The DNA of nuclear models: How AI predicts nuclear masses

TL;DR

The paper introduces an interpretable AI model for nuclear mass predictions that matches or surpasses leading physics models while revealing underlying structure in the learned representations. It shows that the model naturally organizes information into a double-helix in a PC space and that its predictions decompose into macroscopic terms plus Jaffe-factorized microscopic corrections, aligning with Garvey–Kelson ideas and the historically forgotten Jaffe factorization. By combining a physics-grounded symbolic framework with local Jaffe corrections, the authors achieve state-of-the-art, unbiased RMS accuracies (down to roughly 115 keV) for nuclear binding energies, while maintaining interpretability. This work demonstrates a principled human–AI collaboration path to extrapolate into the many unmeasured, unstable nuclei and informs future refinements of nuclear mass models with transparent, physics-based corrections.

Abstract

Obtaining high-precision predictions of nuclear masses, or equivalently nuclear binding energies, $E_b$, remains an important goal in nuclear-physics research. Recently, many AI-based tools have shown promising results on this task, some achieving precision that surpasses the best physics models. However, the utility of these AI models remains in question given that predictions are only useful where measurements do not exist, which inherently requires extrapolation away from the training (and testing) samples. Since AI models are largely black boxes, the reliability of such an extrapolation is difficult to assess. We present an AI model that not only achieves cutting-edge precision for $E_b$, but does so in an interpretable manner. For example, we find that (and explain why) the most important dimensions of its internal representation form a double helix, where the analog of the hydrogen bonds in DNA here link the number of protons and neutrons found in the most stable nucleus of each isotopic chain. Furthermore, we show that the AI prediction of $E_b$ can be factorized and ordered hierarchically, with the most important terms corresponding to well-known symbolic models (such as the famous liquid drop). Remarkably, the improvement of the AI model over symbolic ones can almost entirely be attributed to an observation made by Jaffe in 1969 based on the structure of most known nuclear ground states. The end result is a fully interpretable data-driven model of nuclear masses based on physics deduced by AI.

Figures (11)

• Figure 1: The three most important principal components of the internal representations learned by our AI model for (red) $Z$ and (blue) $N$. The links connect the values of $Z$ and $N$ found in the most stable nucleus of each isotopic chain. Shown is only the range of $(Z,N)$ values where $E_b$ is well described by the volume and asymmetry terms in Eq. \ref{['eq:SEMF']}, with only even values labeled to avoid clutter. The curves show fits of helices to the $Z$ and $N$ representations.
• Figure 2: The six most important PCs of the AI $E_b$ predictions. The scale is linear on $[-1,1]$ and logarithmic otherwise. The first three PCs are approximately smooth functions and largely correspond to macroscopic terms, while all lesser PCs are discrete functions, with most approximately factorizing as $F_Z(Z) + F_N(N)$.
• Figure 3: Relative importance (shading) of neighboring nuclei using (left) Euclidean (purely distance-based) and (right) Jaffe interpolation (target nucleus at center, colored red.)
• Figure 4: Residuals of WS4 including local Jaffe corrections.
• Figure S1: Residuals from the (left) LD and (right) WS4 models. Note that the color scale is linear on $[-1,1]$ and logarithmic otherwise. The lack of nuclear shell corrections is evident in the LD residuals.