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

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

nucl-thMar 16, 2026

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

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

Organizations: College of Physics, Jilin University, Changchun 130012, China. · Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan · RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, Wako 351-0198, Japan

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.

Figures & tables

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.

Model	$\sigma_{\text{pre}}$	$\sigma_{\text{KAN}}$ (train)	$\sigma_{\text{KAN}}$ (test)
WS4	0.286	0.157	0.205
Bhagwat	0.303	0.164	0.214
DZ28	0.407	0.174	0.227
FRDM	0.586	0.208	0.273
HFB31	0.567	0.340	0.356
KTUY	0.715	0.173	0.234

Table 1: Six theoretical models optimized via KAN.

\sigma_{\text{pre}}

denotes the RMS error between the predictions of the bare theoretical mass model and the experimental data, whereas

\sigma_{\text{KAN}}

represents the RMS error between the predictions of the theoretical mass model refined by the KAN and the experimental data. All quantities are given in MeV.

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Interpretation of Crystal Energy Landscapes with Kolmogorov-Arnold Networks

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Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany · Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA · Min H. Kao Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA

Materials Property Prediction Interpretable ML Kolmogorov-Arnold Networks Computational Materials Science

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Characterizing crystalline energy landscapes is essential to predicting thermodynamic stability, electronic structure, and functional behavior. While machine learning (ML) enables rapid property predictions, the "black-box" nature of most models limits their utility for generating new scientific insights. Here, we introduce Kolmogorov-Arnold Networks (KANs) as an interpretable framework to bridge this gap. Unlike conventional neural networks with fixed activation functions, KANs employ learnable functions that reveal underlying physical relationships. We developed the Element-Weighted KAN, a composition-only model that achieves state-of-the-art accuracy in predicting formation energy, band gap, and work function across large-scale datasets. Crucially, without any explicit physical constraints, KANs uncover interpretable chemical trends aligned with the periodic table and quantum mechanical principles through embedding analysis, correlation studies, and principal component analysis. These results demonstrate that KANs provide a powerful framework with high predictive performance and scientific interpretability, establishing a new paradigm for transparent, chemistry-based materials informatics.

Abstract

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