A new model for long-term forecasting of Galactic cosmic rays

The following is a detailed summary of the scientific paper A new model for long-term forecasting of Galactic cosmic rays, incorporating relevant quoted sections from the text:

Background and Motivation

Galactic cosmic rays (GCRs) are highly energetic charged particles that, as they propagate through the heliosphere, are subjected to various transport effects, including spatial diffusion, advection in the outward expanding solar wind, magnetic gradient and curvature drifts, and adiabatic energy losses. These processes result in a net reduction of the GCR intensity reaching the inner heliosphere in a process known as solar modulation. This modulation is intrinsically linked to the temporal variability of solar activity, following the 11-year solar cycle, which is proxied by observables such as the sunspot number (SSN). Understanding this variability is crucial for predict[ing] space radiation environments and assessing exposure risks for spacecraft and crew.

Methodology: The PgLis Forecasting Framework

The authors present a newly developed forecasting framework, referred to as the PgLis model, designed specifically for the long-term forecasting of galactic cosmic-ray fluxes. This model is based on a numerical description of charged particle transport in the heliosphere.

1. Physics and Structure: The core of the the PgLis model involves solving a one-dimensional, spherically symmetric form of the Parker transport equation, including diffusion, solar-wind advection, and adiabatic energy losses. The model incorporates fundamental physical processes such as diffusion, advection, and adiabatic cooling, along with a critical consideration of the charge-sign dependence.

2. Parameterization: To manage complexity and avoid parameter degeneracies inherent in physics-based solutions, the the authors adopted a one-dimensional numerical model. They identified a suitable set of model parameters (= k 0, delta, epsilon) using an information-criteria approach (specifically the Bayesian Information Criterion or BIC), which favors parameterizations that achieve an optimal balance between accuracy and parsimony. The model utilizes a quasi-steady approach where each monthly dataset is matched to a steady-state solution of the transport equation.

3. ** Modeling Drift Effects:** While the model is simplified, it accounts for complex particle motions by introducing a radial effective velocity V c(t) = epsilon(t) V sw. This term captures charges-sign polarity dependence of radial advection, allowing the model to capture how modulation parameters exhibit clear temporal evolution that traces the overall pattern of solar activity.

4. ** Forecasting Strategy:** The framework establishes empirical relationships between the effective model parameters and solar activity proxies. The forecasting strategy is specifically based on Hilbert-Huang transform filtering and cross-correlation between delayed solar proxies and effective model parameters, enabling decadal-scale predictions.

Calibration and Validation

The PgLis model was rigorously validated using multispecies flux measurements from space-based experiments, including PAMELA, AMS-02, and ACE. The calibration process involved fitting the model to these datasets across various timeframes (from 2006 to 2019), spanning two solar cycles.

• The model's performance was assessed by comparing the predicted fluxes against measured data for multiple species (protons, helium, carbon, oxygen, etc.).

• The results show that the model successfully reproduces the cosmic-ray flux across all phases of solar activity and for both species considered.

• In terms of accuracy, the PgLis model demonstrated a consistent reduction in error compared to previous models: The PgLis model shows an overall reduction in reconstruction error in every scenario considered.

Results and Applications

The application of the PgLis model allows for robust long-term planning and radiation-risk assessment.

1. Flux Forecasting: By coupling the model with SSN forecasting models, it enables predictions for the entire Solar Cycle 25. The cross-correlation functions derived are effective in capturing the long-term evolution of the model parameters, isolating trends from short-term fluctuations using Hilbert-Huang Transform (HHT) filtering.

2. Dose Assessment: A practical application is the assessment of radiation doses for astronauts during missions, such as an extravehicular activity (EVA) on the International Space Station (ISS). The model calculates the total radiation dose experienced by astronauts by integrating the solar-modulated GCR flux with fluence-to-dose conversion coefficients.

• The calculated dose rates show a strong anti-correlation with solar activity: At the solar-minimum, dose rates predicted by PgLis (about 0.20 Sv yr-1), indicate that the career limit would be reached in approximately three years of continuous EVA exposure. Conversely, at solar maximum, the predicted dose rate drops to about 0.08 Sv yr-1, extending the estimate to roughly seven years.

Conclusion

The PgLis model provides a robust and accurate method for characterizing GCR transport and forecasting future fluxes. The authors conclude that the choice of SSN as the proxy is motivated by its ability to incorporate delayed responses through the time-lag formalism, and they emphasize that the model's strength lies in its calibration procedure, which combines the energy coverage and temporal information provided by multiple experiments.

As a diligent and fastidious AI researcher, I have analyzed the structure of the PgLis model—a sophisticated hybrid of physics-based numerical transport and empirical time-series correlation. The paper presents a robust framework for modeling GCR flux evolution, parameter estimation, and uncertainty propagation.

To significantly improve current AI systems (e.g., large language models, predictive analytics engines, or specialized scientific solvers), the following architectural enhancements must be implemented:

Improvement: The core of the PgLis model is a simplified 1D solution to the Parker Transport Equation (a Partial Differential Equation, PDE). Instead of relying solely on numerical schemes like Crank-Nicolson, a PINN architecture should be deployed. This network is trained not only to fit the observed data points but also to satisfy the residual constraints derived from Equation (5) and its variants.

What the AI System Can Do:

• Accelerated Simulation: The AI can solve for GCR flux at any specified time t and rigidity P orders of magnitude faster than traditional iterative solvers, providing real-time, high-resolution flux maps.

• Constraint Enforcement: It ensures that the predicted physical behavior (e.g., the relationship between diffusion, advection, and adiabatic losses) remains physically consistent even when extrapolating beyond the training data range.

Improvement: The current method relies on a manual search using the Bayesian Information Criterion (BIC) across defined functional forms (K 1, K 2). This process should be automated using advanced Bayesian Optimization algorithms. This allows the system to intelligently navigate the high-dimensional parameter space (= k 0, delta, epsilon) far more efficiently than manual grid searches.

What the AI System Can Do:

• Optimal Model Selection: Automatically identify and select the statistically superior parameterization (like K 2 coupled with epsilon) without human intervention.

• Robust Parameter Tuning: Adapt to changing data distributions, ensuring that the chosen parameters are not only optimal for historical data but also provide the best predictive capacity for future solar cycle states.

Improvement: The paper uses HHT to filter out short-term stochastic fluctuations (CMEs, Forbush decreases) from the GCR time series before fitting. This entire filtering and trend extraction process must be automated as a dedicated module within the AI pipeline.

What the AI System Can Do:

• Signal Purification: Automatically decompose noisy input time series (e.g., daily AMS-02 or PAMELA data) into Intrinsic Mode Functions (IMFs) and extract only the long-term, narrowband, solar-cycle scale trends (mu about 11 yr).

• Bias Mitigation: Prevent short-term noise from corrupting the correlation analysis, ensuring that the derived parameters truly reflect systematic heliospheric changes rather than transient events.

Improvement: The core of the PgLis model is establishing a functional relationship between model parameters and a delayed solar proxy S(t-tau). This requires an automated engine that handles time lags (tau) and polarity-dependent transformations (Eq. 13).

What the AI System Can Do:

• Predictive Mapping: Given a forecasted smoothed SSN (S(t+ tau)), the system can instantly map this input to the corresponding set of modulation parameters*, enabling direct, long-term GCR flux forecasting.

• Polarity Continuity: Maintain a continuous spline fit across the solar polarity reversal phase without discontinuity, ensuring that the transition between positive and negative magnetic cycles is handled mathematically as a smooth curve, not a broken one.

Improvement: The current method uses bootstrapping to propagate uncertainty from the parameter fitting to the final flux prediction. This should be formalized into a full Bayesian inference framework where the covariance matrix of the parameters is treated as a probabilistic input.

What the AI System Can Do:

• Quantified Risk Assessment: Provide not just a single point prediction for GCR flux, but an associated confidence interval (e.g., 68% C.L.) at every energy and time point, directly reflecting the uncertainty in the input solar proxy S(t-tau) and the model parameters.

• Dynamic Uncertainty Reporting: Automatically identify regions of high uncertainty (such as the negative polarity epoch or low-energy regimes) to prioritize where human intervention or more data is required.

Improvement: The PgLis model' flux prediction must be coupled with a dynamic, orbit-aware dosimetric solver. This module calculates the time-dependent geomagnetic rigidity cutoff P cutoff((t), t) based on ISS orbital parameters and then integrates the resulting flux J Z LEO using ICRP conversion coefficients.

What the AI System Can Do:

• EVA Mission Planning: Calculate instantaneous, body-averaged effective dose rates (H(t) in Sv/year) for an astronaut at specific times, considering real-time orbital position and shielding effectiveness (e.g., simulating varying levels of shielding thickness).

• Impact Assessment: Provide a direct comparison between predicted GCR dose rates and established regulatory limits (e.g., 600 mSv career limit), allowing mission planners to assess radiation risk in real-time.

The modulation of galactic cosmic rays, driven by the evolution of the heliospheric magnetic field, strongly influences the intensity of cosmic rays reaching near-Earth space. Characterizing this process is crucial both for advancing our understanding of cosmic-ray transport and for assessing radiation exposure and related hazards in space environments. Here we present a newly developed forecasting framework built on a numerical description of charged particle transport in the heliosphere and its dependence on solar activity, designed for the long-term forecasting of galactic cosmic-ray fluxes. It solves a one-dimensional, spherically symmetric form of the Parker transport equation, including diffusion, solar-wind advection, and adiabatic energy losses. The model has been validated using multi-species flux measurements from space-based experiments: PAMELA, AMS-02, and ACE. Its strategy is based on Hilbert-Huang transform filtering and cross-correlation between delayed solar proxies and effective model parameters. Our charge-sign- and rigidity-dependent parametric description of the diffusion-advection processes yields good overall agreement with the data, as shown by the reconstruction uncertainty. The robustness of this approach is validated across a broad set of multichannel datasets covering different particle species, energy ranges, and phases of solar activity, supporting its applicability to space radiation monitoring and forecasting. Furthermore, when coupled with solar-proxy forecasting models, it enables decadal-scale predictions of galactic cosmic-ray fluxes, thereby supporting long-term planning and radiation-risk assessment for future space missions.