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arxiv: 2512.17866 · v3 · pith:WW4SMGEMnew · submitted 2025-12-19 · ⚛️ physics.ins-det · hep-ex

Data-Driven Calibration of Large Liquid Detectors with Unsupervised Learning

Scott DeGraw , Steve Biller , Armin Reichold This is my paper

Pith reviewed 2026-05-21 16:28 UTC · model grok-4.3

classification ⚛️ physics.ins-det hep-ex
keywords PMT calibrationliquid scintillation detectorsunsupervised learningSNO+ detectordata-driven calibrationtiming constantsoptical photon transport
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The pith

Unsupervised deep learning extracts timing calibration constants for over 7500 PMTs in SNO+ from background events alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows how to treat PMT calibration constants as learnable parameters inside a neural network whose loss function encodes a simplified model of light traveling from point sources. By training on ordinary physics events the network adjusts those constants to best match the observed PMT hit patterns, turning calibration into a large-scale regression task. The approach is demonstrated on real SNO+ data, where it recovers three constants per PMT across more than 7500 channels using only radioactive background events. A reader would care because the method removes the need for separate calibration runs with external sources and scales to the channel counts of future detectors.

Core claim

By placing a simplified physical model of optical photon transport inside the loss function of an unsupervised neural network and allowing the PMT timing and gain constants to be free parameters, the method regresses accurate per-PMT calibration values directly from unlabeled physics data, as shown by reliable extraction of three constants for each of the over 7500 online PMTs in the SNO+ detector.

What carries the argument

A neural network performing regression on PMT calibration constants by minimizing a loss that compares observed hit times and charges to predictions from a point-source optical transport model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same loss-function approach could be adapted to monitor slow drifts in PMT response during long data-taking periods without interrupting the physics program.
  • Extending the transport model beyond the point-source approximation might reduce systematic biases when events occur near the detector walls.
  • The regression framework could be applied to other large optical detectors by swapping in their specific geometry and light-propagation rules.

Load-bearing premise

Each detected event can be treated as light emitted from a single point source inside the detector volume.

What would settle it

Compare the constants learned from background events against the values obtained from conventional laser or radioactive-source calibration runs in the same SNO+ dataset and check for agreement within expected uncertainties.

Figures

Figures reproduced from arXiv: 2512.17866 by Armin Reichold, Scott DeGraw, Steve Biller.

Figure 1
Figure 1. Figure 1: Standard methods for performing this type of calibration involve dedicated calibration light sources, either deployed in situ or fixed inside the detector. Deployed systems, such as ∗Corresponding author Email address: scott.degraw@physics.ox.ac.uk (Scott DeGraw) arXiv:2512.17866v1 [physics.ins-det] 19 Dec 2025 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: Time walk effect laserballs (also known as diffuser balls) used in SNO [1], SNO+ [2], Super-Kamiokande [3] and JUNO [4] involve dedicated campaigns that are limited in how frequently they can be deployed, use light with different characteristics than physics events, generally stop physics data taking, and can carry a risk of contaminating the detector. Fixed systems in SNO+ [5], Borexino [6] and planned us… view at source ↗
Figure 2
Figure 2. Figure 2: Time residual distribution for 210Po decays from MC. The Jones and Faddy skew-t distribution is fit to the distribution and used as a loss function during training. despite the high effective refractive index difference between scintillator and water (approx￾imately 1.62 and 1.38, respectively). While future studies could try to implement more accurate methods, Monte Carlo (MC) simulation studies in Sectio… view at source ↗
Figure 3
Figure 3. Figure 3: Distributions of PMT timing model residuals over all PMTs. The standard deviation of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Examples of PMT timing models from MC truth and as fitted by the calibration method. The [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Each blue dot represents the delay residual for a PMT. For the PMT [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The position residuals (reconstructed - truth) as predicted by the position reconstruction neural [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of delays found by our calibration method and the standard SNO+ calibration using [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Residual between our calibrations and standard SNO+ calibration delays projected onto a flat map [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: For this study, the same standard SNO+ likelihood-based position reconstruction [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distributions of ∆R for 214BiPo coincidences in data. Distributions are shown for standard SNO+ calibration and our calibration. Combined Bi and Po position resolution values are shown. but our calibration method is blind to crate segmentation and, once we were alerted to this, the effect could clearly be seen in the raw time residuals. Following a lower level electronics calibration, performed shortly aft… view at source ↗
Figure 10
Figure 10. Figure 10: Delay residuals between our calibration and the standard SNO+ calibration for dataset taken [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
read the original abstract

This paper demonstrates a novel method to extract photomultiplier tube (PMT) calibration timing constants in large liquid scintillation detectors from physics data using the machinery of unsupervised deep learning. The approach uses a simplified physical model of optical photon transport in the loss function, with PMT calibration constants treated as free parameters, and the simple assumption that individual events represent point-like emission. The problem is, thus, effectively reduced to that of regression on a very large scale, made tractable by deep learning architectures and automatic differentiation frameworks. Using data from the 9,300 PMTs in the SNO+ detector, the method has been shown to reliably extract 3 calibration constants for each of the over 7,500 online PMTs using radioactive background events. We believe that this basic approach can be straightforwardly generalised for a wide range of applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces a novel unsupervised deep learning method for calibrating photomultiplier tube (PMT) timing constants in large liquid detectors such as SNO+. It incorporates a simplified physical model of optical photon transport into the loss function, with PMT calibration constants as optimizable free parameters, under the assumption of point-like event emission. Applied to radioactive background data from the SNO+ detector's 9,300 PMTs, it extracts three calibration constants for each of over 7,500 online PMTs.

Significance. If the method proves reliable, it represents a significant advancement in detector calibration by enabling data-driven, in-situ determination of PMT parameters without dedicated calibration campaigns. This could enhance the precision and operational efficiency of future large-scale neutrino and dark matter experiments. The use of automatic differentiation and deep learning architectures makes it scalable to high-channel-count detectors. Credit is given for demonstrating the approach on real experimental data from SNO+.

major comments (2)
  1. [Abstract] Abstract: The claim that the method has 'reliably extract[ed]' the calibration constants lacks accompanying quantitative metrics, error bars, or comparisons to independent calibration methods, which is essential to substantiate the reliability assertion.
  2. [Abstract] Abstract: The assumption of point-like emission for individual radioactive background events (used to simplify the optical transport model in the loss function) may introduce model mismatch; beta decays produce finite track lengths and multiple scintillation sites, potentially biasing the extracted PMT timing constants if these effects are absorbed into the fit parameters.
minor comments (1)
  1. The abstract could benefit from a brief mention of the specific deep learning architecture employed and any regularization techniques used to ensure physical consistency.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the potential significance of our unsupervised calibration approach. We address each major comment below and have revised the manuscript accordingly to improve clarity and substantiation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that the method has 'reliably extract[ed]' the calibration constants lacks accompanying quantitative metrics, error bars, or comparisons to independent calibration methods, which is essential to substantiate the reliability assertion.

    Authors: We agree that the abstract would benefit from more explicit reference to supporting evidence. The main text already presents quantitative comparisons to independent calibration runs and reports RMS deviations and per-PMT uncertainties derived from the optimization. We have revised the abstract to include a concise statement of these metrics and to reference the relevant sections, thereby substantiating the reliability claim without altering the overall length substantially. revision: yes

  2. Referee: [Abstract] Abstract: The assumption of point-like emission for individual radioactive background events (used to simplify the optical transport model in the loss function) may introduce model mismatch; beta decays produce finite track lengths and multiple scintillation sites, potentially biasing the extracted PMT timing constants if these effects are absorbed into the fit parameters.

    Authors: We acknowledge that the point-like emission assumption is an approximation whose validity merits explicit discussion. Beta decays in the scintillator do produce finite track lengths and multiple emission sites. However, because the loss function optimizes timing offsets against observed photon arrival times across a large ensemble of events, residual geometric effects are largely absorbed into the per-PMT parameters rather than systematically biasing the relative timing constants. We have added a new paragraph in the methods section that quantifies the expected bias using toy Monte Carlo simulations and shows it to be smaller than the statistical precision achieved on the SNO+ dataset. revision: yes

Circularity Check

0 steps flagged

No significant circularity; method is explicit optimization-based calibration

full rationale

The paper presents an unsupervised learning procedure that embeds a simplified point-like optical transport model into a loss function and treats the three PMT calibration constants per tube as free parameters to be optimized against observed background-event data. The extracted constants are defined as the values that minimize this loss; this is the intended output of any calibration fit rather than a claimed independent prediction or first-principles derivation that reduces tautologically to its inputs. No self-citation chain, uniqueness theorem, or ansatz smuggling is invoked to justify the central result. The approach is self-contained as a data-driven regression technique whose validity is assessed empirically on SNO+ detector data, with the point-like emission assumption stated openly as a modeling choice rather than a derived claim.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on a simplified photon-transport model and the point-like emission assumption; the calibration constants themselves are the fitted quantities.

free parameters (1)
  • PMT timing calibration constants
    Three constants per PMT are treated as free parameters optimized via the loss function on background events.
axioms (1)
  • domain assumption Individual events represent point-like emission
    Invoked to simplify the optical photon transport model placed inside the loss function.

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Reference graph

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