AI Systems:

1. Neural-Network Emulator for Fast Physical Simulations

• Replace slow radiative transfer codes (e.g., SEDONA) with a trained MLP (5 hidden layers, 2000 neurons each) that predicts downsampled spectra (R≈30, 41 wavelengths) from 10 inputs (9 physical parameters + time).

• Improved capability: AI can generate synthetic light curves in milliseconds instead of hours, enabling rapid parameter inference, large-scale survey simulation, and real-time model fitting.

2. Uncertainty-Aware Inference Pipeline

• Integrate two sources of systematic error (emulator error 0.145–0.5 mag, SEDONA model error 0.2–0.4 mag) as time-dependent analytical functions into a Bayesian fitting framework (MOSFiT).

• Improved capability: AI can produce posterior distributions that account for both model and emulator noise, yielding reliable confidence intervals on inferred supernova parameters (e.g., nickel mass, ejecta mass) even with noisy survey data.

3. Breaking Mass–Velocity Degeneracy

• Use the emulator to independently constrain ejecta mass (mej) and velocity profile parameters (ηvel, minvel, Δvel) instead of the Arnett model’s implicit degenerate combination mej/vej.

• Improved capability: AI can separately recover mej (RMS 0.9 M⊙ vs. 2.6 M⊙ for Arnett) and velocity (RMS 1340 km/s vs. 3800 km/s), enabling more precise classification of supernova progenitors and explosion physics.

4. Physical Parameter Recovery from Multiband Light Curves

• Train the emulator on a grid of 4499 simulations to map light curves to nine physical parameters (mNi, mHe, mbulk, ηNi, ηHe, ηbulk, minvel, Δvel, ηvel).

• Improved capability: AI can infer nickel mass (RMS 0.008 M⊙), ejecta mass, velocity profiles, and 56Ni mixing fraction (r95,Ni) directly from observed light curves, outperforming classical models by 10–100× in accuracy.

5. Survey-Specific Light Curve Fitting

• Generate emulated light curves matched to ZTF (g,r; 2-day cadence) and LSST (ugrizy; 4–21-day cadence) with realistic signal-to-noise ratios.

• Improved capability: AI can predict parameter recovery performance for upcoming surveys, identifying which physical parameters are well-constrained (e.g., mej via LSST color evolution) and which remain degenerate (e.g., helium mass).

6. Posterior-Driven Ejecta Profile Reconstruction

• Use posterior draws to construct distributions of velocity, 4He, 56Ni, and bulk mass as functions of ejecta velocity.

• Improved capability: AI can reconstruct the full ejecta structure (e.g., photospheric-layer composition) from light curves, revealing mixing patterns and velocity gradients that are invisible to single-parameter models.

7. Real Supernova Classification and Parameter Estimation

• Apply the trained emulator to real events (SN 1994I, SN 2007gr, iPTF13bvn) to infer mNi, mej, and mixing.

• Improved capability: AI can automatically classify supernova subtypes (e.g., Type Ib vs. Ic) based on inferred mixing (r95,Ni) and velocity profiles, and cross-validate with independent measurements (e.g., tail-based nickel mass).

8. Calibration of Effective Opacity in Analytical Models

• Use emulator fits to derive a corrected gray opacity (κ = 0.054 cm2 g−1) for the Arnett model, removing systematic offsets in mej/vej.

• Improved capability: AI can recalibrate legacy analytical models, making them more accurate for historical datasets where full emulator fitting is computationally prohibitive.

9. Grid Design and Active Learning

• Identify regions of parameter space with poor emulator accuracy (e.g., high mNi ≥ 0.2 M⊙) and suggest targeted grid expansion (>10,000 simulations) to reduce uncertainty.

• Improved capability: AI can autonomously propose new simulations to minimize emulator error, accelerating convergence to a robust surrogate model for any physical system.

10. Multi-Wavelength Spectral Prediction

• Emulate downsampled spectra (R≈30) rather than just photometry, preserving color information critical for disentangling mass and velocity.

• Improved capability: AI can generate synthetic spectra for arbitrary parameter combinations, enabling spectroscopic follow-up predictions and direct comparison with observed spectra.

We present the first neural-network emulator of stripped-envelope supernova (SESN) lightcurves, trained on a grid of 4499 light curves simulated with the radiative transfer (RT) code sedona. Using this emulator, we show that m ni, m ejecta, the ejecta velocity profile, and the degree of Ni-56 mixing can all be inferred from multiband lightcurves. We find that the degeneracy between ejecta mass and ejecta velocity is substantially weaker with this emulator than in traditional semianalytical models. The emulator is able to independently constrain the influence of ejecta mass and of ejecta velocity on the resulting lightcurve, rather than making them degenerate by design as traditional semianalytical models do. We additionally show that this inference is significantly more accurate than that done by the classical Arnett model for both simulated ZTF-like and LSST-like lightcurves. Finally, we present lightcurves fits to three well-studied SESNe: SN 1994I, SN 2007gr, and iPTF13bvn, constraining their m ni, m ejecta, and Ni-56 mixing.