A research team from the Double Chooz collaboration has introduced PhyLiNO, an open-source statistical fitting framework designed to extract neutrino oscillation parameters from complex experimental datasets using an optimized forward-folding likelihood method. Reported in Computing and Software for Big Science, the software resolves a long-standing computational bottleneck in neutrino physics by directly mapping high-dimensional physical models onto observed detector response templates rather than attempting to unfold smeared measurements back into true particle distributions. In experimental particle physics, acquired event spectra inevitably undergo smearing and distortion due to finite detector resolution, energy non-linearities, and operational inefficiencies. Inverting these experimental transformations through numerical unfolding frequently introduces severe mathematical instabilities and challenging regularizations. PhyLiNO bypasses these obstacles by taking theoretical predictions, applying forward-folding models of detector response and background components, and comparing the simulated expectations directly to binned data across multiple experimental setups.
Extracting fundamental leptonic parameters, including the mixing angle theta 13 and effective squared mass splittings, requires fitting theoretical expectations against high-statistics event rates while accounting for extensive systematic uncertainties. The core statistical engine in PhyLiNO employs a binned maximum profile likelihood approach where the event counts in each energy bin follow Poisson statistics. To account for systematic uncertainties and known experimental constraints, the joint Poisson likelihood across all energy bins is multiplied by prior functions representing independent external measurements and theoretical bounds. When parameters are uncorrelated, Gaussian priors describe their standard deviations, whereas multi-parameter dependencies are governed by full covariance matrices. By default, targeted signal parameters such as the leptonic mixing parameters remain unconstrained by prior functions to avoid introducing measurement bias, though external priors can be incorporated when testing specific hypotheses or evaluating nested confidence intervals via Wilks’ theorem.
The computational burden of forward folding traditionally stems from the need to repeatedly recalculate detector response and oscillation models during every iteration of a numerical fit. PhyLiNO addresses this challenge through extensive algorithmic optimization and parallelization, achieving convergence times of approximately five seconds when utilizing graphics processing units. In performance benchmarks conducted on a dedicated computing workstation equipped with an AMD Ryzen Threadripper 3960X processor and an Nvidia RTX 3090 GPU, a baseline single-core fit of Double Chooz data took approximately 39 seconds. Applying CPU multi-threading across 48 available threads reduced the total runtime to 15 seconds, representing an improvement factor of roughly 2.6. Offloading the computationally demanding, event-by-event oscillation probability calculations to the GPU via custom CUDA implementations using Nvidia CUB further shortened the convergence time to around five seconds, providing an overall eightfold acceleration compared to single-threaded CPU execution.
Written in modern C++ up to standard C++20, PhyLiNO is structured around a modular three-component architecture designed to maintain high performance while offering complete experimental flexibility. The first architectural component manages configuration file parsing and integrates an in-memory database class that retains loaded event structures without requiring repetitive disk access during extensive parameter scans or pseudo-experiment iterations. The second component houses the core likelihood functions, which are derived from abstract base classes to permit flexible, runtime assembly of varied experimental models. Within this module, linear algebra operations are handled by the Eigen C++ template library, and minimizations are performed by default using the Minuit2 library from ROOT, although RooFit and RooStats dependencies are omitted to maximize architectural adaptability. The third component handles the structured output of best-fit parameters, exporting final results directly into standard JSON files to streamline integration with downstream analysis chains.
To prevent unnecessary numerical recalculations during fitting, the framework integrates least-recently-used caching mechanisms across its signal and background calculation pipelines. When Minuit2 modifies nuisance parameters, only the model terms directly affected by those parameter variations are recomputed, provided the parameter changes exceed an operational threshold of one part in a trillion. For the Double Chooz configuration, event calculations are handled in three distinct stages: first, simulated Monte Carlo events are weighted by the prompt energy oscillation survival formula; second, the resulting binned spectra are rescaled to account for correlated systematic errors between detector datasets and across energy bins; and third, an optional energy correction applies a second-degree polynomial to match calibrated detector responses. Because each stage depends only on a subset of the parameters, unchanged steps are served instantly from memory cache, minimizing redundant arithmetic operations throughout the minimization process.
PhyLiNO was initially engineered and deployed to analyze data collected by the Double Chooz reactor anti-neutrino disappearance experiment. Operating two nearly identical liquid scintillator detectors located approximately 400 meters and 1050 meters from two nuclear reactor cores, Double Chooz detected electron anti-neutrinos through inverse beta decay reactions, where prompt positron annihilations and delayed neutron captures provide distinct coincidence signatures that suppress environmental backgrounds. The framework simultaneously processed data from the far detector’s standalone operational phase alongside two-detector joint operational runs, binning events between 1 MeV and 20 MeV across 38 energy bins. It accurately incorporated experimental background contributions—including accidental coincidences, cosmogenic spallation products such as lithium-9 and helium-8, and fast neutron scattering—using data-driven templates with fitted rate and shape parameters.
Beyond standard three-flavor oscillation fits and precision measurements of the mixing angle theta 13, the software framework has supported specialized investigations into reactor spectrum shape anomalies and sterile neutrino searches. In extended 3+1 sterile neutrino analyses, researchers introduced two additional fit parameters—a sterile mass splitting and an active-to-sterile mixing angle—into the likelihood framework. Evaluating such models historically required substantial computing time because Wilks’ theorem is often inapplicable to non-standard statistical boundaries, requiring millions of pseudo-experiments to map rigorous statistical confidence limits. PhyLiNO’s rapid convergence enabled exhaustive two-dimensional raster scans across sterile mass splittings ranging from 5 times 10 to the negative fourth electron-volt squared up to 0.5 electron-volt squared, providing rigorous limits without succumbing to previous computational restrictions.
The modularity of the framework also enables conditional dataset splitting, allowing researchers to divide total collected event samples into finer operational subsets that boost overall experimental sensitivity. In Double Chooz, dividing collected neutrino events according to whether both nuclear reactors were active or only one reactor was running eliminated baseline distance ambiguities, yielding an estimated sensitivity improvement of approximately 15 percent for the determination of the mixing parameter sin squared two theta 13. Furthermore, the framework accommodated splitting datasets based on the delayed neutron capture target, separating captures on gadolinium from captures on hydrogen. Although this expanded the three primary experimental histograms into 18 distinct analysis histograms and greatly increased the parameter space, PhyLiNO’s computational throughput allowed these complex configurations to converge seamlessly without sacrificing precision.
To evaluate its versatility beyond short-baseline setups, the developers applied PhyLiNO to a simulated medium-baseline benchmark modeled on the Jiangmen Underground Neutrino Observatory (JUNO) configuration. The benchmark simulated an Asimov pseudo-dataset representing reactor neutrino detection across a 53-kilometer baseline with JUNO-like energy resolution and a near detector located at the Double Chooz near baseline. Fitting the simulated dataset under both normal and inverted neutrino mass ordering hypotheses, the framework accurately recovered the injected input values for normal ordering while successfully demonstrating sensitivity to the disfavored inverted scenario across a simulated 500-day operational period. The test established that the framework can combine disparate experimental datasets into a unified global likelihood, providing particle physicists with a versatile, high-throughput computational platform for next-generation neutrino oscillation studies.
To make the oscillation measurement independent of theoretical flux models, the framework treats the normalizations of the reactor flux expectation as free fit parameters constrained primarily through direct data comparisons between the near and far detectors. Because the detectors possess minor differences and operated over different run periods, the setup incorporates 123 reactor flux parameters divided into three sets of 41 parameters spanning 1 MeV to 11.25 MeV. This uniform binning corresponds to the greatest common divisor of the bin widths. The weighted, normalization-corrected energy spectra form the foundation of an area-conserving spline that undergoes energy correction before conversion back into the original binning, accompanied by a 41-by-41 covariance matrix for each dataset to accommodate uncorrelated shape variations.
Instrumental uncertainties across the detectors are parameterized through second-order polynomials that account for the non-linear visible energy response of the scintillator, spatial non-uniformities inside the detector, and charge non-linearities in the photomultipliers and readout electronics. Because scintillator response is assumed to be fully correlated while the remaining effects are treated as uncorrelated across operational phases, nine polynomial coefficients are consolidated into seven independent parameters. Total detection efficiency uncertainties are described by three constrained parameters dominated by the precision of the total target mass. The framework also specifically models the small flux of electron anti-neutrinos emitted by reactor fuel during reactor-off periods, applying an oscillated shape expectation and prior constraints based on dedicated off-power measurements.
For statistical validation, the software evaluates the goodness of fit by comparing the global best-fit hypothesis to a saturated model whose expectation matches the experimental data exactly. The resulting likelihood ratio follows a chi-squared distribution with degrees of freedom defined by the dimensional difference between the models, enabling p-value calculations. Across full oscillation fits encompassing roughly 300 parameters, the framework achieves convergence within approximately a minute on a typical notebook computer. When custom user routines are not thread-safe, multiprocessing via the Message Passing Interface provides scalable execution, preserving high computational throughput during extensive ensemble analyses.
Subject of Research: Neutrino oscillation analysis framework using forward-folding likelihood fits
Article Title: PhyLiNO: a forward-folding likelihood-fit framework for neutrino oscillation physics
Article References: Hellwig, D., Schoppmann, S., Soldin, P., Stahl, A., & Wiebusch, C. (2025). PhyLiNO: a forward-folding likelihood-fit framework for neutrino oscillation physics. Computing and Software for Big Science, 9(1), Article 11. https://doi.org/10.1007/s41781-025-00142-7
Image Credits: AI Generated
DOI: 10.1007/s41781-025-00142-7
Keywords: neutrino oscillation, particle physics, PhyLiNO, Double Chooz, likelihood fitting, forward folding, GPU acceleration, computational physics, forward-folding, likelihood-fit, framework, neutrino
News Source: Katie Riggs. (November 10, 2026). PhyLiNO Framework Speeds Neutrino Oscillation Fits Using GPU Forward Folding. Scienmag.
