Physicists Borrow the Ising Model to Strip Noise from Particle Detectors

Every modern particle physics experiment faces the same unglamorous but decisive problem: most of the data it records is not signal at all. In the deep, dark water of Lake Baikal, natural luminescence can account for up to 90 percent of the photons registered by a neutrino telescope. At the NICA collider near Moscow, electronic noise and beam-gas interactions make up roughly 55 percent of all hits in the straw-tube tracker of the Spin Physics Detector. Before any physics can be extracted, this background must be stripped away, and the standard tools for doing so are computationally expensive, because they rely on reconstructing full particle trajectories in order to decide which hits are real.

A new study published in The European Physical Journal C proposes a strikingly different approach. Ivan Kharuk, a researcher affiliated with the Institute for Nuclear Research of the Russian Academy of Sciences and the Moscow Institute of Physics and Technology, has developed what he calls the Ising noise filter: a graph-based algorithm that recasts the problem of separating signal from noise as the minimization of an energy functional borrowed from statistical physics. Instead of fitting tracks and discarding inconsistent hits, the method assigns a binary spin to every detector hit and lets the collective dynamics of the spin network do the sorting.

The Ising model, introduced by Ernst Ising a century ago, describes binary variables sitting on the nodes of a graph and interacting through pairwise couplings. When the couplings are ferromagnetic, meaning they favor agreement, the lowest-energy configurations form extended domains of aligned spins. Kharuk exploits exactly this behavior. Each recorded hit becomes a node, characterized by its position, time, and pulse charge, and each pair of hits is connected by an edge whose weight encodes how physically consistent the two hits are with a common origin. Correlated signal hits then reinforce one another and settle into a compact domain of aligned spins, while uncorrelated noise hits find themselves isolated and are driven to the noise state.

The crucial innovation lies in how the couplings are defined. Rather than learning them from data, as a neural network would, the filter builds them from explicit physical laws. For Baikal-GVD, a cubic-kilometer neutrino telescope under construction 1366 meters below the surface of Lake Baikal, the interaction kernel is a weighted sum of three terms. The first rewards hits that are close in both space and time. The second encodes the fact that a relativistic muon travels at nearly the speed of light, so hits along its track satisfy a strict time-distance relation. The third captures the propagation of Cherenkov light through water at roughly c/1.35, the characteristic signature of both cascade and track-like neutrino events. The measured pulse charge enters as a local field, biasing high-amplitude hits toward the signal class, while a global threshold acts like an external magnetic field pulling spins toward the noise state.

The dynamics are deliberately simple. All spins start in the signal state, and at each synchronous update a hit survives only if the total support it receives from its coupled neighbors and its own charge exceeds the threshold. Otherwise it flips to noise. Two to five iterations are enough for the system to settle into a local energy minimum. Kharuk tested greedy, single-spin, and synchronous update rules and found identical precision and recall within statistical uncertainties, which means the entire algorithm reduces to a handful of matrix-vector multiplications and can be fully vectorized on modern hardware. Notably, he runs the filter at zero temperature rather than using simulated annealing, because the true global minimum of the energy is the trivial all-noise state; any finite-temperature dynamics would pull the system away from the physically meaningful metastable configuration where the signal lives.

Applied to Monte Carlo data from the Baikal-GVD collaboration, the filter achieves 97 percent recall for astrophysical neutrinos, with 89 percent event selection efficiency under the standard quality cuts of at least eight signal hits on at least two strings. At this operating point its noise-rejection accuracy matches that of the scan-fit algorithm currently used by the collaboration, which searches over muon directions for maximal cliques of causally consistent hits but becomes computationally prohibitive for events with more than 150 hits. Compared with a U-Net-like neural network previously developed for the same task, which reaches 99 percent precision and 96 percent recall, the Ising filter attains comparable recall with somewhat lower precision but orders of magnitude fewer floating-point operations, making it suitable for online filtering in resource-constrained environments.

The second test case is the SPD straw barrel tracker at the NICA collider, currently under construction at JINR in Dubna. Here no sub-nanosecond timing is available, so the filter must rely entirely on geometry. The tracker consists of 30 concentric cylindrical layers of 10-millimeter straw tubes in a 1-tesla solenoidal field, and charged particles follow helical trajectories whose curvature is set by their transverse momentum. Kharuk defines three geometric kernels: three-dimensional spatial proximity between hits on adjacent layers, transverse-plane proximity to recover sensitivity to high-pseudorapidity tracks where the z-displacement dominates, and a radial-chord alignment term that penalizes tangential hit pairs, exploiting the fact that consecutive hits from the same track sit at nearly the same azimuthal angle.

On a toy Monte Carlo sample of 500 events with an average of five primary tracks each and 2 percent channel occupancy, the filter reaches 96.7 percent precision and 97.4 percent recall, an F1 score of 0.97. Under more realistic conditions with five overlapping collision events per read-out frame, performance degrades only modestly, to 92.5 percent precision and 96.3 percent recall. Benchmarked as a pre-processing stage for an extended Kalman filter track fit, the standalone Ising filter processes one frame in roughly 60 milliseconds, cuts the total track-fitting time in half, suppresses fake tracks roughly six-fold, from about 38 to 6 per frame, and leaves tracking efficiency essentially unchanged while improving average hit purity from 84 to 87 percent.

The same physics-informed philosophy then extends to the track-finding stage itself. The Peterson-Hopfield network, a Hopfield-type neural network operating on oriented pairs of hits called doublets, links consecutive doublets with an excitatory coupling and penalizes doublets that share a hit but are not consecutive. Kharuk replaces the standard geometry-agnostic cosine-kink coupling with two constraints derived from helical track geometry: a transverse bending angle term, which for same-track triplets averages 0.17 radians versus 0.86 radians for fakes, and a z-slope consistency term that vanishes exactly for a perfect helix regardless of pseudorapidity. Combined with Ising pre-filtering, this lifts the TrackML score from 0.5 for the standard network on unfiltered hits to 0.91, while speeding up total execution by a factor of about 2.5.

Beyond the two benchmarks, the appeal of the method is its portability. Adapting it to a new experiment requires only a model of the dominant signal propagation process and a realistic Monte Carlo sample for tuning the handful of hyperparameters. The Cherenkov kernels developed for Baikal-GVD apply directly to IceCube, KM3NeT, and the planned Baikal-HUNT extension, while the helical-geometry kernels suit any solenoidal tracker, including the straw-tube tracker of NA62 at CERN. Because every parameter encodes a specific propagation law rather than a learned weight, the filter is less exposed to the domain shift that degrades neural networks trained on simulation when confronted with real data, from photosensor aging to seasonal background variations. In an era when experiments drown in data, a century-old model of magnetism may prove one of the most economical ways to keep the signal afloat.

Subject of Research: Physics-informed Ising-model-based noise filtering for particle detectors

Article Title: Ising noise filter: physics-informed filtering for particle detectors

Article References: Kharuk, I. (2026). Ising noise filter: physics-informed filtering for particle detectors. The European Physical Journal C, 86(10), Article 1171. https://doi.org/10.1140/epjc/s10052-026-16383-8

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16383-8

Keywords: Ising model, particle detectors, noise filtering, Baikal-GVD, neutrino telescope, SPD detector, NICA collider, track reconstruction, statistical physics, graph algorithms, Cherenkov radiation, computational physics