⚛️ nuclear experiments

Automated Physics-Informed Neural-Networks-Based Calibration of Highly Segmented Silicon Telescopes

This paper presents a fully automated, physics-informed neural network framework that efficiently calibrates highly segmented silicon telescope arrays by simultaneously optimizing detector gains and geometrical corrections through global minimization of reconstructed excitation energy widths, as demonstrated by its successful application to PISTA fission data.

Original authors: M. Rejmund, A. Lemasson, P. Morfouace, D. Ramos, J. Taieb, J. D. Frankland

Published 2026-09-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: M. Rejmund, A. Lemasson, P. Morfouace, D. Ramos, J. Taieb, J. D. Frankland

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 heart of modern nuclear physics, scientists are trying to understand the building blocks of matter by smashing atoms together at incredible speeds. To make sense of these collisions, they need to know exactly what particles were created, how much energy they carried, and the precise angle at which they flew away. Imagine trying to reconstruct a car crash by looking at the scattered debris; if you cannot measure the speed and direction of every piece of metal with extreme accuracy, the story of the crash remains a mystery. For decades, researchers have relied on silicon detectors, which act like high-speed cameras that capture the energy and path of these subatomic particles. As these detectors have become more advanced, they have been sliced into thousands of tiny, independent strips to capture finer details. However, this increase in detail has created a massive headache for the scientists who must calibrate them.

Calibration is the process of tuning a detector so that its raw electrical signals translate into correct physical measurements. In the past, scientists could adjust each channel of a detector one by one, a slow and tedious task that relied heavily on human judgment. But when a detector has thousands of channels, this old method becomes impossible. It is too slow, prone to human error, and often fails to ensure that all parts of the detector agree with one another. The challenge is to find a way to tune this complex machine automatically, using the laws of physics as a guide, so that the data it produces is perfectly consistent.

A team of researchers at GANIL in France has solved this problem by teaching a computer to calibrate the detector for them. They developed a new system that uses a type of artificial intelligence known as a neural network. Instead of asking a human to tweak thousands of settings individually, they set up a mathematical puzzle where the computer must find the perfect settings that make the physics work out correctly. The system relies on a fundamental rule of nature: when two particles collide and bounce off each other without breaking apart, their total energy and the angles at which they fly away are locked together in a precise relationship. If the detector is not calibrated correctly, this relationship will look broken. The computer's job is to adjust the detector's settings until the data fits this perfect physical pattern.

The researchers tested this method on a specific array of detectors called PISTA, which is made of eight trapezoidal telescopes, each containing thousands of tiny silicon strips. These telescopes are designed to catch light nuclei produced when heavy uranium atoms collide with carbon atoms. The team fed the computer raw data from these collisions, along with a small amount of known calibration data from alpha particles. The neural network then began its work, adjusting the gain, or sensitivity, of every single strip, and even making tiny corrections to the physical position of the telescopes themselves. It did this by constantly checking its work against the two-body kinematics constraint, ensuring that the reconstructed energy of the collision matched the theoretical expectation of zero excitation energy for elastic scattering.

The results were striking. The computer found the correct settings in just a few minutes, a task that would have taken human experts weeks or months to complete using traditional methods. Once calibrated, the detector produced data that aligned perfectly with theoretical predictions. The researchers could clearly see the distinct bands of different atomic elements, such as carbon and oxygen, separated with high precision. The energy resolution, which measures how clearly the detector can distinguish between similar energy levels, improved significantly. In fact, the system achieved a resolution where the spread of the data was approximately 0.436 MeV, allowing scientists to see details in the nuclear reactions that were previously blurred.

One of the most important aspects of this new approach is that it does not require the scientists to build a complex model of how the detector works internally. They do not need to simulate the exact behavior of every electron inside the silicon. Instead, the system learns directly from the experimental data, guided only by the unbreakable laws of physics. This makes the method robust and adaptable. The researchers found that the calibration was consistent across all the different telescopes in the array, proving that the system could handle the complexity of thousands of channels without losing its way. The method also successfully corrected for small misalignments in the physical placement of the detectors, adjusting for shifts as small as a few millimeters and angle changes of a few degrees.

The study demonstrates that machine learning can be a powerful partner in experimental physics, not just as a tool for analyzing data, but as a fundamental part of the measurement process itself. By embedding physical laws directly into the training of the neural network, the researchers created a self-consistent system that is both efficient and reliable. This approach offers a solution for the next generation of detectors, which are expected to be even larger and more complex. As nuclear physics pushes toward higher resolutions and more intricate experiments, the ability to calibrate these massive systems automatically will be essential. The work confirms that when artificial intelligence is guided by the solid ground of physical principles, it can solve problems that are too large and too intricate for human hands alone, opening the door to clearer views of the atomic world.

Technical Summary: Automated Physics-Informed Neural-Networks-Based Calibration of Highly Segmented Silicon Telescopes

Problem Statement
Modern nuclear physics experiments increasingly rely on highly segmented silicon detector arrays to achieve fine angular resolution and large solid-angle coverage for transfer and multi-nucleon transfer reactions. While this granularity enhances experimental capabilities, it introduces significant challenges for detector calibration. Traditional calibration methods, which typically operate on a channel-by-channel basis through iterative and often manual adjustments, become inefficient, difficult to scale, and prone to subjective biases. These conventional approaches struggle to maintain global consistency across hundreds or thousands of individual channels, particularly when each channel samples only a limited fraction of the physical phase space with reduced statistics. There is a critical need for robust, reproducible, and scalable calibration strategies capable of handling high-dimensional data and exploiting correlations between detector segments.

Methodology
The authors propose a fully automated, data-driven calibration framework based on neural networks, specifically designed for highly segmented silicon telescope arrays. The method reformulates calibration as a global optimization problem rather than a series of independent channel adjustments.

Physics-Informed Optimization: The core of the approach is the minimization of the width (Root Mean Square Deviation, RMSD) of the reconstructed excitation energy ( $E^*$ ) under two-body kinematics constraints. The system assumes elastic scattering events where the target excitation energy is zero ( $E^*_{target} = 0$ ).
Neural Network Architecture: The model employs three independent sub-models that share a common loss function:
1. A sub-model for $\Delta E$ gain ( $a_k$ ) as a function of the strip number.
2. A sub-model for residual energy ( $E_{res}$ ) gain ( $b_l$ ) as a function of the strip number.
3. A sub-model for geometric placement corrections, specifically vertical shift ( $\delta y$ ) and polar angle shift ( $\delta \theta$ ) for each telescope.
Loss Function and Constraints: The loss function integrates physics constraints directly. It processes two types of events:
- Experimental events: Undergo full kinematic reconstruction to calculate $E^*$ based on total energy ( $E_{tot}$ ) and emission angle ( $\theta_L$ ).
- Calibration events: Use pre-experiment three-alpha calibration data to anchor the absolute energy scale and correct offsets, preventing degeneracies between gain and angular corrections.
Data Utilization: The method relies exclusively on experimental data and established physical principles (two-body kinematics) without requiring explicit modeling of the detector response. It utilizes data from the Particle-Identification Silicon-Telescope Array (PISTA) involving the elastic scattering of $^{238}\text{U}$ on $^{12}\text{C}$ .

Key Contributions

Global Calibration Strategy: The paper introduces a strategy that determines detector gains and geometrical corrections simultaneously, ensuring coherence and self-consistency across all detector channels.
Scalability and Automation: The framework is fully automated and computationally efficient, achieving convergence within approximately two minutes, a significant improvement over the weeks or months required for traditional channel-by-channel calibration.
Handling Degeneracies: By combining alpha calibration data (anchoring the energy scale) with two-body kinematics constraints (enforcing global energy-angle correlation), the method effectively lifts partial degeneracies between detector gains and angular corrections.
Modular Design: The use of independent sub-models sharing a common loss function allows for the independent determination of gains while maintaining constant geometric corrections per telescope.

Results
The method was validated using experimental data from the PISTA array (specifically telescopes at azimuthal angles $\phi = 90^\circ, 135^\circ, 180^\circ$ ).

Excitation Energy Resolution: The reconstructed excitation energy spectra showed excellent agreement with theoretical kinematics. The achieved standard deviation for the excitation energy resolution was $\sigma_{E^*} = 0.436(10)$ MeV for the combined telescopes. Individual telescope resolutions ranged from $0.350(10)$ MeV to $0.490(10)$ MeV, consistent with Monte Carlo simulations after refining the estimated beam profile width.
Particle Identification (PID): The calibration enabled high-quality particle identification. The two-dimensional correlation between energy loss and residual energy showed well-separated bands for different atomic numbers and mass numbers. The one-dimensional PID spectra demonstrated consistent isotope separation across all telescopes, with a standard deviation of $\sigma_{PID} = 0.03$ PID units.
Geometric Corrections: The derived placement corrections ( $\delta \theta \approx +3.2^\circ$ , $\delta y \approx 0$ mm) were consistent with independent mechanical survey data, providing additional validation of the procedure.
Reproducibility: The training process demonstrated high stability, with calibration coefficients showing only modest random variations ( $\pm 2\%$ for $\Delta E$ gains, $\pm 0.5\%$ for $E_{res}$ gains) across channels, regardless of dataset subsampling.

Significance and Claims
The paper claims that this framework provides a general, adaptable, and efficient solution for calibrating complex detector systems in modern nuclear physics. By embedding domain knowledge (physics constraints) directly into the optimization process, the approach avoids the limitations of purely empirical models while retaining the flexibility of data-driven methods. The authors assert that the method is particularly suitable for next-generation detector systems characterized by increasing granularity and complexity. The work demonstrates that physics-informed machine learning can successfully address complex calibration problems, offering a robust, reproducible, and time-efficient alternative to conventional manual procedures. The authors note that the framework is adaptable to other experimental configurations and could potentially be extended to multi-body reaction channels in future developments.

Technical Summary: Automated Physics-Informed Neural-Networks-Based Calibration of Highly Segmented Silicon Telescopes

More like this