The Correlation Frobenius Distance is introduced, a single normalized score for correlation fidelity at layer-wise and voxel-wise scales, and encoded the soft per-sample structure available in a shower as two physics-aware auxiliary losses: a variance-stabilized voxel residual loss grounded in counting statistics, and a graph Laplacian loss over the detector geometry.
Abstract
Monte Carlo simulation of calorimeter showers is a principal bottleneck for the High-Luminosity LHC, and diffusion models have emerged as fast, high-fidelity surrogates. Their denoising objective is purely statistical, however: a model can minimize it while placing the physics wrong. Existing physics-informed generative methods cannot close this gap, because they assume a closed-form law, a governing PDE residual or a hard per-sample constraint, that a shower does not supply: no per-sample PDE governs a stochastic cascade, and energy conservation fixes only one scalar per shower. Standard metrics ignore the correlation structure across calorimeter layers and voxels, comparing showers only in a physics feature space. We address both gaps. We introduce the Correlation Frobenius Distance (CFD), a single normalized score for correlation fidelity at layer-wise and voxel-wise scales. We then encode the soft per-sample structure available in a shower as two physics-aware auxiliary losses: a variance-stabilized voxel residual loss grounded in counting statistics, and a graph Laplacian loss over the detector geometry. We combine both with denoising through GradBlend, which anchors the step magnitude to the denoising gradient while letting the auxiliary steer its direction, yielding Lantern, a physics-guided diffusion surrogate. On CaloChallenge Dataset 2, injecting the physics losses through task-symmetric rules such as PCGrad, GradNorm, IMTL-G, and ConFIG inflates FPD by 2-100x relative to denoising alone, whereas GradBlend admits the same signal without regression and, with the Laplacian loss, Lantern improves both FPD and CFD. Our ablation on the auxiliary loss scheduler shows that the voxel residual loss, whose gradient conflicts with denoising, requires a terminal denoising-only phase to preserve shower fidelity, whereas the non-conflicting Laplacian loss is insensitive to the schedule.
The finite transverse granularity of a segmented electromagnetic calorimeter fundamentally limits the precision with which the observables of a shower can be reconstructed, among them its position, its lateral profile, and the direction of the incident particle. We show that a substantial fraction of the information suppressed by the segmentation can be inferred under physical constraints, and that it propagates to downstream physics quantities. The reconstruction is cast as an inverse problem and solved with a generative model constrained by the low-order spatial moments of the shower, driving the solution toward physically consistent energy distributions rather than image similarity alone. Using the undoped CsI calorimeter of the KOTO experiment as a reference system, the reconstruction reduces the per-event residual of these moments with respect to the truth-level reference by roughly 40-62% in a representative 1 GeV bin. The inferred morphology also generalizes beyond the training objective: on a $K_{L}\to\pi^{0}\nu\bar\nu$ Monte Carlo sample it improves the reconstruction of the photon incident angle, a quantity never used during training, and of the $\pi^{0}$ decay vertex. These results indicate that finite segmentation is better viewed as a limit on what a calorimeter measures directly than as an absolute limit on the physics information it retains, with the recoverable fraction depending on the observable and growing with the shower energy.
Non-intrusive optical measurement techniques are widely used to obtain high-resolution pressure, temperature, and velocity fields, but they often suffer from random data loss caused by geometric obstruction, surface reflection, or illumination non-uniformity. Conventional reconstruction methods usually depend on high-fidelity CFD priors or large paired datasets, which limits their flexibility for arbitrary missing patterns and scarce experimental samples. This study proposes a Physics-Informed Multi-Scale Resampled Denoising Diffusion Probabilistic Model (MSR-DDPM) for missing-data reconstruction in optical flow measurements. The method shifts the reconstruction paradigm from deterministic mapping to probabilistic distribution modeling. Three features are introduced: a multi-scale hierarchical reconstruction strategy that reduces computational cost by 56% and improves stability; embedded physics-informed constraints, including divergence and gradient-continuity terms, to enhance physical consistency and reduce dependence on large training datasets; and an optional conditional diffusion module that incorporates auxiliary low-fidelity data for extreme missing-data scenarios. The framework is validated for incompressible velocity-field imputation using turbine cascade passage data, demonstrating its ability to recover complex unsteady flow structures. For missing ratios of 10%-45%, MSR-DDPM achieves high-accuracy reconstruction with Symmetric Mean Absolute Percentage Error (SMAPE) below 6% without auxiliary data. Under more severe missing ratios of 45%-65%, auxiliary guidance substantially recovers flow details and reduces reconstruction errors by approximately 60%. These results indicate that MSR-DDPM offers a flexible, data-efficient, and physically consistent solution for missing-data imputation in complex experimental flow measurements.
Bo Yu, Pingting Chen, JunKui Mao· Journal of turbomachinery· 0 citations
The PhysDiff-VTON framework establishes a new paradigm for synthesizing photorealistic try-on images that adhere to physical constraints while maintaining intricate garment details, advancing the practical applicability of diffusion models in fashion technology.
Shibin Mei, Bingbing Ni· Neural Information Processin...· 3 citations
Fast simulation of electromagnetic calorimeter showers via deep generative models requires learning a distribution conditioned on the incident energy and angles (θi,ϕi) of the primary particle. We show that for the LEMURS universal-mesh representation of the FCCeeCLD silicon–tungsten sampling calorimeter (a co-rotating cylindrical grid aligned with the photon direction), this three-parameter conditioning problem reduces to one parameter plus a deterministic post-processing step. Analysing the complete FCCeeCLD subset of 939 010 Geant4 events, we identify a hierarchy of four residual angular effects, set against the dominant energy dependence of the normalised shower shape, whose Kullback–Leibler divergence DKL between extreme energy bands is of order 10−1. Against this scale, the normalised longitudinal profile depends weakly on the polar angle, at the DKL≲7×10−3 level. This residual factorises multiplicatively into a universal sampling-layer pattern and an empirically characterised angular amplitude with twelve-fold azimuthal modulation. Three further effects admit closed-form analytic descriptions: a sampling-fraction correction of a few percent, an azimuthal dipole proportional to |cosθi|, and a dodecagonal imprint on the dipole amplitude. We validate the factorised operator directly, without training any model: applying it to near-normal-incidence Geant4 showers reproduces independent oblique-incidence targets, and each correction acts exclusively on the observable it targets: an orthogonality exact by construction and confirmed numerically. The dominant shower physics therefore depends solely on the incident energy, with all angular dependence captured by analytic closed-form corrections and a compact empirical tabulation applied as a post-processing step. Generative models for this detector can accordingly be designed with a one-dimensional conditioning space, eliminating the need to learn angular interpolation over the full acceptance.
J. A. Chala Casanova, V. Manian· Machine Learning: Science an...· 0 citations
Accurate and efficient simulation of edge plasma turbulence is critical for predicting confinement in fusion devices, yet Direct Numerical Simulations (DNS) remain computationally expensive. To address this bottleneck, we present a physics-informed data-driven closure scheme demonstrated on the Hasegawa-Wakatani (HW) system. Instead of using "black-box" neural networks, we leverage the Direct Interaction Approximation (DIA) to derive a rigorous closure structure with six transport coefficients, which are then identified from high-fidelity data using Physics-Informed Neural Networks (PINNs). Crucially, this approach decouples training from simulation: once the coefficients are learned, they are integrated into standard low-resolution solvers, ensuring numerical stability and physical interpretability. The resulting model (EHW-C) reproduces the spectral cascades and particle flux of high-resolution DNS with a tenfold speed-up, successfully capturing complex phenomena like inverse cascades via negative diffusion coefficients. This work serves as a proof-of-concept for developing high-fidelity, accelerated reduced-order models for more complex tokamak turbulence codes.
Kun-Peng Li, Youngwoo Cho, X. Garbet et al.· Plasma Science and Technolog...· 0 citations
Simulating the ALICE Zero Degree Calorimeter (ZDC) neutron detector responses at the LHC is computationally expensive, requiring complex Monte Carlo chains. We develop a generative surrogate, focusing on Normalizing Flows (NFs). Through transfer learning, we pre-train on the full imbalanced dataset and fine-tune specialized models for different particle types ($\gamma$, $n$, $\Lambda$, $K_S^0$, $\Sigma^+$) using two gradual-unfreezing schemes. As standard ZDC metrics like Wasserstein distance overlook conditional structure, we introduce refined metrics: conditional weighted MAE, dispersion ratio, and Jaccard co-activation error, that better capture physics-relevant input-output dependencies and response variability. Our ensemble of fine-tuned models achieves a Wasserstein distance of $1.61 \pm 0.02$, outperforming baselines across all metrics. This work provides a generalizable NF-based framework for LHC detector simulation, combining NFs, conditional fine-tuning, and physics-motivated evaluation.
E. Majerz, Jacek Otwinowski, W. Dzwinel et al.· 0 citations
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