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LinacNet: A Composable Particle-Cloud Surrogate Model for Linear Accelerators, and Its Path to Larger Machines

LinacNet introduces a composable, PointNet-based surrogate model that predicts complete macro-particle clouds for individual linear accelerator segments, enabling high-fidelity, end-to-end beam simulations that can be chained together to potentially scale toward the modeling of much larger and more complex future collider facilities.

Original authors: Emmanuel Goutierre, Christelle Bruni, johanne Cohen, Hayg Guler, Michèle Sebag

Published 2026-08-27

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CC BY 4.0

Original authors: Emmanuel Goutierre, Christelle Bruni, johanne Cohen, Hayg Guler, Michèle Sebag

Original paper licensed under CC BY 4.0 (https://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

Particle accelerators are the massive engines of modern physics, shaping streams of charged particles into tight, high-energy beams to probe the fundamental building blocks of matter. From creating new materials to treating cancer, these machines rely on the precise coordination of thousands of components, all tuned to exacting standards. To keep them running, scientists rely on detailed computer simulations that model how these particles move and interact. However, these simulations are incredibly slow; a single run can take days, and every time the machine's settings change, the entire calculation must start over. To speed things up, researchers have turned to artificial intelligence to build "surrogate models"—fast, learned shortcuts that predict outcomes without running the full physics engine. But for years, these shortcuts had a critical flaw: they could only predict a few summary numbers, like the size or energy of the beam. While useful for a quick check, these numbers are useless for the next step in the process, because the next part of the machine or the next computer code needs to see the entire, complex cloud of individual particles to function.

A team of researchers has now built a new kind of AI model that solves this problem by predicting the entire cloud of particles, not just a few summary statistics. Called LinacNet, this system was tested on the linear accelerator of ThomX, a compact facility in France that produces bright X-rays for scientific research. The machine is divided into twenty-five distinct sections, or segments, where the beam is accelerated and shaped. Instead of trying to guess the final result of the whole machine at once, the researchers trained a separate AI module for each of these twenty-five segments. Each module learns to take a cloud of particles entering a segment and predict exactly how that cloud will look when it exits, including the position and momentum of every single particle within it. Because the output of one module is a complete cloud of particles, it can be fed directly into the next module, just as if the real machine were passing the beam along. This allows the entire chain of twenty-five modules to be linked together, creating a fast, end-to-end prediction of the beam's journey from start to finish.

The researchers trained these modules using thirty thousand detailed computer simulations of the ThomX accelerator, a process that would have taken months to run on the actual physics software but was completed much faster with the AI. They found that for a single segment, the model was astonishingly accurate, predicting the behavior of the particles with a level of precision that exceeded the resolution of the physical sensors installed on the real machine. The model could distinguish between particles that survived the journey and those that were lost, and it did so while maintaining the complex relationships between all the particles in the cloud. When the researchers linked all twenty-five modules together to simulate the entire accelerator, the system remained faithful to the physics, successfully describing the beam from the beginning to the end. However, they discovered a subtle tension in how to train the system: if they trained each segment to be perfect on its own, small errors would pile up as the beam traveled through the chain, eventually ruining the final prediction. The solution was to train the segments while also keeping an eye on the final result, a balancing act that kept the errors from drifting apart.

This work suggests a new way to handle the massive, complex machines of the future, such as the proposed Future Circular Collider, which would be tens of kilometers long and involve dozens of different subsystems. Building a single, giant AI model for such a facility would be impractical, but a library of small, interchangeable modules like LinacNet could be shared and updated by different teams around the world. Each team could train the model for their specific section of the machine, and these pieces could be snapped together to simulate the whole system. While the current study was limited to a fifty-megaelectronvolt accelerator, the approach offers a plausible path toward simulating machines an order of magnitude larger and more complex. The researchers emphasize that while the method works well in simulation, the next step is to test it on real, measured data from the machine and to see if this modular, cloud-based approach can truly scale to the international collaborations required for the next generation of particle physics.

Technical Summary: LinacNet

Problem Statement

Detailed numerical simulations (e.g., ASTRA) remain the standard for particle accelerator design and operation but are computationally expensive, often requiring days for complex scenarios. While machine learning (ML) surrogates have been developed to accelerate this process, existing approaches typically output only a limited set of derived beam observables (e.g., beam size, emittance, mean energy). This limitation prevents the chaining of simulations, as subsequent beamline elements or tracking codes require a full particle distribution (a "beam") as input, not just a summary of statistics. Consequently, current surrogates cannot serve as modular components in multi-stage accelerator systems, such as the proposed Future Circular Collider (FCC), where the output of one subsystem must seamlessly become the input of the next.

Methodology: LinacNet Architecture

LinacNet addresses this gap by predicting the complete macro-particle cloud for a linear accelerator segment rather than a scalar summary. The model is designed to be composable, meaning its output (a set of particles) matches the format of its input, allowing modules to be chained sequentially.

Input Representation: The beam is treated as a point cloud of macro-particles. Each particle $\zeta$ is represented by an 8-dimensional vector: position $(x, y, z)$ , momentum $(p_x, p_y, p_z)$ , intrinsic time $t$ , charge $q$ , and a survival indicator.
Network Architecture: The model adapts the PointNet architecture, which is permutation-invariant and processes unordered sets of points.
- Local Encoding: A Multi-Layer Perceptron (MLP) $\gamma$ encodes each particle independently.
- Global Context: A second MLP $\eta$ followed by a symmetric pooling operator $\kappa$ condenses the entire cloud into a global descriptor $K(D_i)$ . The authors found that a charge- and survival-weighted maximum pooling was the most effective and efficient choice.
- Conditioning: Control parameters $c$ for the specific accelerator segment are injected into the network, either alongside per-particle features or concatenated with the global descriptor.
- Prediction: A regression MLP $\chi$ combines the particle's local encoding with the global descriptor to predict the new coordinates as a residual to the input: $\hat{\zeta}_{i+1} = \chi(\gamma(\zeta_i), K(D_i)) + \zeta_i$ . A separate head predicts particle survival, enforcing the physical constraint that lost particles cannot reappear.
Training Strategy: The system is trained on 30,000 ASTRA simulations of the ThomX linac (divided into 25 segments). The training involves a trade-off between independent segment training (minimizing error for a single segment given the true input) and end-to-end (E2E) training (minimizing error for the final beam given the initial beam). A hybrid loss function interpolates between these two objectives to balance local fidelity with global consistency.

Key Contributions

Composable Surrogate Modeling: LinacNet is a surrogate designed to output the entire particle cloud rather than a handful of derived quantities. This design enables the chaining of modules to simulate entire beamlines, allowing the surrogate to interoperate with itself and conventional tracking codes.
Point-Cloud Adaptation for Beam Dynamics: The work successfully adapts PointNet to 8-dimensional macro-particles conditioned on segment control settings, demonstrating that point-cloud representations are viable for high-dimensional, sparse beam physics data.
Modularity: The architecture allows individual segments to be built, trained, validated, and replaced independently, facilitating a library-based approach to accelerator simulation.

Experimental Results

The model was evaluated on the ThomX linac (50 MeV) using a dataset of 30,000 simulations.

Single Segment Performance: A single module trained on the first segment (the most challenging due to space-charge effects) achieved an $R^2$ score above 0.99 for both beam observables and the full particle distribution. The residuals were smaller than the resolution of the installed diagnostic equipment (0.1 mm for position, 0.01 nC for charge).
End-to-End Performance: When chaining all 25 segments, the model maintained a faithful description of the beam ( $R^2_{D, 0 \to i} \ge 0.8$ across the machine). However, a structural tension was observed: purely independent training yields high segment-level accuracy but leads to error compounding in E2E predictions, while E2E training improves global accuracy at the cost of segment-level precision. A balanced loss weighting was found to be the most effective strategy.
Hyperparameter Sensitivity: The width of the global MLP was found to be critical; a width of zero (collapsing to a Siamese network) caused a sharp performance drop, while a width of just 5 was sufficient to capture necessary particle interactions. The balance between observable and distribution losses ( $w_O$ ) was the most significant hyperparameter.

Significance and Future Outlook

The paper positions LinacNet not as a final solution for all accelerator physics, but as a proof of concept for a modular, composable approach to surrogate modeling.

Scalability: The authors argue that this design is a plausible route toward simulating machines an order of magnitude larger and more complex than ThomX, such as the FCC. The ability to assemble a "library" of interoperable, segment-level surrogates is essential for facilities where a single monolithic simulation is infeasible.
Infrastructure: The modular nature of LinacNet aligns with emerging cloud-based, shared ML infrastructures (e.g., AI INFN platform), allowing different teams to maintain models for specific subsystems without retraining a monolithic model for every design change.
Limitations: The paper explicitly notes that the tension between local and end-to-end accuracy remains an open problem. Furthermore, while the approach works for a 50 MeV linac, its transferability to multi-institutional, multi-decade projects like the FCC requires further testing. The work also highlights the need for continual learning to handle machine drift over operational lifetimes.

In summary, LinacNet demonstrates that predicting full particle clouds is a workable strategy for maintaining surrogate compositability, offering a potential pathway to digital twins for next-generation, large-scale accelerator complexes.