Physics-Informed Self-Supervised Learning for Joint Wire Calibration and Interaction Position Reconstruction in Multi-Wire Parallel Plate Avalanche Counters
Authors: Antoine Lemasson, Maurycy Rejmund
Organizations: GANIL, CEA/DRF - CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France.
Scientific instruments require accurate calibration to convert detector signals into reliable physical observables. Conventional calibration procedures typically rely on dedicated calibration measurements, analytical response models or labelled reference data, limiting their ability to adapt to changing operating conditions and detector aging. We present a physics-informed self-supervised learning framework that jointly performs wire calibration and interaction position reconstruction in Multi-Wire Parallel Plate Avalanche Counters (MWPPACs) without requiring labelled position measurements or dedicated calibration runs. The method formulates detector calibration as a latent optimization problem in which global wire gains and event-wise interaction positions are estimated simultaneously using supervision derived exclusively from detector geometry and charge-energy consistency constraints. A detector-independent neural network reconstructs sub-wire interaction positions from local charge distributions, eliminating the need to assume analytical induction profiles by learning the detector response directly from experimental data. The end-to-end differentiable framework enables continuous detector self-calibration while improving the uniformity and accuracy of position reconstruction. Experimental evaluation on the entrance MWPPAC tracking detectors of the VAMOS++ magnetic spectrometer demonstrates stable convergence, improved spatial homogeneity and enhanced position resolution. Beyond the detector studied, the method establishes a general framework for physics-informed self-supervised calibration of scientific instruments and is a step toward autonomous intelligent instrumentation capable of continuous adaptation during operation. In this paradigm, detector calibration is no longer a prerequisite for an experiment but an integral part of the measurement process itself.
Figures & tables
Figure 3: Training Convergence of Residuals: The evolution of the training and validation RMSD of the residuals ΔX1 , ΔX2 , ΔY1 , ΔY2 obtained for the number N of adjacent sensing wires, see Eq. ( 13 ), (a) N=3 , and (b) N=5 .
Figure 4: Training Convergence of Coefficients and Values of Coefficients: (a) The evolution of the mean value of the coefficients cX1 , cY1 , cX2 , cY2 as a function of the epoch number. (b) Individual values of the coefficients cX1 as function of wire number.
Figure 5: Spatial Distribution of Residuals: Two-dimensional correlation of the residuals ΔX1 (a) and (b) and ΔX2 (c) and (d) as a function of the interaction position in the X1 and X2 planes, respectively. Panels (a) and (c) illustrate the results obtained using the conventional method ( Vandebrouck et al. (2016) ) using hyperbolic secant function ( Lau and Pyrlik (1995) ), while panels (b) and (d) illustrate the results obtained in the presented framework. Both approaches used N=3 adjacent sensing wires.
this work (mm)
Conventional (mm)
σΔX1
0.179(1)
0.193(1)
σΔX2
0.293(1)
0.317(1)
σΔY1
0.242(1)
0.252(1)
σΔY2
0.401(2)
0.418(1)
σXtarget
0.433(2)
0.468(2)
σYtarget
0.572(2)
0.592(2)
Table 1: Summary of the widths of the residuals, the reconstructed position on the target and the position resolution, inferred using the reference wires, obtained employing the conventional method and the presented framework.
Figure 6: Reconstructed Beam Profile: Reconstructed beam profile on the target (a) Xtarget and (b) Ytarget . The results obtained using the conventional method ( Vandebrouck et al. (2016) ) using hyperbolic secant function ( Lau and Pyrlik (1995) ) are indicated in black, while the results obtained in the presented framework are indicated in red. Both approaches used N=3 adjacent sensing wires.
Figure 7: Position Resolution (a) Two-dimensional projection of the events on the plane in front of the detector, where the 100μ m reference wire is located. The projection was obtained using the current framework. (b) One-dimensional projection on a plane perpendicular to the reference wire. The results obtained the conventional method are indicated in black and the results obtained the proposed framework are indicated in red.
Calibration remains one of the principal obstacles to the deployment of machine learning in scientific instrumentation because it typically relies on expert intervention, dedicated procedures, and manually labelled data. We introduce a physics-informed self-supervised framework that jointly learns latent detector calibration parameters and task-specific predictions directly from raw measurements without requiring pre-calibrated signals or external labels. The method exploits known physical constraints to generate pseudo-labels iteratively, transforming calibration into a self-supervised optimization problem. The approach is demonstrated for ionic charge-state determination in the VAMOS++ magnetic spectrometer, where the calibration of a segmented ionization chamber and the inference of ionic charge states are learned simultaneously. Starting from a weak prior on the mean ionic charge state, the model progressively refines its predictions through iterative fractional pseudo-labelling driven by the discrete nature of atomic masses. Beyond accurate ionic charge-state reconstruction, the inferred calibration coefficients provide a compact representation of the detector state that enables automated monitoring of gain drifts, pressure variations, and detector aging. The resulting labels can subsequently be transferred to specialized models that quantify detector imperfections and track their spatial and temporal evolution. These results establish a general paradigm for self-calibrating and self-monitoring scientific instruments and represent a step toward intelligent experimental systems capable of autonomous calibration, analysis, and performance optimization.
Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems. We introduce Amortized Physics-Informed Calibration (APIC), a population-level extension of KOH that leverages Neural Processes to perform scalable Bayesian inference across realizations. Our framework employs a two-branch latent architecture to disentangle instance-specific physical parameters from shared, state-dependent structural discrepancies. By integrating differentiable physics into an amortized inference backbone, APIC enables rapid calibration of unseen realizations from sparse observations while quantifying uncertainty. Experiments on the damped spring oscillator, the Lotka-Volterra system, and the advection-diffusion PDE with misspecified physics demonstrate improved parameter recovery and consistent identification of the systemic discrepancy structure compared to other calibration approaches.
Aishwarya Venkataramanan, Sai Karthikeya Vemuri, Joachim Denzler
The quality of recorded data depends on the stability of the sensor system that acquires it. Sensor motion and aging can degrade the performance and stability of downstream data-driven methods. We present a Wasserstein-GAN-inspired approach for unsupervised inference of physically interpretable transformation parameters that map a changed detector response distribution back to a nominal reference distribution. In contrast to standard generative modeling, the generator is used as a learnable calibration transformation whose trainable weights represent the sought parameters, while the critic provides a distributional distance signal via the Wasserstein objective. We validate the approach on a tracking-detector toy model with controlled layer shifts and demonstrate its application on high-granularity Geant4-simulated calorimeter data with cell-wise aging effects. The method recovers aging coefficients for individual cells with correlation to ground truth and improves agreement between calibrated and reference energy-sum distributions, while exhibiting the expected degradation at increasing channel-to-channel noise levels. These results indicate that adversarial distribution matching can serve as a data-driven component of calibration strategies in settings where direct labels for degradation parameters are unavailable.
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