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Physics-Informed Self-Supervised Learning for Joint Wire Calibration and Interaction Position Reconstruction in Multi-Wire Parallel Plate Avalanche Counters

This paper presents a physics-informed self-supervised learning framework that enables the simultaneous, label-free calibration of wire gains and reconstruction of interaction positions in Multi-Wire Parallel Plate Avalanche Counters by leveraging geometric and charge-energy constraints, thereby transforming detector calibration into an integral, continuous part of the measurement process.

Original authors: Antoine Lemasson, Maurycy Rejmund

Published 2026-09-25

📖 7 min read🧠 Deep dive

CC BY 4.0

Original authors: Antoine Lemasson, Maurycy Rejmund

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of high-energy physics, scientists build massive machines to catch fleeting particles and measure their paths with extreme precision. These machines are essentially giant, complex cameras made of wires and gas, designed to record where a particle hits and how much energy it carries. However, for these cameras to tell the truth, every single wire inside them must be perfectly calibrated. If a wire is slightly off, the entire picture of the particle's journey becomes distorted. Traditionally, fixing these wires requires stopping the experiment, running special test beams, and manually adjusting settings based on known reference points. This process is slow, interrupts valuable research time, and assumes the detector will stay the same forever. In reality, detectors age, electronic signals drift, and conditions change, meaning the calibration can become outdated almost as soon as it is finished.

A team of researchers at GANIL in France has developed a new way to keep these detectors accurate without ever stopping the experiment or needing a special test run. They created a system that teaches the detector to calibrate itself while it is actually doing its job. Instead of relying on pre-labeled data or human intervention, the system uses the laws of physics that govern how particles move and how energy is conserved to figure out the correct settings. By treating the detector's own measurements as a puzzle where the pieces must fit together perfectly according to physical rules, the system can continuously adjust its internal settings to ensure the data it collects is reliable. This approach turns the act of measurement into an act of self-correction, allowing the instrument to adapt to changes in real time.

The specific detector tested in this study is a Multi-Wire Parallel Plate Avalanche Counter, a device that uses a grid of thin wires to detect charged particles. When a particle passes through, it creates a cloud of electrical charge that spreads across several nearby wires. To know exactly where the particle passed, scientists usually have to guess the shape of that charge cloud based on mathematical formulas. If the formula is wrong, or if the wires have changed their sensitivity, the calculated position will be off. The researchers replaced this guessing game with a learning process. They built a computer model that looks at the pattern of charge on the wires and learns, on the fly, how to translate that pattern into a precise location.

What makes this method unique is that it does not need to know the correct answer beforehand. In most machine learning, a computer learns by being shown thousands of examples with the right answers already written down. Here, the computer learns by checking its own work against the laws of geometry and energy. The detector consists of two separate layers of wires placed one after the other. Because the particles travel in straight lines, the position recorded by the first layer must match up with the position recorded by the second layer in a predictable way. If the computer's calculation of the position is wrong, the two layers will not line up. The system uses this mismatch as a signal to adjust the sensitivity of the wires until the layers align perfectly. At the same time, it checks that the total amount of electrical charge collected matches the energy loss measured by another part of the machine.

The researchers applied this method to the entrance tracking detectors of the VAMOS++ magnetic spectrometer, a large instrument used to study nuclear reactions. They fed the system millions of real experimental events where particles were flying through the detector. Without any prior knowledge of the wire settings or the exact particle positions, the system began to optimize itself. It adjusted the gain, or sensitivity, of every single wire and refined its understanding of how to read the charge patterns. The process was remarkably fast, reaching a stable and accurate state in less than a minute of training time. The system successfully learned the unique behavior of the detector, including the subtle ways the wires responded to the passing particles, without ever being told what those behaviors were.

The results showed a clear improvement over the standard methods used in the field. When the researchers compared the new self-calibrating system to the traditional approach, which relies on fixed mathematical formulas to interpret the charge, the new method produced a sharper, more uniform picture. The positions of the particles were reconstructed with greater precision, reducing the uncertainty in their location by about 33 to 44 percent depending on the specific wire being tested. The new system also eliminated small, jagged errors that appeared in the old method, which were caused by the mathematical formulas failing to perfectly match the real-world behavior of the detector. By learning directly from the data, the system captured the true shape of the charge distribution, leading to a smoother and more accurate reconstruction of the particle paths.

This work demonstrates that scientific instruments can be designed to be self-aware and self-correcting. The framework does not just fix the wires once; it creates a continuous loop where the detector constantly checks its own performance against physical reality. If the wires drift or the electronics change, the system notices the inconsistency in the data and automatically corrects it. This means that future experiments could run for longer periods without the need for frequent, time-consuming calibration stops. The method is not limited to this specific detector; the researchers showed that the part of the system responsible for reading the position can be applied to detectors of different sizes and shapes without needing to be rewritten. Only the part that adjusts the specific wires needs to be retrained for a new machine.

The implications of this approach extend beyond just one type of detector. It represents a shift in how scientific instruments are managed, moving away from a model where calibration is a separate, manual task done before an experiment begins. Instead, calibration becomes an integral part of the measurement process itself. The detector is no longer a static tool that must be perfectly tuned before use; it is an adaptive system that learns and improves as it operates. This capability is particularly valuable for complex experiments where conditions change rapidly or where the detectors are subjected to aging and wear. By embedding the laws of physics directly into the learning process, the researchers have created a path toward fully autonomous scientific instruments that can maintain their own accuracy throughout their lifetime.

The study confirms that it is possible to achieve high-precision calibration without labeled data or dedicated test runs. The system successfully solved the dual problem of figuring out the wire settings and the particle positions at the same time, a task that was previously thought to require external reference points. The success of this method suggests that many other scientific instruments could benefit from similar self-supervised approaches, provided they have enough internal redundancy and physical constraints to guide the learning. As scientific facilities become more complex and the demand for continuous, high-quality data grows, the ability of instruments to adapt and self-calibrate will likely become a standard feature rather than an experimental novelty. The detector, in this new paradigm, is calibrated by the experiment itself.

Technical Summary: Physics-Informed Self-Supervised Learning for MWPPAC Calibration

1. Problem Statement

Scientific instruments, particularly particle detectors, require accurate calibration to convert raw sensor signals into reliable physical observables. Conventional calibration relies on dedicated calibration runs, analytical response models (e.g., assuming Gaussian or hyperbolic secant charge distributions), or supervised learning with labelled reference data. These approaches suffer from significant limitations:

Operational Disruption: Calibration often requires interrupting normal experiment operations.
Rigidity: Analytical models may become invalid due to detector aging, electronic drifts, or changing operating conditions.
Data Scarcity: Obtaining accurately labelled position data for self-supervised training is often difficult, expensive, or impossible.
Decoupled Optimization: Traditional methods typically estimate wire gains and interaction positions independently, ignoring the mutual dependency between calibration accuracy and reconstruction precision.

This work addresses the challenge of performing joint wire calibration and interaction position reconstruction in Multi-Wire Parallel Plate Avalanche Counters (MWPPACs) without labelled position measurements or dedicated calibration runs.

2. Methodology

The authors propose a physics-informed self-supervised learning framework that formulates detector calibration as a latent optimization problem. The core innovation is the simultaneous estimation of global detector parameters (wire gains) and event-specific latent variables (interaction positions) using only intrinsic physical constraints.

2.1. Latent Variable Formulation

The framework optimizes two distinct categories of unknowns:

Global Latent Variables: Calibration coefficients (gains) for every sensing wire. These are shared across all events and account for detector-specific characteristics (electronic response, aging, mechanical tolerances).
Local Latent Variables: Sub-wire interaction offsets ( $\delta x$ ) for every detected particle. These are event-specific and derived from local charge distributions.

2.2. Neural Architecture

The system employs an end-to-end differentiable architecture consisting of:

Calibration Subnetworks: Four independent neural networks (one per detector plane) that predict multiplicative gain coefficients for all wires. To ensure the output represents a constant detector parameter rather than an event-dependent quantity, these networks receive a dummy scalar input sampled from a uniform distribution.
Universal Position Reconstruction Network: A single shared network that estimates the sub-wire interaction offset ( $\delta x$ ) based on the local calibrated charge distribution of a small neighborhood of adjacent wires (centered on the wire with maximum charge). Crucially, this network is detector-independent; it does not receive absolute coordinates or wire indices, learning only the relationship between local charge profiles and position.

2.3. Physics-Informed Objective Function

Since no labelled data is available, supervision is derived exclusively from two physical consistency constraints:

Geometric Consistency: The MWPPAC system consists of two redundant detector planes separated by a known distance. The trajectory of a particle originating from a target region implies a deterministic geometric relationship between the reconstructed positions on the two planes ( $X_{P1} = X_{C2} \frac{D_1}{D_2}$ , etc.). The loss function minimizes the residuals ( $\Delta X = X_P - X_C$ ) between projected and reconstructed positions.
Charge-Energy Consistency: The total calibrated charge collected by a detector plane must be proportional to the energy loss measured in a downstream ionization chamber ( $\sum Q_{cal} = f E_{IC}$ ). This constraint resolves the normalization ambiguity of the gain coefficients.

The total objective function is a weighted sum of geometric and charge-energy losses, optimized via standard back-propagation.

3. Key Contributions

Unified Self-Supervised Formulation: The first framework to jointly optimize wire calibration and interaction position reconstruction in MWPPACs using only physically derived consistency constraints, eliminating the need for labelled interaction positions.
Detector-Independent Learning: Introduction of a position reconstruction network that learns the local induction profile directly from data without assuming an analytical functional form (e.g., Gaussian), making the model transferable to detectors with different dimensions or wire counts.
Continuous Adaptation: A method enabling continuous detector self-calibration during normal operation, capable of adapting to slow detector evolution (aging, drifts) without interrupting experiments.
End-to-End Optimization: A differentiable framework where improved calibration enhances position reconstruction, and improved reconstruction provides stronger geometric constraints for calibration, creating a mutually reinforcing optimization loop.

4. Experimental Results

The framework was evaluated using experimental data from the VAMOS++ magnetic spectrometer (E850 experiment), specifically the entrance Dual Position Sensitive MWPPAC tracking detectors.

Convergence: The self-supervised optimization converged rapidly (within ~0.5 minutes) to a stable solution, with training and validation residuals showing no overfitting.
Spatial Homogeneity: Unlike conventional methods using analytical induction profiles (hyperbolic secant), which exhibited local discontinuities and clustering near wires, the proposed framework produced smooth, uniform residual distributions across the detector surface.
Position Resolution:
- The reconstructed beam profile on the target showed reduced width ( $\sigma_{Xtarget}$ improved from 0.468 mm to 0.433 mm; $\sigma_{Ytarget}$ from 0.592 mm to 0.572 mm).
- Position resolution, validated independently using 100 $\mu$ m reference wires, improved by 33% (front wire) and 44% (rear wire) compared to the conventional method.
Implicit Profile Learning: The results confirmed that the network successfully learned the true detector induction profile from experimental data, removing artifacts associated with incorrect analytical assumptions.

5. Significance and Claims

The paper positions this work as a significant step toward autonomous intelligent instrumentation. The authors claim that:

Paradigm Shift: Detector calibration is transformed from a prerequisite (performed before an experiment) into an integral part of the measurement process itself.
Generalizability: The methodology establishes a general framework applicable to a broad class of scientific instruments where redundant measurements or known physical relationships (e.g., charge conservation, geometric projection) provide sufficient supervisory information.
Operational Impact: By enabling continuous self-calibration, the approach reduces experimental downtime, improves measurement reliability under evolving conditions, and simplifies the operation of complex facilities.
Modularity: The framework is modular; detector-specific knowledge is introduced solely through the physics-informed objective function, allowing the same learning architecture to be applied to different subsystems (e.g., ionization chambers, focal-plane detectors) by simply changing the physical constraints.

The authors conclude that while the current work focuses on linear gain calibration, the principle of combining differentiable machine learning models with detector-specific physical constraints provides a foundation for the next generation of adaptive, self-calibrating scientific instruments.