Neutrino Oscillation Parameter Estimation Using Structured Hierarchical Transformers

2026-03-21

AI Summary

This work addresses the high computational cost of traditional methods for parameter inference on high-dimensional, nonlinear neutrino oscillation probability maps. It formulates atmospheric neutrino oscillation parameter estimation as a supervised regression task over structured oscillation graphs and introduces the first hierarchical Transformer architecture tailored to this problem, explicitly capturing dependencies across angular and energy dimensions while incorporating surrogate simulation constraints to enforce physical consistency. The study further innovates by integrating a distribution-free conformal prediction mechanism with guaranteed coverage for rigorous uncertainty quantification. Experimental results demonstrate that the proposed method matches the accuracy of Markov chain Monte Carlo baselines while reducing computational cost by approximately 240× and accelerating inference by 33×, all while producing tight and reliable prediction intervals that maintain nominal 90% coverage.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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$\times$ fewer FLOPs and 33$\times$ 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.

Problem

• Neutrino Oscillation
• Parameter Estimation
• High-Dimensional Inference
• Computational Bottleneck
• Oscillation Probability Maps

Innovation

• Hierarchical Transformers
• Neutrino Oscillation Parameter Estimation
• Structured Data Modeling
• Uncertainty Quantification
• Surrogate Simulation Constraint