⚛️ nuclear experiments

Nuclear Data Evaluation Utilizing Bayesian Monte Carlo Methods

This paper utilizes Bayesian Monte Carlo methods to iteratively update TALYS 2.0 model parameters against experimental copper reaction data, establishing physically defensible uncertainty bands for proton-induced cross sections and demonstrating the potential of neural network surrogates to screen future nuclear data evaluations.

Original authors: Catherine E. Apgar, Lee A. Bernstein, Yun-Hsuan Lee, Wilson Lin, Alan B. McIntosh, Dmitri G. Medvedev, Jonathan T. Morrell, Ellen M. O'Brien, C. Etienne Vermeulen, Andrew S. Voyles

Published 2026-10-28

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Catherine E. Apgar, Lee A. Bernstein, Yun-Hsuan Lee, Wilson Lin, Alan B. McIntosh, Dmitri G. Medvedev, Jonathan T. Morrell, Ellen M. O'Brien, C. Etienne Vermeulen, Andrew S. Voyles

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of nuclear science, there is a constant need to know exactly how atoms behave when they are struck by other particles. This knowledge is not just abstract theory; it is the foundation for creating medical isotopes that save lives, powering industrial processes, and ensuring national security. To predict these outcomes, scientists rely on massive libraries of data that have been carefully measured and checked by experts. However, while we have a very clear picture of how neutrons interact with matter, the data for charged particles, such as protons, is often missing or incomplete. When the experimental data is absent, scientists must turn to computer models to guess the results. These models are powerful, but they contain hundreds of adjustable settings, like the dials on a complex radio. Without real-world measurements to guide them, these settings can be turned in ways that produce inaccurate predictions, leading to inefficient production of vital materials or unwanted radioactive impurities.

A team of researchers set out to improve how these computer models are tuned, specifically for reactions involving protons hitting natural copper. They used a sophisticated statistical approach known as Bayesian Monte Carlo, which can be thought of as a highly organized way of testing millions of different combinations of settings to see which ones best match the real world. Instead of guessing randomly, they started with a broad range of possibilities based on the model's default settings and then used a large collection of existing experimental data to gradually narrow down the most likely options. Their goal was not to replace the experts who manually evaluate data, but to create a method that could automatically establish a reliable range of uncertainty for these predictions, showing exactly how confident we can be in the results.

The researchers focused on a specific set of data involving protons striking copper atoms, which produces a variety of different residual isotopes. They gathered nearly 2,600 independent data points from previous experiments to serve as a training ground. Using a supercomputer, they ran the nuclear reaction code, known as TALYS, thousands of times. In the first round, they tested 3,000 different variations of the model's settings. They then compared the computer's predictions against the actual experimental measurements. To decide which variations were good and which were bad, they used a scoring system that measured the difference between the prediction and the reality. Crucially, they treated every single data point with equal importance, ensuring that no single experiment or specific type of reaction dominated the results.

After identifying the best-performing variations from the initial round, the team refined their approach. They froze the choices for the discrete model options—essentially deciding which fundamental physical theories to use—and then focused on fine-tuning the continuous numerical parameters. They ran five more generations of calculations, each time using the results of the previous round to guide the next. With each step, they adjusted the settings to be closer to the values that produced the best match with the experimental data. This iterative process allowed them to progressively shrink the range of uncertainty. By the end of the fifth generation, the median error in their predictions had dropped by more than 70 percent compared to the starting point. The uncertainty bands around their predictions became significantly tighter, meaning the model could now predict the outcome of these reactions with much greater precision.

However, the story did not end with a perfect solution. When the researchers tested their newly refined model against a different set of data—specifically, cumulative measurements that include the effects of decay chains from parent isotopes—they found that the improvements did not transfer perfectly. While the model became better at predicting the direct products of the reaction, it struggled to maintain that same level of accuracy for the cumulative totals. In some cases, the uncertainty bands actually widened for these specific isotopes. This revealed a fundamental limitation: a model that is perfectly tuned to one type of data does not necessarily generalize well to all related scenarios. The study suggests that while automated methods can significantly reduce uncertainty, they cannot yet replace the need for human experts to apply physical insight when adjusting models for different types of nuclear reactions.

The team also explored whether artificial intelligence could speed up this process. They trained a simple neural network to predict how well a set of model settings would perform without actually running the full, time-consuming computer simulation. While the neural network could not accurately predict the exact scores, it proved surprisingly good at ranking the settings. It could tell the difference between a likely good set of parameters and a likely bad one. This suggests that in the future, such a tool could be used as a filter to screen out poor options quickly, allowing researchers to focus their computing power only on the most promising candidates.

Ultimately, this work demonstrates a powerful new way to handle the uncertainty in nuclear data. By using a systematic, iterative approach, the researchers were able to tighten the confidence intervals for proton-induced reactions on copper, providing a clearer picture of what to expect when these reactions occur. The study confirms that the default settings in current nuclear models are a strong starting point, requiring only minor adjustments to fit the data well. Yet, it also serves as a reminder that science is not a simple matter of finding a single perfect answer. The inability of the refined model to perfectly predict cumulative results highlights that the complexity of nuclear physics still demands a careful, physics-informed human touch to ensure safety and accuracy in the production of medical and industrial isotopes.

Technical Summary: Nuclear Data Evaluation Utilizing Bayesian Monte Carlo Methods

Problem Statement
Despite the rapid growth of experimental nuclear data, significant gaps persist, particularly regarding charged-particle reactions essential for isotope production in medical, industrial, and national security sectors. The lack of evaluated experimental data for these reactions forces reliance on theoretical models, which can result in low yields and isotopic impurities. While libraries like ENDF/B-VIII.0 provide robust data for neutron-induced reactions, evaluated data for charged-particle reactions remains sparse. The nuclear reaction modeling code TALYS-2.0 is widely used to predict cross-sections, but its flexibility—featuring over 400 tunable parameters—presents a challenge: systematically varying these parameters to establish physically defensible uncertainty bands without overfitting or requiring computationally prohibitive exhaustive searches.

Methodology
This work employs an iterative Bayesian Monte Carlo (BMC) approach to adjust TALYS 2.0 parameters and establish uncertainty bands for proton-induced reactions on natural copper (natCu). The study focuses on 85 specific parameters (a subset of the total available) to explore predictive capabilities against experimental data.

Data Selection: The analysis utilizes the EXFOR dataset for natCu(p,x) reactions up to 200 MeV. The dataset comprises 24 independent residual product cross sections (approx. 2600 data points from 34 experiments) used for iterative model updating. A separate set of 23 cumulative cross sections (approx. 1600 data points) was withheld for validation. Experimental data with uncertainties below 5% or no listed uncertainty were assigned a 15% uncertainty to prevent overfitting on potentially inaccurate points.
Prior Sampling: An initial prior distribution was generated using 3,000 TALYS calculations. Discrete model parameters (e.g., level density models, pre-equilibrium modes) were selected randomly, while continuous parameters were sampled using Sobol sequences from a truncated lognormal distribution centered on default TALYS values. This approach ensures broad coverage of the high-dimensional parameter space while maintaining physical constraints.
Goodness-of-Fit and Weighting: The study investigated four definitions of the reduced $\chi^2$ statistic to determine the best metric for aggregating discrepancies across channels and datasets. The "nested" $\chi^2$ metric was selected, which averages $\chi^2$ values across datasets and channels to avoid over-weighting specific datasets with high data density. To prevent overfitting and manage effective sample size (ESS), these $\chi^2$ values were normalized against a reference calculation (TALYS 2.0 with 100 excitation energy bins).
Iterative Updating: A proposal-posterior approach was used. After the initial generation, discrete parameters were fixed based on the best-performing sample. Continuous parameters for subsequent generations were resampled from distributions centered on the weighted posterior mean and spread, derived from the previous generation's performance. This process was repeated for five additional generations (1,000 runs each) to refine the parameter set and reduce uncertainty.
Surrogate Modeling: Various machine learning models, including neural networks, were tested to predict TALYS performance ( $\chi^2$ ) and automate the iteration process, aiming to screen inputs and reduce computational load.

Key Results

Parameter Optimization: After five iterative generations, the median $\chi^2$ value improved by 71.7% compared to the initial uninformed ensemble. However, the "best" $\chi^2$ value showed minimal improvement, suggesting the initial 3,000 Sobol-sampled inputs had already explored near-optimal parameter combinations.
Uncertainty Reduction: The iterative process successfully narrowed the uncertainty bands for many independent residual products. For example, the uncertainty for $^{64}$ Cu was reduced by 64.6%. However, the reduction was not uniform; some isotopes saw minimal improvement or even increased uncertainty.
Validation Limitations: When validated against the withheld cumulative cross-section data, the improvements observed in the independent data did not fully transfer. While the median $\chi^2$ for the cumulative validation improved by 35.2%, the overall mean $\chi^2$ for the cumulative validation actually increased by a modest 6.7%. Furthermore, the containment of experimental data within the $\pm 1\sigma$ uncertainty bands remained relatively constant (~68%), indicating the bands were well-calibrated but that the parameter adjustments optimized for independent products did not generalize perfectly to cumulative products.
Surrogate Model Performance: A neural network surrogate failed to accurately predict absolute $\chi^2$ values across generations, with $R^2$ values degrading significantly. However, the model retained useful ranking capabilities (Spearman $\rho$ remained high), suggesting it could effectively screen and down-select inputs for future evaluations.

Significance and Claims
The authors explicitly state that this work is not intended to reproduce or improve upon existing evaluated nuclear data libraries (like TENDL) but rather to explore alternatives and understand the strengths and weaknesses of purely theoretical modeling approaches.

The primary significance lies in demonstrating that an iterative Bayesian Monte Carlo approach can successfully establish uncertainty bands and refine TALYS parameters for charged-particle reactions. The study highlights that while a "holistic" approach can reduce uncertainty for specific independent channels, it faces limitations when applied to cumulative products, underscoring the continued necessity for physics-informed evaluations. Additionally, the findings suggest that while surrogate models may not replace full TALYS calculations for precise $\chi^2$ prediction, they hold promise as screening tools to optimize computational resources by identifying high-performing parameter sets for further evaluation.

A scientific accuracy reviewer checked the draft against the paper and flagged these problems:

Summary claims median chi-squared for cumulative data improved by 35.2%, but paper states it improved by 35.2% while mean increased; the summary conflates the specific metric improvement with the overall result context or misattributes the 35.2% figure to the wrong comparison basis (median vs mean) in a way that obscures the paper's finding that the holistic fit worsened. (the paper says: "median χ2 of cumulative validation of 35.2% the overall mean χ2 for the cumulative validation actually increased by a modest 6.7%")

Produce a corrected version of the draft. Fix ONLY what the reviewer flagged (verify each point against the paper) and keep everything else — the structure, the level of detail, the terminology — unchanged. Output ONLY the corrected summary.

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