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
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.
Figure 3: Three example energy slices for the surrogate model of fCherenkov for muons (top) and electrons (bottom).
Figure 4: Example of the parametrization of fγt0 for muons in water after subtracting t0=s/c , which accounts for the t0 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 σ 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 wgeo assigned to the hit. (Right) The calculated overlap probability wgeo as a function of the normalized impact parameter b/r . As the smoothing width σ 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 ).
Figure 7: Computation times for an SK-like detector geometry, shown as a function of the number of rays ( Nrays ) and the number of propagation iterations ( K ). Lines are linear fits presented in the legend.
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 λs and the absorption length λa at 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 λs , absorption length λa , 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 ( t0 ), 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, Nrays .
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 ).
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× 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.
Felix J. Yu, Berthy T. Feng, Nicholas Kamp +1
Harvard University · NSF IAIFI · Massachusetts Institute of Technology
Transfer and multi-nucleon transfer reactions are essential tools for probing nuclear structure and reaction dynamics, requiring precise determination of the identity, energy, and emission angles of reaction products. The increasing granularity of modern silicon telescope arrays enhances experimental capabilities but challenges detector calibration, as conventional channel-by-channel approaches become inefficient and difficult to scale. In this work, we present a fully automated, physics-informed calibration framework based on neural networks, specifically designed for highly segmented silicon detector arrays. The method formulates calibration as a global optimization problem, in which detector gains and geometrical corrections are determined simultaneously by minimizing the width of the reconstructed excitation energy under two-body kinematics constraints. The approach relies exclusively on experimental data and well-established physical principles, without requiring explicit modeling of detector response. A distinctive feature is the use of multiple neural network sub-models sharing a common loss function with embedded physics constraints, enabling coherent and self-consistent calibration across all detector channels. This strategy ensures scalability, robustness, and reproducibility, making it particularly suitable for next-generation detector systems with increasing complexity. The performance of the method is demonstrated using experimental data from the Particle-Identification Silicon-Telescope Array (PISTA) in high-resolution fission studies in inverse kinematics. The results show excellent agreement with theoretical kinematics, high-quality particle identification, and a significant improvement in calibration efficiency. The proposed framework provides a general and adaptable solution for the calibration of complex detector systems in modern nuclear physics experiments.
M. Rejmund, A. Lemasson, P. Morfouace +3
GANIL, CEA/DRF - CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France · CEA, DAM, DIF, F-91297, Arpajon, France · Universit´e Paris-Saclay, CEA, LMCE, F-91680, Bruy`eres-le-Chˆatels, France
Simulating optical tactile sensors presents significant challenges due to their high deformability and intricate optical properties. To address these issues and enable a physically accurate simulation, we propose DOT-Sim: Differentiable Optical Tactile Simulation. Unlike prior simulators that rely on simplified models of deformable sensors, DOT-Sim accurately captures the physical behavior of soft sensors by modeling them as elastic materials using the Material Point Method (MPM). DOT-Sim enables rapid calibration of optical tactile sensor simulation using a small number of demonstrations within minutes, which is substantially faster than existing methods. Compared to current baselines, our approach supports much larger and non-linear deformations. To handle the optical aspect, we propose a novel approach to simulating optical responses by learning a residual image relative to the real-world idle state. We validate the physical and visual realism of our method through a series of zero-shot sim-to-real tasks. Our experiments show that DOT-Sim (1) accurately replicates the physical dynamics of a DenseTact optical tactile sensor in reality, (2) generates realistic optical outputs in contact-rich scenarios, (3) enables direct deployment of simulation-trained classifiers in the real world, achieving 85% classification accuracy on challenging objects and 90% accuracy in embedded tumor-type detection, and (4) allows precise trajectory following with a policy trained from demonstrations in simulation, with an average error of less than 0.9 mm.
Yang You, Won Kyung Do, Aiden Swann +3
Stanford University, United States · University of Cambridge, United Kingdom