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Bridging Theory and Data: Correcting Nuclear Mass Models with Interpretable Machine Learning

Yanhua Lu, Tianshuai Shang, Pengxiang Du, Jian Li, Haozhao Liang

Abstract

Nuclear mass prediction is one of the core issues in nuclear physics research, yet it faces the challenge of small-sample datasets with high complexity. This study introduces the Kolmogorov-Arnold Network (KAN) into the refinement of nuclear mass models, proposing an efficient and interpretable solution. By constructing the KAN-WS4 hybrid model, the prediction accuracy is significantly improved (the root mean square error is reduced from 0.3 MeV to 0.16 MeV). Furthermore, leveraging the intrinsic interpretability of KAN, feature importance analysis reveals that the proton number is the most critical factor influencing residuals, indicating potential systematic biases in proton-related terms within existing theoretical models. The method's generality is demonstrated across five mass models. This study shows that KAN provides a novel approach to small-sample, high-complexity scientific problems. Its interpretability facilitates the data-driven discovery of physical laws, promising broad applicability to key nuclear physics issues.

Bridging Theory and Data: Correcting Nuclear Mass Models with Interpretable Machine Learning

Abstract

Nuclear mass prediction is one of the core issues in nuclear physics research, yet it faces the challenge of small-sample datasets with high complexity. This study introduces the Kolmogorov-Arnold Network (KAN) into the refinement of nuclear mass models, proposing an efficient and interpretable solution. By constructing the KAN-WS4 hybrid model, the prediction accuracy is significantly improved (the root mean square error is reduced from 0.3 MeV to 0.16 MeV). Furthermore, leveraging the intrinsic interpretability of KAN, feature importance analysis reveals that the proton number is the most critical factor influencing residuals, indicating potential systematic biases in proton-related terms within existing theoretical models. The method's generality is demonstrated across five mass models. This study shows that KAN provides a novel approach to small-sample, high-complexity scientific problems. Its interpretability facilitates the data-driven discovery of physical laws, promising broad applicability to key nuclear physics issues.
Paper Structure (6 sections, 4 equations, 4 figures, 1 table)

This paper contains 6 sections, 4 equations, 4 figures, 1 table.

Table of Contents

  1. introduction
  2. THEORETICAL FRAMEWORK
  3. Kolmogorov-Arnold network
  4. Small-sample datasets with high complexity
  5. Results and discussion
  6. SUMMARY AND PROSPECTS

Figures (4)

  • Figure 1: Comparison between (a) traditional machine learning frameworks (Multi-Layer Perceptron, MLP) and (b) Kolmogorov-Arnold Networks (KAN).
  • Figure 2: Differences (in MeV) between the nuclear masses predicted by KAN models and the experimental nuclear masses. (a) Data distributions of the training set and test set; (b) all dataset: (c) training set; (d) test set.
  • Figure 3: The training and test mass differences $\Delta M$ (in MeV) of the KAN model (red dots) with the WS4 nuclear mass model (black squares) as a reference. The shade (white) regions indicate the training (test) areas. (a) The Sn isotopic chain; (b) The Pb isotopic chain; (c) $N=82$ isotonic chain; (d) $N=126$ isotonic chain.
  • Figure 4: (a) Framework diagram of a KAN trained on the nuclear mass residual dataset, and (b) the corresponding analysis of feature importance.