ExpertSim: Fast ZDC Detector Simulator

• ExpertSim is a fast detector simulation framework for ALICE’s ZDC that uses a Mixture-of-Generative-Experts to handle multimodal response regimes.
• It employs a learned router to assign particle conditions to specialized GAN-based experts, resulting in improved simulation fidelity over single-generator models.
• Empirical results show lower Wasserstein distances and significantly faster CPU/GPU inference, addressing high-energy physics computational bottlenecks.

ExpertSim is a fast detector-simulation framework for the Zero Degree Calorimeter (ZDC) in the ALICE experiment at CERN, designed as a learned surrogate for computationally expensive Monte Carlo simulation. Its defining feature is a Mixture-of-Generative-Experts architecture in which a router assigns each particle condition to one of several specialized GAN-based experts, rather than forcing a single generator to model the full heterogeneity of detector responses. In the reported setting, this specialization targets distinct response regimes in ZDC data and yields substantially better fidelity than prior single-generator baselines while preserving near-single-model inference speed (Będkowski et al., 28 Aug 2025).

1. Motivation and problem formulation

ExpertSim was proposed for a specific bottleneck in high-energy physics computing: detector-response simulation in ALICE relies heavily on Monte Carlo methods that are high-fidelity but computationally expensive. The paper notes that, in 2023, over 540,000 CPU devices were used for ALICE computations. It also notes that recent generative machine-learning methods can accelerate simulation by tens to hundreds of times, but standard single-model generators struggle when the detector-response distribution is strongly multimodal (Będkowski et al., 28 Aug 2025).

The ZDC is presented as a case where this heterogeneity is pronounced. Its responses are described as falling into roughly three broad types: low-intensity, dispersed responses; medium-intensity responses; and high-intensity, focused responses. A central claim of ExpertSim is therefore architectural rather than merely algorithmic: detector-response simulation is not one homogeneous generation problem but a mixture of physically distinct regimes. This directly motivates the use of multiple experts plus a learned router, rather than a single larger generator (Będkowski et al., 28 Aug 2025).

A common misconception is to read this as a standard large-scale MoE design borrowed from NLP. The paper explicitly distinguishes its use of MoE from the usual NLP/vision setting in which MoE is primarily a parameter-scaling strategy. Here, the purpose is to represent physically distinct detector-response regimes while keeping inference fast (Będkowski et al., 28 Aug 2025).

2. Detector setting and data representation

The target detector is the Zero Degree Calorimeter, which measures energy from non-interacting nuclei in heavy-ion collisions and helps determine collision centrality. The detector contains two devices: the proton calorimeter ZP and the neutron calorimeter ZN (Będkowski et al., 28 Aug 2025).

The response is represented as a 1-channel image. For ZP, the resolution is $56 \times 30$; for ZN, it is $44 \times 44$. Each training example consists of an image response $x$ and a conditional vector $c$ with 9 variables: energy, mass, charge, 3 spatial coordinates, and 3 momentum coordinates. The learning problem is therefore conditional image generation: produce detector-response images from particle properties (Będkowski et al., 28 Aug 2025).

Evaluation is reported on the five readout channels PMTc1 and PMT1–4. The main quantitative metric is the 1st Wasserstein distance between generated and real distributions. The reported dataset sizes are 344k proton samples and 400k neutron samples, with an 80/20 train-test split (Będkowski et al., 28 Aug 2025).

3. Architecture and generative mechanism

ExpertSim has two principal components: a router network and three generative experts. The router is a multilayer fully connected network that takes the particle condition vector $c$ as input and outputs an assignment to one of the experts. Its purpose is to route similar particle conditions to the same expert, balance expert usage, and promote specialization (Będkowski et al., 28 Aug 2025).

Each expert is a conditional DCGAN-like module comprising a generator $G(z,c)$, a discriminator $D(x,c)$, and an auxiliary regressor. The generator maps latent noise $z \sim \mathcal{N}(0,1)^k$ and the condition $c$ to a generated calorimeter image,

$\hat{x} = G(z,c).$

The discriminator receives the image and the condition and distinguishes real from fake samples. The auxiliary regressor predicts the coordinates of the peak-intensity pixel, interpreted as the shower center, to improve geometric accuracy (Będkowski et al., 28 Aug 2025).

The use of GANs is itself part of the design logic. The paper argues that GANs are appropriate because the priority is fast generation, and GAN inference is typically cheaper than likelihood-based or diffusion-based alternatives. ExpertSim therefore couples a routing mechanism for heterogeneity with a backbone chosen for low-latency generation (Będkowski et al., 28 Aug 2025).

4. Training objectives and expert specialization

The router is regularized by two explicit losses. The expert utilization loss encourages balanced expert use through entropy maximization: $44 \times 44$0 where $44 \times 44$1 is the number of experts and $44 \times 44$2 is the batch-average gating probability for expert $44 \times 44$3. The expert differentiation loss encourages the experts to generate measurably different outputs using mean image intensity,

$44 \times 44$4

$44 \times 44$5

The resulting router objective is

$44 \times 44$6

These terms are meant to prevent routing collapse and force the experts to occupy different response regimes (Będkowski et al., 28 Aug 2025).

Each expert uses a composite objective extending adversarial training. Beyond the adversarial term, the paper includes intensity regularization,

$44 \times 44$7

and an auxiliary regression loss for the shower-center coordinates,

$44 \times 44$8

The final expert loss is

$44 \times 44$9

The diversity term $x$0, adapted from SDI-GAN, is used to encourage latent-space variation to translate into image-space variation (Będkowski et al., 28 Aug 2025).

Reported mean intensities show that the experts do not become redundant but separate into distinct regimes.

Expert	Proton mean	Neutron mean
Expert 1	119	108
Expert 2	53	82
Expert 3	70	125

The intended specialization is that one expert handles low-intensity, diffuse responses, another medium-intensity responses, and another high-intensity, focused responses. The reported mean-intensity differences are consistent with that interpretation (Będkowski et al., 28 Aug 2025).

5. Empirical results, ablations, and limitations

The main fidelity comparison is reported as mean 1st Wasserstein distance over five runs.

Model	Proton WS	Neutron WS
GAN	2.47	2.42
SDI-GAN	2.35	2.31
SDI-GAN + IR	2.29	2.04
SDI-GAN + IR + AR	2.07	1.89
ExpertSim	1.59	1.34
Monte Carlo	0.47	0.34

These results place ExpertSim clearly ahead of the compared generative baselines, though still short of Monte Carlo fidelity. The paper states that the method improves by more than 15% over the previous state of the art. It also reports that ExpertSim is best in every intensity quartile for both proton and neutron responses, with proton quartile WS values of 1.06, 1.16, 1.27, and 7.06, and neutron quartile WS values of 2.20, 4.02, 5.62, and 5.69 (Będkowski et al., 28 Aug 2025).

The performance claims are paired with a speed argument. For generation of 10,000 responses, a three-expert model requires 314 seconds on CPU and 3.27 seconds on GPU, compared with 11,172 seconds for Monte Carlo on CPU. The reported router overhead is about 2%, and GPU inference for 1 to 5 experts remains in the range of roughly 3.20 to 3.55 seconds. The stated implication is that specialization improves fidelity without materially changing the low-latency character of GAN inference (Będkowski et al., 28 Aug 2025).

Ablation results indicate that the choice of three experts is not arbitrary. With 2, 3, 4, and 5 experts, the reported proton/neutron WS values are 2.71/1.76, 1.59/1.34, 3.26/1.63, and 3.07/3.12, respectively, making three experts the best-performing configuration. Router regularization is also critical: removing $x$1 causes poor specialization and very bad WS, with proton 6.80 and neutron 8.01; removing $x$2 also hurts performance and can cause routing collapse. The default values are $x$3 and $x$4 (Będkowski et al., 28 Aug 2025).

The paper is explicit about limitations. ExpertSim still requires careful router regularization, introduces more hyperparameters than a single GAN, does not yet match Monte Carlo fidelity, and is tailored to problems where the data naturally decomposes into a few regimes. This makes it better understood as a fast, structured surrogate than as a full replacement for Monte Carlo (Będkowski et al., 28 Aug 2025).

6. ExpertSim as a broader simulation paradigm

Although ExpertSim is a specific particle-detector simulator, the surrounding literature suggests a broader pattern in which simulation systems are organized around expert knowledge, expert-curated targets, or expert-like interactive workflows. A plausible implication is that the importance of ExpertSim lies not only in its ZDC application but also in the architectural principle of decomposing difficult simulation tasks into specialized components with explicit coordination (Będkowski et al., 28 Aug 2025).

In policy evaluation, "PolicySimEval" defines the first benchmark designed to evaluate the capability of agent-based simulations in policy assessment tasks. It contains 20 comprehensive scenarios, 65 targeted sub-tasks, and 200 auto-generated tasks, together with expert-annotated solutions and a multi-dimensional metric suite covering Argument Coverage, Behavior Calibration, Language and Ethics, Outcome Effectiveness, and System Performance. The best-performing system, ReAct-RAG with GPT-4o, reaches only 24.5% coverage rate on comprehensive scenarios, 15.04% on sub-tasks, and 14.5% on auto-generated tasks, underscoring the difficulty of expert-like simulation in policy domains (Kang et al., 11 Feb 2025).

In autonomous driving, "ForSim: Stepwise Forward Simulation for Traffic Policy Fine-Tuning" addresses covariate shift, multimodal realism, and non-reactive rollouts through a stepwise planning–execution–replanning process. It selects at each virtual timestep the candidate trajectory that best matches a fixed reference mode after temporal alignment, executes the selected candidate through a PID controller coupled with a kinematic bicycle model, and recomputes surrounding-agent predictions at every virtual timestep. When integrated into RIFT, this stepwise closed-loop design improves safety while maintaining efficiency, realism, and comfort, emphasizing that expert-grade simulation fidelity depends on closed-loop multimodal interaction rather than open-loop rollout alone (Chen et al., 2 Feb 2026).

In electromagnetic simulation, "RadioSim Agent" combines LLMs with deterministic EM/ray-tracing simulators and vision-enabled reasoning. Its Reason–Act–Observe loop lets an LLM interpret natural-language objectives, call simulate_radio_environment() with mechanisms such as LOS, REF, GREF, NLOS, and BEL, and then summarize resulting pathloss heatmaps. This suggests a different but related form of expert simulation: the coupling of flexible reasoning to physically grounded tools so that natural-language interaction does not replace first-principles computation (Hussain et al., 8 Nov 2025).

In instructional practice, "EducaSim: Interactive Simulacra for CS1 Instructional Practice" uses generative student agents with personas, memory retrieval based on time of creation, importance, and semantic similarity, an LLM-based speaker oracle, and post-session feedback and self-reflection. It was deployed in a six-week CS1 course supporting 20,000 students and 1,300 volunteer teachers, with 254 logged sessions and a mean session duration of 15 minutes 45 seconds. Here, expert simulation is not physical surrogate modeling but role-play rehearsal in which a structured multi-agent environment approximates the dynamics that novice teachers need to practice (Mohne et al., 12 Mar 2026).

A related scenario-based ABM line argues for separating programmers from domain experts and policy-makers through a disconnected architecture in which a Scenario packages input variables, Policies, and one BehaviourFlow per agent type. Built in Python on Mesa and Mesa-Geo, this design lets experts reshape behavior and interventions without editing code, extending the idea of expert-centered simulation from model training to model governance and experiment design (Nallur et al., 2024). At the opposite end of the scientific spectrum, "SIMEX: Simulation of Experiments at Advanced Light Sources" provides complete start-to-end simulation of photon experiments from source generation through beam transport, sample interaction, scattering, detector response, and downstream analysis, showing that expert-oriented simulation can also mean end-to-end orchestration of heterogeneous high-fidelity physics modules (Fortmann-Grote et al., 2016).

Taken together, these works suggest that "ExpertSim" names both a specific ZDC simulator and a broader systems idea: simulation becomes more effective when heterogeneous regimes, expert judgments, or domain-specific modules are represented explicitly rather than absorbed into a single undifferentiated model. In the ZDC setting, that principle appears as a Mixture-of-Generative-Experts; in other domains, it appears as benchmarked expert targets, stepwise closed-loop dynamics, tool-augmented reasoning, multi-agent rehearsal, scenario-layer separation, or start-to-end experimental digital twins (Będkowski et al., 28 Aug 2025).