First Estimation of Model Parameters for Neutrino-Induced Nucleon Knockout Using Simulation-Based Inference
Authors: Karla Tame-Narvaez, Steven Gardiner, Aleksandra Ćiprijanović, Giuseppe Cerati
Organizations: Fermi National Accelerator Laboratory, Batavia, Illinois 60510 USA · Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637 · NSF-Simons AI Institute for the Sky (SkAI), 172 E. Chestnut St., Chicago, IL 60611
To enable an accurate determination of oscillation parameters, accelerator-based neutrino experiments require detailed simulations of nuclear interaction physics in the GeV regime. While substantial effort from both theory and experiment is currently being invested to improve the fidelity of these simulations, their present deficiencies typically oblige experimental collaborations to resort to empirical tuning of simulation model parameters. As the precision requirements of the field continue to become more stringent, machine learning techniques may provide a powerful means of handling corresponding growth in the complexity of future neutrino interaction model tuning exercises. To study the suitability of simulation-based inference (SBI) for this physics application, in this paper we revisit a tuned configuration of the GENIE neutrino event generator that was originally developed by the MicroBooNE collaboration. Despite closely reproducing the adopted values of four physics parameters when confronted with the tuned cross-section predictions as input, we find that our trained SBI algorithm prefers modestly different values (within MicroBooNE's assigned uncertainties) and achieves slightly better goodness-of-fit when inference is run on the experimental data set originally used by MicroBooNE. We also find that our trained algorithm can create a fair approximation of an alternative neutrino scattering simulation, NuWro, that shares only a subset of its physics model parameters with GENIE.
Figures & tables
Figure 1: Neural Posterior Estimate of the four parameters for a single test event. The gray dashed lines indicate the true values while the blue contours represent the estimates at 68% and 95% confidence intervals.
Figure 2: Comparison of true and predicted values for each parameter is shown for a subset of 200 test events, including 1σ error bars. Overall, the predictions closely follow the true values with narrow uncertainty bands, with only θ3 exhibiting some scatter and larger visible error bars.
Figure 3: Histograms of pulls for 1000 test events for each parameter. All four parameter distributions (red solid line) are centered close to zero and somewhat narrower than the standard normal distribution (black dashed line), suggesting that the uncertainties may be overestimated.
Figure 4: Residual distribution (in percentages) of four parameters for 1000 test events. The gray dashed lines indicate the zero value (perfect prediction). The distributions of residuals are very narrow and show no visible biases, i.e, they are all centered around zero. Additionally, all deviations are within a few percent.
Figure 5: Posterior coverage of the θi parameters for 1000 test events (colored solid lines). D(θi) and TARP curves show combined model performance over all parameters, and are plotted with solid and dashed black lines, respectively. The diagonal black dotted line indicates perfect uncertainty calibration. The gray regions indicate thresholds of 10% (dark gray) and 20% (light gray) uncertainty miscalibration. All curves are within the 20% band and are showing slight underconfidence, which is preferred compared to an overconfident model with too narrow error bars.
Model
θ1
θ2
θ3
θ4
σθ1
σθ2
σθ3
σθ4
χ2 (T2K data, 58 bins) c
MicroBooNE Tune a
1.10
1.66
1.00
0.85
±0.10
±0.50
+1.00(-0.00)
±0.40
115.10
Inferred MicroBooNE Tune b
1.09
1.67
0.94
0.85
±0.003
±0.01
±0.01
±0.007
113.07
NuWro
-
-
-
-
-
-
-
-
126.73
Inferred NuWro b
1.10
0.70
0.09
0.57
±0.003
±0.015
±0.013
±0.007
126.93
Inferred T2K a
1.04
1.85
0.65
1.07
+0.11(-0.12)
+0.55(-0.24)
+0.24(-0.18)
+0.27(-0.30)
107.29
Table 1: Inferred parameters, their uncertainties, and the corresponding χ2 values obtained when comparing with the T2K measurement. Some values are also presented in Fig. 9 : MicroBooNE Tune (red), Inferred MicroBooNE Tune (violet), and Inferred T2K (blue). The agreement between the original and NPE fits is excellent, both for the MicroBooNE Tune and NuWro. The NPE fit to the T2K data provides the overall best χ2 . Not all θ parameters are shared between the NuWro and GENIE physics models, so we omit their values in the NuWro row of the table.
Figure 6: Comparison of the T2K cross-section data (black points) to the NuWro [ 33 ] (solid cyan), NPE-inferred NuWro (dashed cyan), MicroBooNE Tune [ 5 ] (solid red), and NPE-inferred T2K (dashed blue) model predictions in two different slices of cosθ .
Figure 7: Variation of the T2K histograms over one thousand simulated events. The solid line denotes the mean (central) value, while the shaded blue region represents the corresponding 1σ variations obtained from samples drawn using the covariance matrix.
Figure 8: Neural Posterior Estimate of the four parameters for the T2K central value. The gray dashed lines represent the inferred central values while the blue contours represent the estimates at 68% and 95% confidence intervals.
Figure 9: The red points correspond to the MicroBooNE fit parameters and uncertainties reported in Ref. [ 5 ] . In blue, we display the four parameters θi inferred by our network using T2K data as input, together with their corresponding error bars, computed using throws from the data covariance matrix as described on the main text. The orange bands indicate the prior ranges employed to train the SBI, as defined in Section II . As a validation, the violet points show the parameters inferred using the exact MicroBooNE histogram, exhibiting excellent agreement (with very small error bars, which are not visible on the figure) and thus corroborating the validity of our analysis. Overall, we observe a very good correspondence between the T2K-inferred parameters and the true MicroBooNE values.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Figure 10: Comparison of the T2K cross-section data (black points) to the NuWro [ 33 ] (solid cyan), NPE-inferred NuWro (dashed cyan), MicroBooNE Tune [ 5 ] (solid red), and NPE-inferred T2K (dashed blue) model predictions in different slices of cosθ .
Neutrino oscillations encode fundamental information about neutrino masses and mixing parameters, offering a unique window into physics beyond the Standard Model. Estimating these parameters from oscillation probability maps is, however, computationally challenging due to the maps' high dimensionality and nonlinear dependence on the underlying physics. Traditional inference methods, such as likelihood-based or Monte Carlo sampling approaches, require extensive simulations to explore the parameter space, creating major bottlenecks for large-scale analyses. In this work, we introduce a data-driven framework that reformulates atmospheric neutrino oscillation parameter inference as a supervised regression task over structured oscillation maps. We propose a hierarchical transformer architecture that explicitly models the two-dimensional structure of these maps, capturing angular dependencies at fixed energies and global correlations across the energy spectrum. To improve physical consistency, the model is trained using a surrogate simulation constraint that enforces agreement between the predicted parameters and the reconstructed oscillation patterns. Furthermore, we introduce a neural network-based uncertainty quantification mechanism that produces distribution-free prediction intervals with formal coverage guarantees. Experiments on simulated oscillation maps under Earth-matter conditions demonstrate that the proposed method is comparable to a Markov Chain Monte Carlo baseline in estimation accuracy, with substantial improvements in computational cost (around 240× fewer FLOPs and 33× faster in average processing time). Moreover, the conformally calibrated prediction intervals remain narrow while achieving the target nominal coverage of 90%, confirming both the reliability and efficiency of our approach.
Giorgio Morales, Gregory Lehaut, Antonin Vacheret +2
Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYC. Caen, France · Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen. Caen, France
Simulation-based inference (SBI) with machine learning is an increasingly important tool for solving inverse problems in science and engineering, including parameter inference and the inversion of detector effects. We provide an overview of the Bayesian and frequentist statistical frameworks, describe how machine-learning-based SBI methods, such as neural posterior estimation and neural likelihood estimation, can be used for parameter estimation within these frameworks, and show that the same methods can also be applied to Empirical Bayes or unfolding tasks. We also discuss how to validate inference results and the limitations of SBI with machine learning.
Maximilian Dax, Theo Heimel, Gilles Louppe
ELLIS Institute Tübingen, Max Planck Institute for Intelligent Systems, Tübingen AI Center, Tübingen, Germany · CP3, Université catholique de Louvain, Louvain-la-Neuve, Belgium · Montefiore Institute, University of Liège, Belgium
Neural simulation-based inference enables parameter estimation for complex models, but typically requires the user to specify a simulator encoding a fixed model structure. We present a framework for joint model selection and parameter estimation that combines large language models for program synthesis with neural simulation-based inference. Given a natural language description of the system and data under investigation, an LLM proposes candidate simulator programs which are iteratively refined via feedback-driven mutation and evaluated using neural density estimation. The approach enables simulation-based inference over a pool of models, not just parameters within a fixed model. On benchmarks spanning deterministic dynamics, stochastic epidemic models, and dark matter substructure inference from gravitational-lensing images, the method identifies plausible model families from open-ended prompts, with accuracy that reflects the information content of the data and identifiability of candidate models.
Siddharth Mishra-Sharma
Faculty of Computing & Data Sciences Boston University · Boston University