Physics Instrument Design with Reinforcement Learning

TL;DR

The paper tackles the challenge of designing complex physics instruments, a high-dimensional optimization problem often constrained by gradient-based methods. It proposes a PPO-based reinforcement learning framework to design calorimeters and spectrometers through mixed continuous-discrete actions, optimizing returns $G_t$ under policies $\pi(a|s)$ learned via interaction with simulation environments. Two empirical studies demonstrate that RL can autonomously generate high-performing detector layouts, achieving notably improved hadronic energy resolution and momentum reconstruction compared with baselines, and outlines a roadmap of extensions (GNNs, off-policy methods, surrogate simulators) for more complex designs and future facilities like the FCC. The work argues that RL offers a scalable, flexible path to automated instrument design that can navigate combinatorial design spaces beyond what differentiable optimization can readily handle, while acknowledging opportunities for hybrid approaches with differentiable methods.

Abstract

We present a case for the use of Reinforcement Learning (RL) for the design of physics instrument as an alternative to gradient-based instrument-optimization methods. It's applicability is demonstrated using two empirical studies. One is longitudinal segmentation of calorimeters and the second is both transverse segmentation as well longitudinal placement of trackers in a spectrometer. Based on these experiments, we propose an alternative approach that offers unique advantages over differentiable programming and surrogate-based differentiable design optimization methods. First, Reinforcement Learning (RL) algorithms possess inherent exploratory capabilities, which help mitigate the risk of convergence to local optima. Second, this approach eliminates the necessity of constraining the design to a predefined detector model with fixed parameters. Instead, it allows for the flexible placement of a variable number of detector components and facilitates discrete decision-making. We then discuss the road map of how this idea can be extended into designing very complex instruments. The presented study sets the stage for a novel framework in physics instrument design, offering a scalable and efficient framework that can be pivotal for future projects such as the Future Circular Collider (FCC), where most optimized detectors are essential for exploring physics at unprecedented energy scales.

Figures (5)

• Figure 1: Agent-environment interaction in Reinforcement Learning (adapted from sutton2018reinforcement)
• Figure 2: Reinforcement Learning for instrument design
• Figure 3: Design of uniform sampling calorimeter with proximal policy optimization (PPO). The top two plot shows the performance of the calorimeter as a function of iterations. The performance is represented by the resolution, calculated as $\frac{\sigma(E_{\mathrm{pred}}/E_{\mathrm{true}})}{\mu(E_{\mathrm{pred}}/E_{\mathrm{true}})}$, where $\sigma$ denotes the standard deviation and $\mu$ denotes the mean. The middle plot shows the cumulative reward during the episode (one design). In both of these figures, the the best design (as per the cumulative reward value) is chosen over intervals of 5000 designs and the resolution for different types of particles is plotted. The x-axis is shared between the two figures. The bottom plot shows the best designs found during different intervals
• Figure 4: Design of spectrometer with Reinforcement Learning. The top two plot shows the performance of the calorimeter as a function of iterations. The performance is represented by the resolution, calculated as $\frac{\sigma(p_{\mathrm{pred}}/p_{\mathrm{true}})}{\mu(p_{\mathrm{pred}}/p_{\mathrm{true}})}$, where $\sigma$ denotes the standard deviation and $\mu$ denotes the mean. The top plot shows the cumulative reward during the episode (one design). In both of these figures, the the best design (as per the cumulative reward value) is chosen over intervals of 400 designs and the resolution for different types of particles is plotted. The x-axis is shared between the two figures. The bottom illustration shows the best designs found during different intervals during the training process. The magnet section is shown as the stripped section at the very middle and the number of sensors is shown as a color bar on the right side
• Figure 5: The top left figure shows the process of line fitting in Region A and right figure, Region C. Bottom figure shows the reconstructed trajectories in the two regions. The color of the line correspond to goodness of the fit or residuals and a darker color indicates lower residuals