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A Differentiable Neural Surrogate for Photon Propagation in Neutrino Telescopes
Felix J. Yu, Berthy T. Feng, Nicholas Kamp, Carlos A. Argüelles
TL;DR
Photon propagation in IceCube is costly because realistic simulations must model light transport through complex, strongly scattering ice. candela learns a differentiable source–receiver photon Green’s function and composes point-source responses into complete events, achieving substantial speedups while retaining MC-level fidelity in nearly all tested cases.
Problem
Accurate photon-propagation simulation is computationally costly because IceCube’s heterogeneous, strongly scattering ice affects photon trajectories, yields, and arrival times.
Method
candela learns a differentiable SIREN-based photon Green’s function that predicts source–receiver yields and arrival-time distributions, then composes localized energy-deposit responses into complete events.
Results
50–100× speedups were achieved relative to standard MC photon propagation while photon yields and arrival-time distributions remained within MC statistical uncertainty in nearly all tested cases.
Takeaways & Limitations
candela provides a practical foundation for faster simulation and gradient-based reconstruction and calibration in large-volume complex media.
Takeaways & Limitations
candela begins to separate from the MC statistical floor near sensor saturation, a regime that may matter in future simulation-based studies.
Abstract
from arXiv · showhide
Large-volume neutrino telescopes infer neutrino properties from Cherenkov light, but simulating the transport of billions of photons through highly scattering ice or water is computationally costly. We introduce candela, a differentiable SIREN neural field that learns the photon Green's function of the IceCube Neutrino Observatory, a cubic-kilometer detector embedded in Antarctic glacial ice. Given a point-like energy deposit and sensor, it predicts the expected photon yield and full arrival-time distribution at the sensor. Complete events are simulated by decomposing charged-particle energy deposits into point-like sources and superposing their predicted sensor responses. Trained on Monte-Carlo simulations, candela generates events $50$--$100\times$ faster than existing methods, with cost scaling only weakly with neutrino energy. It keeps median yields within $2\%$ of the MC expectation and timing distributions at the MC statistical floor across six photon-count decades. The model also provides end-to-end gradients with respect to event parameters and opens a path toward optimizing scattering-medium properties, which often dominate systematic uncertainties in neutrino telescopes.
1 Introduction
IceCube’s complex, heterogeneous ice makes accurate photon-propagation simulation computationally expensive, despite its importance for neutrino inference and detector studies. candela addresses this bottleneck with a differentiable learned surrogate that preserves photon yields and timing distributions.
- IceCube uses Cherenkov-light amount and timing to infer properties of astrophysical neutrinos and support reconstruction, classification, and sensor design.
- Depth-dependent optical properties, dust, anisotropy, and tilted ice layers complicate photon trajectories and arrival times.
- 100,000 GPU-hours were consumed by photon-propagation simulations in a 2019 IceCube campaign.
- Existing approaches use lookup tables, detailed photon-by-photon Monte Carlo, or spline representations, but dense tables remain necessary.
- Prior differentiable models provide either spatial gradients tied to one sensor layout or ray-tracing-based calibration and reconstruction, without candela’s full source-direction and arrival-time representation.
- candela learns an IceCube photon Green’s function and achieves 50–100× acceleration while matching arrival-time distributions within MC statistical uncertainty across ∼6 photon-count decades.
2 A neural field for photon transport
candela models photon transport through a shared source–receiver neural field, then composes point-source responses into complete events. Its inputs encode geometry and detector position, while its outputs separate photon yield from residual arrival-time structure.
- candela decomposes particle energy losses into localized sources, evaluates each source response independently, and superposes the resulting light fields.
- The source–receiver query uses track-frame geometry (R, Φ, l), source direction and energy, and absolute positions to account for spatially varying ice.
- Residual time τ = t − Δt_sr removes emission time plus unscattered propagation time, leaving scattering-induced delays and broadening for the neural field to model.
- The field outputs expected per-energy photon yield Λ and a unit-normalized residual arrival-time density π, with deposited energy scaling each source response.
- A six-layer, width-512 SIREN represents π with an eight-component inverse-Gaussian mixture while sharing the field across source–receiver queries.
- The complete event is formed by evaluating source–receiver pairs in parallel, integrating predicted rates over time bins, and summing contributions at each sensor.
- Differentiable tensor operations preserve gradients with respect to source positions, directions, and deposited energies for reconstruction and other gradient-based applications.
3 Results
On independent matched-energy events, candela substantially reduces generation time while reproducing photon yields and arrival-time distributions close to the PPC statistical reference.
- Event-level agreement: Candela reproduces spatial light patterns, first-hit-time progression, and arrival-time structure from prompt peaks through long scattering tails.The agreement extends over four orders of magnitude in probability across bright, near-track, and far-track sensors.
- Speed and statistical fidelity: 50–100× speedups result from candela requiring only 10–20 ms per event with weak energy dependence, compared with increasingly costly PPC propagation.Both methods were evaluated on the same NVIDIA RTX 5090 GPU.
- Speed and statistical fidelity: Figure 3 reports wall time, yield ratio, and KS timing distance using bin medians and 16th–84th percentile bands, with PPC–PPC defining the MC floor.The panels summarize independent test events and sensors under matched energy losses.
- Speed and statistical fidelity: The median candela-to-reference photon-yield ratio remains within approximately 2% of perfect agreement across tested sensor brightness.The comparison uses high-statistics PPC expectations and includes a single-PPC control for finite-photon variation.
4 Conclusion
Candela is a differentiable neural surrogate that accelerates IceCube photon transport while retaining MC-level fidelity in nearly all tested cases. Its efficiency and differentiability support faster simulation and future gradient-based reconstruction and calibration.
- Conclusion: Candela learns a shared source–receiver Green’s function and linearly composes point-source responses for complete IceCube events.The surrogate predicts photon yields and arrival-time distributions while separating transport from event-specific energy deposits.
- Conclusion: 50–100× faster event generation is achieved while photon yields and arrival-time distributions remain within the MC statistical limit in nearly all tested cases.The conclusion combines computational efficiency with fidelity across the evaluated events.
- Conclusion: The method’s differentiability lays groundwork for efficient gradient-based reconstruction and calibration in large-volume complex natural media.The reported outlook extends beyond faster simulation to optimization-oriented uses.
- Limitations and outlook: Candela begins to separate from the MC statistical floor near sensor saturation, a regime largely ignored in practice but potentially relevant to future simulation-based studies.This is the stated limitation and scope boundary.
A.1 Arrival-time distributions
Candela models the sharply onset and long-tailed arrival-time distributions produced by scattering media with an eight-component mixture of inverse-Gaussian components.
- Arrival-time model: Photon propagation produces arrival-time distributions with a sharp onset followed by a long, geometry-dependent tail.The inverse-Gaussian family is introduced as a primitive suited to this behavior.
- Arrival-time model: Each inverse-Gaussian component uses parameters µ > 0 for characteristic arrival time and λ > 0 for width.Its functional form is also characteristic of diffusive transport with absorption.
- Arrival-time model: A single inverse Gaussian cannot represent the prompt and multiply scattered paths present in heterogeneous ice, so candela uses an eight-component mixture.The mixture broadens the model’s representation of transport-path diversity.
- Arrival-time model: The residual-time coordinate u(τ) is nonnegative, and Zj denotes the mass of component j within the arrival-time range represented in training.The network predicts component parameters and mixture weights.
- Arrival-time model: Because components are normalized individually, pj directly gives the fraction of in-range photons assigned to component j, with the weights summing to one.This makes the mixture weights interpretable as in-range photon fractions.
A.2 Lightcuts
The Lightcuts-inspired aggregation scheme reduces the cost of composing many cascade sources by recursively merging track-adjacent sources while preserving energy-weighted spatial and energy information.
- Lightcuts aggregation: Muon tracks containing thousands of cascade sources are organized into a binary tree, whose leaves are individual sources and root represents the full track.Per-sensor traversal decides whether clusters should be refined or retained.
- Lightcuts aggregation: Each cluster preserves total deposited energy and is represented spatially by its energy-weighted centroid.Its source-energy conditioning variable is the energy-weighted mean member energy rather than the cluster sum.
- Lightcuts aggregation: Clusters are compared using the parent predicted yield, the sum of child predictions, and an additional closest-track-point response because centroids can miss strong sensor-response regions.The criterion accounts for extended clusters near sensors.
- Lightcuts aggregation: At ϵLC = 10−5, generation time is substantially reduced while photon-yield and arrival-time fidelity remain indistinguishable from exact source-by-source composition.Setting ϵLC = 0 recovers exact composition.
A.3 Differentiability
candela enables gradient-based reconstruction of deposited energy from simulated through-going muon events. The reconstruction closely tracks the true in-volume deposited energy across the tested range.
- Event setup: 1500 through-going muons spanning 1 TeV to 1 PeV were simulated, with energy losses generated using PROPOSAL and propagated using PPC.Events with fewer than 20 detected photons were discarded.
- Differentiable parameterization: The deposition profile combines a minimum-ionizing component of approximately 0.26 GeV m−1 with non-negative stochastic deposits grouped along adjacent track segments.The track direction, impact point, and reference time are fixed from a geometric line fit.
- Gradient-based inference: Deposited energies are fitted by maximizing an extended Poisson log-likelihood over all operational receivers, including receivers with zero observed photons.The likelihood uses candela’s predicted photon yields and observed receiver counts.
- Result: The reconstruction closely follows the identity relation, with a median log-ratio of −0.03 and an interquartile range of 0.12.Automatic differentiation supplies gradients through the network, and two to three yield-recalculation iterations suffice for convergence.