Machine Learning for the Prediction of Converged Energies from Ab Initio Nuclear Structure Calculations - Universal neural network for nuclear observable extrapolation

Aug 5, 2026

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Nuclear structure theory requires reliable extrapolation of observables beyond finite model spaces accessible to modern ab initio methods, together with robust uncertainty estimates. A universal machine-learning framework is introduced to learn observable-specific convergence patterns that are independent of nucleus and interaction. Trained on fully converged few-body calculations, artificial neural networks produce accurate predictions for ground-state energies of light nuclei such as 6Li, 12C, and 16O, using input sequences from no-core shell model runs and comparing results to classical extrapolations.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Abstract

Universal machine learning approach

Training strategy using few-body systems

Predictions for light nuclei and comparison to classical extrapolations

14 Mar 2023 Machine Learning for the Prediction of Converged Energies from Ab Initio Nuclear Structure Calculations Marco Knölla , Tobias Wolfgrubera , Marc L. Agela , Cedric Wenza , Robert Rotha,b aInstitut für Kernphysik, Fachbereich Physik, Technische Universität Darmstadt, Schlossgartenstr. 2, 64289 Darmstadt, Germany b Helmholtz Forschungsakademie Hessenfür FAIR, GSI Helmholtzzentrum, 64289 Darmstadt, Germany Abstract The prediction of nuclear observables beyond the ﬁnite model spaces that are accessible through modern ab initio methods, such as the no-core shell model, pose a challenging task in nuclear structure theory. It requires reliable tools for the extrapolation of observables to inﬁnite many-body Hilbert spaces along with reliable uncertainty estimates. In this work we present a universal machine learning tool capable of capturing observable-speciﬁc convergence patterns independent of nucleus and interaction. We show that, once trained on few-body systems, artiﬁcial neural networks can produce accurate predictions for a broad range of light nuclei. In particular, we discuss neural-network predictions of ground-state energies from no-core shell model calculations for 6Li, 12 C and 16 O based on training data for 2H, 3H and 4He and compare them to classical extrapolations. Introduction. The major goal of nuclear structure theory is the ing particle number [14] sets severe limits for converged cal- [Email addresses:](Email addresses: mknoell@theorie.ikp.physik.tu-darmstadt.de)[ mknoell@theorie.ikp.physik.tu-darmstadt.de](Email addresses: mknoell@theorie.ikp.physik.tu-darmstadt.de)[ ](Email addresses: mknoell@theorie.ikp.physik.tu-darmstadt.de)(Marco Knöll), [robert.roth@physik.tu-darmstadt.de](robert.roth@physik.tu-darmstadt.de) (Robert Roth) culations. Even with access to high performance computing and methods to accelerate convergence, such as the similarity renormalization group (SRG) [15, 16], one is inevitably confronted with incomplete convergence of the many-body calculation. Hence, there is a need for extrapolation procedures that provide robust predictions for the converged observables along with reliable uncertainty estimates. Traditional extrapolation schemes typically rely on empirical exponential or polynomial parametrizations of the modelspace dependence of observables [3, 14, 17] . Recent physicsmotivated parametrizations, like the infrared extrapolation schemes derived from e􀀋ective theories [18–22], have proven successful in speciﬁc cases, but impose additional constraints on the many-body calculations. With increasing popularity of machine learning, artiﬁcial neural networks (ANNs) have entered the ﬁeld of nuclear structure physics, e.g., through large-scale approaches based on experimental data [23, 24], theoretical applications in the form of Bayesian machine-learning [25], neural-network quantum states [26–28], and many more. For a comprehensive overview and further reading we refer to [29, 30] . While ANNs have excelled in classiﬁcation and interpolation tasks, precise extrapolations remain challenging [31] . However, ﬁrst applications to NCSM and CC calculations have demonstrated the potential of machine learning as an extrapolation tool supplementing ab initio many-body methods [32, 33] . So far, these applications extrapolate NCSM or CC ground-state observables by emulating their model-space dependence, more precise, their functional dependence on the model-space truncation parameter and the harmonic-oscillator (HO) frequency ~􀀊 of the underlying single-particle basis. The ANNs are trained to mimic this functional dependency for a speciﬁc interaction, nucleus, and eigenstate and are then used to extrapolate the observable to Preprint submitted to Elsevier March 15, 2023 a su􀀎ciently large model space. These approaches essentially replace the traditional exponential parametrization of the manybody data by an ANN, which contains many more parameters. The training proces

FAQs

What problem does the paper address in nuclear structure theory?

It addresses how to extrapolate nuclear observables to infinite many-body Hilbert spaces when ab initio calculations are only available in finite model spaces, while also providing reliable uncertainty estimates.

How does the proposed universal machine-learning tool work?

It trains an artificial neural network to recognize observable-specific convergence patterns from short sequences of no-core shell model results over increasing truncation parameters and multiple harmonic-oscillator frequencies, then outputs the converged observable value.

What training data is used and what nuclei are predicted?

Training uses fully converged few-body systems with mass number A ≤ 4 across many Hamiltonians, and the paper discusses ground-state energy predictions for light nuclei including 6Li, 12C, and 16O.

Aug 5, 2026

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