Title: Advancing Few-Body Nuclear Theory with Artificial Intelligence: Application of AI for the Efficient Solution of Faddeev-Yakubovsky Equations in Nuclear Physics.
1. Project Summary
Keywords: few-body nuclear physics, Faddeev-Yakubovsky equations, Efimov physics, halo nuclei, machine learning, neural networks, AI-driven numerical methods, neutron-rich nuclei.
Understanding the structure of neutron-rich halo nuclei is a cornerstone of contemporary nuclear physics. Systems such as 6He, 11Li, 14Be, and 22C, where one or more loosely bound neutrons form a halo around a core, encode universal quantum phenomena (Efimov physics) and are actively studied at world-class facilities (GANIL-SPIRAL2, FAIR, RIKEN). Reliable theoretical predictions require solving the Faddeev-Yakubovsky (FY) equations for systems of up to six particles — a task whose numerical cost grows prohibitively with the number of particles and whose algebraic formulation currently limits its applicability.
This PhD project, embedded in the international ANR–FAPESP project FBCUBES (France-Brazil Collaboration on Universal Behavior of Exotic Nuclear Systems), proposes a paradigm shift by integrating Artificial Intelligence (AI) into the production-level FY and Schrödinger code suite developed at IPHC, Strasbourg (SO-FY). Three complementary paths of increasing difficulty are pursued: (i) mesh optimization using Generative Adversarial Networks (GANs) trained on pseudo-data or algebraic models; (ii) neural network solutions replacing traditional basis expansions in the FY and Schrödinger equations; (iii) computation of multi-neutron cross-section observables to refine the underlying numerical basis.
The PhD student will be based at INPHYNI (Nice) in daily collaboration with the IPHC team (Strasbourg), within an international environment spanning France and Brazil. The project is funded by the ANR-FAPESP FBCUBES grant.
2. Detailed Research Project Description
2.1. Scientific Context and Motivation
The structure of neutron-rich nuclei at and beyond the neutron dripline is a cornerstone of contemporary nuclear physics. These exotic systems act as a lens into the nature of the nuclear interaction, revealing rare configurations of protons and neutrons that maximize binding energy or extend orbiting time in resonance states. Upcoming experimental programs — GANIL-SPIRAL2 in France, FAIR in Germany, and RIKEN in Japan — will produce unprecedented data on systems with large numbers of valence neutrons, demanding a theoretical framework capable of matching this experimental ambition.
Many of these systems form halo nuclei: quantum objects in which one or more loosely bound neutrons extend far beyond the nuclear core, probing classically forbidden spatial regions. Paradigmatic examples include the Borromean nucleus 11Li (n+n+9Li), 14Be (n+n+12Be), 6He (n+n+4He), and 22C (n+n+20C) [1]. These systems lie in the regime of Efimov physics [2], where two or more particles interacting via short-range forces exhibit universal behavior governed by a small number of parameters (the scattering lengths of the subsystems), largely independently of the microscopic details of the interaction.
The Faddeev-Yakubovsky (FY) equations [3, 4] provide the rigorous mathematical framework for computing the wave functions and observables of such few-body systems from first principles. The IPHC group (R. Lazauskas, Strasbourg) has pioneered this approach in nuclear physics, developing a production-level FY and Schrödinger solver code suite (SO-FY), and achieved the first exact solution of the five-body problem and the interpretation of the tetraneutron signal [5]. However, the FY method is currently limited to systems of up to five particles in practice, and its algebraic formulation imposes severe constraints on the coordinate system and the treatment of
the Pauli exclusion principle.
The central problem: no reliable theoretical calculation can currently be performed for the static and dynamic properties of systems with more than three valence neutrons plus a core. This prevents quantitative predictions for experiments at GANIL, FAIR, and RIKEN, particularly in interpreting Dalitz-plot distributions for multi-neutron breakup reactions.
2.2. Originality and Scientific Challenges
Challenge 1: Extending the FY framework to four valence neutrons
The FY method is powerful but limited by its algebraic formulation, which accounts for the Pauli exclusion principle and the translationally-invariant coordinate system. Establishing the chart of halo systems requires solutions capable of treating five-body systems (four valence neutrons plus a core). The combinatorial growth of Faddeev components and the size of the numerical basis make a brute-force extension prohibitive; a paradigm shift in the numerical strategy is required.
Challenge 2: Integrating non-local Ab Initio potentials
The FBCUBES consortium will generate microscopic neutron-core (n-c) and neutron-neutron-core (n-n-c) potentials from Ab Initio methods (Brazilian partners, ITA). These potentials are non-local and energy-dependent. Compatibility with the FY equations is only achievable if the energy dependence takes the form specific to the full A-body system, which requires substantial extensions of the current algebraic FY formulation.
Challenge 3: Computing multi-neutron continuum observables
Interpreting the breakup reactions measured at GANIL-SPIRAL2, RIKEN, and FAIR through Dalitz-plot distributions requires computing multi-neutron cross-section observables in the continuum. FY solutions in the continuum are at the frontier of what current solvers can handle, both in terms of accuracy and of scalability to systems with more than three fragments. Proposed solution: AI supplementing the FY and Schrödinger solvers Data-driven models based on neural networks show great promise for solving differential equations and learning the structure of high-dimensional quantum states [6, 7]. The INPHYNI group has already made initial attempts in this direction. This project pursues three complementary paths of increasing difficulty to reduce the numerical cost and improve the accuracy and performance of SO-FY:
[*]Mesh optimization using AI: AI algorithms will identify and prioritize the most relevant basis elements to enhance computational efficiency and accuracy, utilizing standard tools such as Generative Adversarial Networks (GANs) trained on pseudo-data or algebraic models.
[*]Neural network solutions to the FY and Schrödinger equations: The potential of replacing traditional basis expansions in the FY and Schrödinger equations with neural network-based representations will be explored, aiming to improve scalability to systems with more than three fragments in the continuum.
[*]Multi-neutron cross-section computation: More challenging multi-neutron cross-section variables will be computed and fed back to the mesh parameters to understand and refine the underlying numerical basis, enabling comparison with breakup experiments (Dalitz plots) at GANIL, RIKEN, and FAIR.
A key identified risk is that direct AI model implementation may lack efficiency; the planned response is to develop a physics-guided version, leveraging the algebraic structure of the FY equations to constrain the AI model. A second phase of the project then extends this work beyond the elastic regime, developing a mixed OpenMP/MPI parallelization to address the computational demands of applying the extended FY solver to 5- and 6-body systems in the continuum.
2.3. Technical Approach and Three-Year Milestones
The project unfolds in three successive phases, each building on the results of the previous one. Initial attempts are already underway within the INPHYNI–IPHC collaboration, providing the PhD student with a concrete starting point from day one.
Year 1 — AI-assisted mesh optimization
The student will begin by acquiring a thorough understanding of the SO-FY codebase and of the sensitivity of the FY solutions to the choice of numerical basis. The first scientific objective is to develop GAN-based mesh optimizers — trained on pseudo-data and on algebraic models of the nuclear interaction — capable of identifying and prioritizing the most relevant basis elements. These optimizers will be benchmarked on two-neutron halo nuclei (6He, 11Li) for which exact reference solutions exist. By the end of Year 1 the student is expected to deliver a working prototype of the AI-optimized mesh, document it in a benchmark report, and present the results
at an international FBCUBES consortium meeting.
Year 2 — Neural network representations and cross-section computation Building on the mesh-optimization experience, the student will explore replacing traditional basis expansions in the FY and Schrödinger equations with neural network-based representations, targeting systems with three valence neutrons. In parallel, multi-neutron cross-section observables will be computed and fed back to the mesh parameters, enabling the first comparison with breakup data (Dalitz plots) from GANIL-SPIRAL2 and RIKEN. The microscopic neutron-core potentials provided by the Brazilian partners will be integrated into the solver at this stage. The expected
outcome is a first journal publication on AI-assisted FY solvers (target: Phys. Rev. C) and an
oral contribution at an international conference.
Year 3 — Extension beyond the elastic regime and dissemination
The final year is devoted to pushing the solver beyond the elastic regime through a mixed OpenMP/MPI parallelization strategy, allowing the treatment of four-neutron halo systems (8He, 22C) in the continuum. The results feed into the systematic computation of the binding-energy chart of ns+core systems. The thesis is written in parallel with the preparation of a second publication, and the SO-FY+AI modules are made publicly available on the CNRS GitLab repository.
Throughout the three years the student will have access to Tier-0 national HPC resources (CINES, TGCC, IDRIS) through the FBCUBES computational allocation, as well as to the INPHYNI local cluster and the CCIN2P3 distributed-memory partition.
Bibliography
[1] I. Tanihata et al., Measurements of interaction cross sections and nuclear radii in the light p-shell
region, Phys. Rev. Lett. 55, 2676 (1985). doi:10.1103/PhysRevLett.55.2676
[2] V. Efimov, Energy levels arising from resonant two-body forces in a three-body system, Phys. Lett. B
33, 563 (1970). doi:10.1016/0370-2693(70)90349-7
[3] L. D. Faddeev, Scattering theory for a three-particle system, Sov. Phys. JETP 12, 1014 (1961).
INSPIRE-HEP
[4] O. A. Yakubovsky, On the integral equations in the theory of N particle scattering, Sov. J. Nucl. Phys.
5, 937 (1967). INSPIRE-HEP
[5] R. Lazauskas, Solution of the n–4He elastic scattering problem using the Faddeev-Yakubovsky equations,
Phys. Rev. C 97, 044002 (2018). doi:10.1103/PhysRevC.97.044002
[6] I. E. Lagaris, A. Likas, and D. I. Fotiadis, Artificial neural networks for solving ordinary and partial
differential equations, IEEE Trans. Neural Netw. 9, 987 (1998). doi:10.1109/72.712178
[7] G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural networks,
Science 355, 602 (2017). doi:10.1126/science.aag2302
[8] P. Recchia, A. Kievsky, L. Girlanda, and M. Gattobigio, Variational Monte Carlo with neural network
quantum states for few-body nuclei, Few-Body Syst. 65, 102 (2024). doi:10.1007/s00601-024-01965-7
[9] X. Jin, M. Gattobigio et al., Advancing Machine Learning Applications in Quantum Few-Body Systems,
arXiv:2603.12668 (2026, submitted to Few-Body Syst.). arXiv:2603.12668
[10] A. Kievsky, M. Gattobigio, L. Girlanda, and M. Viviani, Efimov Physics and Connections to Nuclear
Physics, Annu. Rev. Nucl. Part. Sci. 71, 465 (2021). doi:10.1146/annurev-nucl-102419-032845
6
[11] M. Gattobigio and A. Kievsky, Universality and scaling in the N-body sector with short-range
interactions, Phys. Rev. A 90, 012502 (2014). doi:10.1103/PhysRevA.90.012502
[12] T. Frederico, M. Gattobigio et al., Universal properties of the four-boson system near a Feshbach
resonance, Phys. Rev. A 108, 033302 (2023). doi:10.1103/PhysRevA.108.033302
[13] A. Deltuva, M. Gattobigio et al., Gaussian characterization of two-neutron halo nuclei, submitted to
Phys. Rev. C (2026).
3. Supervision
3.1. Thesis Supervisor — Mario Gattobigio
Position Maître de Conférences (Associate Professor), Université Côte d’Azur
Laboratory INPHYNI (UMR 7010), CNRS / Université Côte d’Azur, Nice
Email
Mario.Gattobigio@univ-cotedazur.fr
Tel. +33 (0)4 89 15 27 76
Scientific profile
Mario Gattobigio (MC since 2007 at UCA, HDR 2015) has 58 peer-reviewed publications, 9 conference proceedings, and 2 preprints (2026), with 1,206 citations and an h-index of 21 (Google Scholar, April 2026). He contributes 60% of his research time to W.P. 3 of FBCUBES. His expertise rests on three pillars that are each directly relevant to this PhD project.
1. Machine Learning applied to few-body quantum problems. Gattobigio has a sustained and unique track record at the intersection of AI and quantum few-body physics. He supervised the PhD of Paolo Recchia (UCA, 2019–2022, thesis: Tackling Quantum Few-Body Problems with Neural Networks [8]) and co-supervised R. A. M. Zen (NUS Singapore, 2017–2022, Data-Driven Modelling and Optimization with Deep Learning). As Co-PI of the PHC Merlion grant Deep Quantum Artificial Intelligence For and From Quantum Physics (Campus France / NUS, 2018– 2019), he initiated the integration of deep learning into few-body variational methods. This line of research culminates in the 2026 preprint Advancing Machine Learning Applications in Quantum Few-Body Systems [9] (arXiv:2603.12668, submitted to Few-Body Systems), which constitutes a direct proof of concept for Task 3.c of FBCUBES.
2. Efimov-like universal physics and halo nuclei. Gattobigio is a leading expert on Efimov physics and its connections to nuclear physics. He authored the invited review Efimov Physics and Connections to Nuclear Physics [10] (Annual Review of Nuclear and Particle Science 71, 2021) and has a long series of publications establishing universality and scaling in the N-body sector [11]. The universal behaviour governed by scattering lengths — the hallmark of Efimov physics — is precisely the regime that controls the structure of neutron-rich halo nuclei such as 6He, 11Li, and 22C, which are the primary targets of FBCUBES. The collaboration with FBCUBES co-PI T. Frederico (ITA, Brazil) on the universal tetramer [12] further illustrates this connection. This expertise ensures that the AI tools developed in Task 3.c are guided by deep physical understanding of the systems they model.
3. Stochastic Variational Method (SVM) with Correlated Gaussians. Gattobigio is an expert in the Stochastic Variational Method (SVM) with adaptive optimized Correlated Gaussians (CG), a variational technique that provides highly accurate solutions for few-body bound states. CG calculations are computationally independent of the FY solver and can therefore always serve as a benchmark and as a supplementary source of information whenever FY results need validation. The recent preprint Gaussian characterization of two-neutron halo nuclei [13] (submitted to Phys. Rev. C, 2026), demonstrates the direct application of this methodology to the halo nuclei studied in FBCUBES. This dual competence — FY via the IPHC collaboration and SVM-CG at INPHYNI — gives the PhD student access to two complementary, mutually validating theoretical frameworks.
Key publications and preprints (2023–2026, relevant to this project)
1. [Preprint 2026] Z. Jin, P. Recchia, and M. Gattobigio, Advancing Machine Learning Applications in Quantum Few-Body Systems, arXiv:2603.12668 [physics.comp-ph], submitted to Few-Body Systems (2026). [
doi.org]
2. [Preprint 2026] A. Deltuva, M. Gattobigio, D. Jurčiukonis, and A. Kievsky, Gaussian characterization of two-neutron halo nuclei, submitted to Phys. Rev. C (2026).
3. P. Recchia, D. Basu, M. Gattobigio, C. Miniatura, S. Bressan, The Steepest Slope toward a Quantum Few-Body Solution: Gradient Variational Methods for the Quantum Few-Body Problem, Few-Body Systems 65, 102 (2024). [
doi.org]
4. P.-Y. Duerinck, A. Deltuva, J. Dohet-Eraly, M. Gattobigio, A. Kievsky, R. Lazauskas et al., Excited state of the α particle: A benchmark study, Phys. Rev. C 112, 044001 (2025). [
link.aps.org]
5. T. Frederico and M. Gattobigio, Universal tetramer limit-cycle at the unitarity limit, Phys. Rev. A 108, 033302 (2023). [
doi.org]