End-to-end Differentiable Calibration and Reconstruction for Optical Particle Detectors

Omar Alterkait; César Jesús-Valls; Ryo Matsumoto; Patrick de Perio; Kazuhiro Terao

hep-exFeb 27, 2026

End-to-end Differentiable Calibration and Reconstruction for Optical Particle Detectors

Authors: Omar Alterkait, César Jesús-Valls, Ryo Matsumoto, Patrick de Perio, Kazuhiro Terao

Organizations: Department of Physics and Astronomy, Tufts University, 574 Boston Ave, Medford, MA 02155, USA · The NSF AI Institute for Fundamental Interactions, MIT, Cambridge, MA 02139, USA · European Organization for Nuclear Research (CERN), 1211 Geneva 23, Switzerland · Department of Physics, Institute of Science Tokyo, Meguro, Tokyo 152-8551, Japan · Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan · SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA

Abstract

Large-scale homogeneous detectors with optical readouts are widely used in particle detection, with Cherenkov and scintillator neutrino detectors as prominent examples. Analyses in experimental physics rely on high-fidelity simulators to translate sensor-level information into physical quantities of interest. This task critically depends on accurate calibration, which aligns simulation behavior with real detector data, and on tracking, which infers particle properties from optical signals. We present the first end-to-end differentiable optical particle detector simulator, enabling simultaneous calibration and reconstruction through gradient-based optimization. Our approach unifies simulation, calibration, and tracking, which are traditionally treated as separate problems, within a single differentiable framework. We demonstrate that it achieves smooth and physically meaningful gradients across all key stages of light generation, propagation, and detection while maintaining computational efficiency. We show that gradient-based calibration and reconstruction greatly simplify existing analysis pipelines while matching or surpassing the performance of conventional non-differentiable methods in both accuracy and speed. Moreover, the framework's modularity allows straightforward adaptation to diverse detector geometries and target materials, providing a flexible foundation for experiment design and optimization. The results demonstrate the readiness of this technique for adoption in current and future optical detector experiments, establishing a new paradigm for simulation and reconstruction in particle physics.

Figures & tables

Figure 1: Examples of four detector geometries built parametrically using LUCiD.

Figure 2: An example muon event generated with PhotonSim . The particle origin is denoted with a red star symbol and the photons creation time is indicated in color. A total of 1k photons chosen at random are also represented by arrows.

Panel of Figure 3 — Figure 3: Three example energy slices for the surrogate model of $f^{\mathrm{Cherenkov}}$ for muons (top) and electrons (bottom).

Figure 4: Example of the parametrization of $f^{t_{0}}_{\gamma}$ for muons in water after subtracting $t_{0}=s/c$ , which accounts for the $t_{0}$ correction arising from the particle slowdown in the medium. Data points are shown as circular markers colored by particle energy (see colorbar), with lines of matching colors representing the predictions from Eq. 6 .

Figure 5: Visualization of the grid-based sensor lookup on the top cap of an SK-like detector. A single active grid cell is mapped to a specific subset of assigned sensors, allowing the intersection algorithm to ignore the remaining inactive sensors.

Figure 6: (Left) Geometric definition of the photon relaxation model. A photon with Gaussian width

\sigma

passes a sensor of radius

r

at an impact parameter

b

. The purple shaded region illustrates the integral of the photon’s probability density over the sensor surface, which determines the weight

w_{\rm geo}

assigned to the hit. (Right) The calculated overlap probability

w_{\rm geo}

as a function of the normalized impact parameter

b/r

. As the smoothing width

\sigma

increases, the response transitions from a non-differentiable step function (binary) to a smooth curve that provides useful gradients even when the ray strictly misses the sensor (

b/r>1

Panel of Figure 7 — Figure 7: Computation times for an SK-like detector geometry, shown as a function of the number of rays ( $N_{\mathrm{rays}}$ ) and the number of propagation iterations ( $K$ ). Lines are linear fits presented in the legend.

Panel of Figure 8 — Figure 8: Example of a 1.5 GeV muon data-like event in the SK-like detector. Dark noise is not included.

Figure 9: Example data-like events and associated differentiable predictions for various detector geometries. The color intensity represents the observed counts in logarithmic scale.

Figure 10: The calibration loss over the scattering length

\lambda_{s}

and the absorption length

\lambda_{a}

405

nm, near their true values (red star), for a single laser source. Compensating changes in the two leave the total collected light almost unchanged and differ only in how that light is distributed across the sensors, which is what opens the narrow valley. White streamlines show the normalized descent field. Left: raw gradient descent runs across the valley and along it, the signature of ill-conditioning. Right: the Fisher-preconditioned step rescales the two directions so that the streamlines point toward the minimum.

Figure 11: Full calibration convergence. A single joint Gauss–Newton fit recovers the complete optical model, run from three perturbed starting points (line style; dotted lines mark the truth). Top: the per-wavelength scattering length $\lambda_{s}$ , absorption length $\lambda_{a}$ , and quantum efficiency at the five calibration wavelengths (color). Bottom: the wavelength-independent specular and diffuse reflectivities of the walls and sensors, and the recovery of the full set of per-sensor efficiencies (recovered versus true, RMS $0.9\%$ ). Curves are shown as a running mean over the trajectory, and the horizontal axis is truncated at $100$ iterations for the parameters that settle early while spanning the full $600$ for the diffuse reflectivities, which are the slowest. The optical constants converge to the underlying Super-Kamiokande water model and the reflectivities to their injected values.

Figure 12: Two-dimensional loss landscape for different parameter combinations, with associated gradient streamlines, as observed in a randomly selected data-like event. The true parameter values are indicated by red stars.

Figure 13: Evolution of reconstruction errors for 1 GeV muons over optimization iterations for the track vertex position, direction, interaction time (

t_{0}

), and particle momentum. The histograms on the right of each panel show the distribution of the final reconstructed values.

Figure 14: Tracking performance as a function of the number of rays,

N_{\mathrm{rays}}

Figure 15: Tracking performance as a function of the simulated muon energy.

Figure 16: Tracking performance as a function of the number of photosensors.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 17: Example of a 1 GeV muon data-like Cherenkov (red) vs scintillation (blue) light fraction compared to the matching differentiable prediction in a JUNO-sized detector using 5% WbLS as detector medium.

Figure 18: Likelihood scan and associated gradients of the scintillation yield scale

S

for the data-like event in Fig. 17 . The loss is a negative-log likelihood in the observed vs predicted sensor photoelectrons.

Figure 19: The fraction of initial photon intensity remaining active in the simulation as a function of the number of propagation iterations (

K

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