Global Framework for Emulation of Nuclear Calculations

TL;DR

This work presents BANNANE, a hierarchical multi-fidelity Bayesian neural network that globally emulates ab initio nuclear calculations across isotopic chains by fusing LEC samples from chiral EFT with multi-fidelity inputs. The model uses learnable embeddings for proton number $Z$, neutron number $N$, and fidelity level $e_{ m max}$, a shared latent representation, and fidelity-specific attention-based regression heads to produce predictive means and uncertainties for observables like the binding energy $E_B$ and charge radius $R_{ch}$. It demonstrates accurate predictions across the oxygen chain, robust zero-shot and fidelity-extrapolation capabilities, and enables variance-based Sobol sensitivity analysis to reveal how LECs drive uncertainties differently for energies and radii, offering a data-efficient tool to guide future experiments and high-fidelity computations. The approach provides a scalable pathway to connect fundamental nuclear forces to macroscopic observables with quantified uncertainties, potentially accelerating nuclear theory and experimental design across the nuclear chart.

Abstract

We introduce a hierarchical framework that combines ab initio many-body calculations with a Bayesian neural network, developing emulators capable of accurately predicting nuclear properties across isotopic chains simultaneously and being applicable to different regions of the nuclear chart. We benchmark our developments using the oxygen isotopic chain, achieving accurate results for ground-state energies and nuclear charge radii, while providing robust uncertainty quantification. Our framework enables global sensitivity analysis of nuclear binding energies and charge radii with respect to the low-energy constants that describe the nuclear force.

Figures (10)

• Figure 1: BANNANE architecture overview. The input LECs, along with categorical embeddings for proton number ($Z$), neutron number ($N$), and fidelity level ($e_{\text{max}}$), are processed through a Bayesian shared-latent layer and a multi-head attention mechanism. Fidelity-specific prediction heads refine the base prediction at higher $e_{\text{max}}$ for each fidelity ranging from 2, outputting mean ($\mu_N^f$) and uncertainty ($\sigma_N^f$) estimates for nuclear observables.
• Figure 2: Full-chain training on the oxygen isotopes. BANNANE predictions versus IMSRG reference results for test samples at the highest fidelity $e_{\text{max}}=10$, for $E_{B}$ and $R_{ch}$. Error bars indicate $1\sigma$ uncertainty from BANNANE's posterior, and the average Root Mean Squared Error (RMSE) is displayed for each one.
• Figure 3: Learnt embedding space. Projection of the attention map to 2 dimensions using t-distributed Stochastic Neighbor Embedding (t-SNE) dimensionality reduction applied to the latent space for test LEC samples. The line and colored background show the decision boundary of a simple linear classifier to the reduced space to illustrate the separation between shells.
• Figure 4: Extrapolation to $^{15}$O. (a) Residual distribution of the binding energy $E_B$ (%) for BANNANE predictions compared to IMSRG reference values at $e_{\text{max}} = 6, 8, 10$, when no training samples for $^{15}$O were included. (b) Residual distribution for $E_B$ predictions when only low-fidelity data ($e_{\text{max}} = 4$) was used in training. The inclusion of low-fidelity data significantly reduces systematic bias and improves the overall accuracy of the extrapolated predictions.
• Figure 5: Emulator-driven convergence of binding energies $E_B$ for oxygen isotopes as a function of $e_\text{max}$. Results are compared to fully converged VS-IMSRG results Stroberg:2021 at $e_\text{max} =14$ using the EM(1.8/2.0) nuclear interaction in purple squares. Solid lines represent experimental results from wang2021ame.