Multi-body wave functions using unsupervised deep neural networks

• Project Area: Foundation of "Machine Learning Physics" --- Revolutionary Transformation of Fundamental Physics by A New Field Integrating Machine Learning and Physics
• Project/Area Number: 23H04526
• Research Category: Grant-in-Aid for Transformative Research Areas (A)
• Allocation Type: Single-year Grants
• Review Section: Transformative Research Areas, Section (II)
• Research Institution: Institute of Physical and Chemical Research
• Principal Investigator: 内藤 智也 国立研究開発法人理化学研究所, 数理創造プログラム, 基礎科学特別研究員 (40962915)
• Project Period (FY): 2023-04-01 – 2025-03-31
• Project Status: Completed (Fiscal Year 2024)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2024: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2023: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 教師なし学習 / ディラック方程式 / 量子多体問題

Outline of Research at the Start

原子、分子、固体中の電子や、原子核中の核子などの量子多体問題を厳密に解くことができれば、系の様々な性質は原理的にはすべて計算が可能となる。しかしながら、量子多体問題の基底状態は数値的に求めることすら非常に困難であり、そのため多くの近似手法が数十年に渡り開発されてきた。本研究では、深層ニューラルネットワークと機械学習の知見を用い、新たな量子多体問題の計算手法を開発する。また、本研究で得られた知見をもとに、密度汎関数理論などの既存の量子多体計算の手法へフィードバックする。

Outline of Annual Research Achievements

身の回りの物質の性質の多くは、物質を構成する電子の振る舞いにより記述され、原子核の性質は原子核を構成する核子の振る舞いによって記述される。核子と電子は双方ともシュレディンガー方程式に従うフェルミオンである。したがって、多体シュレディンガー方程式を解くことによりこれらの性質を調べることができる。しかしながら、多体シュレディンガー方程式をそのまま解くことは非常に困難であり、今まで長年にわたり様々な研究が行われ、様々な手法が提案されてきた。その中でも多くの手法は、変分原理に基づく手法である。
ここで、変分原理では計算精度は試行関数が記述可能な空間に大きく依存する。そこで、任意の関数を任意の精度で記述可能なニューラルネットワークを試行関数に用いることで、計算精度を大きく向上させることができる。
本年度は、本手法を相対論的量子力学の基礎方程式であるディラック方程式に適用する研究を行った。原子核構造や超重元素の電子状態においては、相対論効果が重要になる場合があることが知られている。しかしながら、相対論的量子力学の基礎方程式であるディラック方程式では、負エネルギー解の存在により、単純に変分原理を適用すると「変分崩壊」と言われる、負の無限に計算が発散してしまう問題が知られており、その問題を解決するために「逆ハミルトニアン法」と呼ばれる手法が1990年代に提案された。本手法が、ニューラルネットワークを用いた教師なし機械学習にも適用可能であることを、一体問題ではあるものの示した。

Research Progress Status

令和6年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和6年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] 吉林大学(中国)
• [Int'l Joint Research] 吉林大学(中国)
• [Journal Article] 164Pb: A possible heaviest N = Z doubly magic nucleus (2025)
  • Author(s): Tomoya Naito, Masaaki Kimura, and Masaki Sasano
  • Journal Title: Physical Review Research Volume: 7 Issue: 1 Pages: 013050-013050
  • DOI: 10.1103/physrevresearch.7.013050
  • Peer Reviewed / Open Access
• [Journal Article] Polaronic neutron in dilute α matter: A p-wave Bose polaron (2025)
  • Author(s): Hiroyuki Tajima, Hajime Moriya, Tomoya Naito, Wataru Horiuchi, Eiji Nakano, Kei Iida
  • Journal Title: Physical Review C Volume: 111 Issue: 2 Pages: 025802-025802
  • DOI: 10.1103/physrevc.111.025802
  • Peer Reviewed / Open Access
• [Journal Article] Accurate and precise quantum computation of valence two-neutron systems (2024)
  • Author(s): Sota Yoshida, Takeshi Sato, Takumi Ogata, Tomoya Naito, and Masaaki Kimura
  • Journal Title: Physical Review C Volume: 109 Issue: 6 Pages: 064305-064305
  • DOI: 10.1103/physrevc.109.064305
  • Peer Reviewed
• [Journal Article] QCD-based charge symmetry breaking interaction and the Okamoto-Nolen-Schiffer anomaly (2024)
  • Author(s): Hiroyuki Sagawa, Tomoya Naito, Xavier Roca-Maza, Tetsuo Hatsuda
  • Journal Title: Physical Review C Volume: 109 Issue: 1
  • DOI: 10.1103/physrevc.109.l011302
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Possible inconsistency between phenomenological and theoretical determinations of charge symmetry breaking in nuclear energy density functionals (2024)
  • Author(s): Tomoya Naito, Gianluca Colo, Tetsuo Hatsuda, Haozhao Liang, Xavier Roca-Maza, and Hiroyuki Sagawa
  • Journal Title: Il Nuovo Cimento C Volume: 47 Pages: 52-52
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Comparative study on charge radii and their kinks at magic numbers (2023)
  • Author(s): Tomoya Naito, Tomohiro Oishi, Hiroyuki Sagawa, Zhiheng Wang
  • Journal Title: Physical Review C Volume: 107 Issue: 5 Pages: 054307-054307
  • DOI: 10.1103/physrevc.107.054307
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Nuclear many-body effects on particle emission following muon capture on 28Si and 40Ca (2023)
  • Author(s): Futoshi Minato, Tomoya Naito, Osamu Iwamoto
  • Journal Title: Physical Review C Volume: 107 Issue: 5 Pages: 054314-054314
  • DOI: 10.1103/physrevc.107.054314
  • Peer Reviewed
• [Journal Article] Effects of Coulomb and isospin symmetry breaking interactions on neutron-skin thickness (2023)
  • Author(s): Tomoya Naito, Gianluca Colo, Haozhao Liang, Xavier Roca-Maza, Hiroyuki Sagawa
  • Journal Title: Physical Review C Volume: 107 Issue: 6 Pages: 064302-064302
  • DOI: 10.1103/physrevc.107.064302
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Multi-body wave function of ground and low-lying excited states using unornamented deep neural networks (2023)
  • Author(s): Tomoya Naito, Hisashi Naito, and Koji Hashimoto
  • Journal Title: Phys. Rev. Research Volume: 9 Issue: 3 Pages: 033189-033189
  • DOI: 10.1103/physrevresearch.5.033189
  • Peer Reviewed / Open Access
• [Journal Article] Calibration of nuclear charge density distribution by back-propagation neural networks (2023)
  • Author(s): Yang Zu-Xing、Fan Xiao-Hua、Naito Tomoya、Niu Zhong-Ming、Li Zhi-Pan、Liang Haozhao
  • Journal Title: Physical Review C Volume: 108 Issue: 3 Pages: 034315-034315
  • DOI: 10.1103/physrevc.108.034315
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Revisiting the extraction of charge radii of 40Ca and 208Pb with muonic atom spectroscopy (2023)
  • Author(s): Hui Hui Xie, Tomoya Naito, Jian Li, Haozhao Liang
  • Journal Title: Physics Letters B Volume: 846 Pages: 138232-138232
  • DOI: 10.1016/j.physletb.2023.138232
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] From Density to Energy Density Functional (2025)
  • Author(s): Tomoya Naito
  • Organizer: International symposium: TRIP Usecase: Nuclear Transmutation 2025
  • Int'l Joint Research / Invited
• [Presentation] Isospin symmetry breaking energy density functional based on quantum chromodynamics (2025)
  • Author(s): Tomoya Naito, Gianluca Colo, Tetsuo Hatsuda, Xavier Roca-Maza, and Hiroyuki Sagawa
  • Organizer: VIIth Topical Workshop on Modern Aspects in Nuclear Structure―The Many Facets of Nuclear Structure― (Bormio2025)
  • Int'l Joint Research
• [Presentation] What Is The Possible Heaviest N = Z Nuclei? (2025)
  • Author(s): Tomoya Naito
  • Organizer: Advancing physics at next RIBF (ADRIB25)
  • Invited
• [Presentation] SCRIT のための理論計算 (2025)
  • Author(s): 内藤智也
  • Organizer: 粒子ビーム科学研究領域セミナー
  • Invited
• [Presentation] Impact of the isospin symmetry breaking on nuclear properties (2024)
  • Author(s): Tomoya Naito
  • Organizer: SSNET'24―International Conference on Shapes and Symmetries in Nuclei: from Experiment to Theory―
  • Int'l Joint Research / Invited
• [Presentation] Quantum multi-body problems using unsupervised machine learning (2024)
  • Author(s): Tomoya Naito
  • Organizer: 77th OMEG Workshop
  • Int'l Joint Research / Invited
• [Presentation] Isospin symmetry breaking energy density functional based on quantum chromodynamics (2024)
  • Author(s): Tomoya Naito, Gianluca Colo, Tetsuo Hatsuda, Xavier Roca-Maza, and Hiroyuki Sagawa
  • Organizer: RCNP-CENuM-OMEG Symposium on Nuclear Structure, Reaction, and Astrophysics (NuSRAP2024)
  • Int'l Joint Research
• [Presentation] Impact of the isospin symmetry breaking on nuclear densities (2024)
  • Author(s): Tomoya Naito
  • Organizer: Low-Energy Electron Scattering for Nucleon and Exotic Nuclei (LEES2024)
  • Int'l Joint Research
• [Presentation] Microscopic determination of the isospin symmetry breaking energy density functional (2024)
  • Author(s): Tomoya Naito, Gianluca Colo, Tetsuo Hatsuda, Xavier Roca-Maza, and Hiroyuki Sagawa
  • Organizer: NuSym24, XII International Symposium on Nuclear Symmetry Energy
  • Int'l Joint Research
• [Presentation] QCD-based charge independence breaking energy density functional (2024)
  • Author(s): Tomoya Naito, Gianluca Colo, Tetsuo Hatsuda, Xavier Roca-Maza, and Hiroyuki Sagawa
  • Organizer: The 10th International Conference on Quarks and Nuclear Physics (QNP2024)
  • Int'l Joint Research
• [Presentation] Mirror skin and isospin symmetry breaking (2024)
  • Author(s): 内藤智也
  • Organizer: 第2回「新しいスキンを考える会」
  • Invited
• [Presentation] KISS で目指す究極の原子核密度汎関数 (2024)
  • Author(s): 内藤智也
  • Organizer: RIBF mini-workshop "How can laser spectroscopy at KISS contribute valuable insights to nuclear models?"
  • Invited
• [Presentation] Towards First-Principles Energy Density Functionals (2024)
  • Author(s): Tomoya Naito
  • Organizer: ICCUB HadNucAtUB Seminar
  • Int'l Joint Research / Invited
• [Presentation] Quantum multi-body problems using unsupervised machine learning (2024)
  • Author(s): Tomoya Naito
  • Organizer: ICCUB HadNucAtUB Seminar
  • Int'l Joint Research / Invited
• [Presentation] Density distribution of Ca (2024)
  • Author(s): 内藤智也
  • Organizer: 東京工業大学ハドロンセミナー
  • Invited
• [Presentation] Impact of the isospin symmetry breaking on the nuclear equation of state---Towards accurate description of nuclear structure--- (2024)
  • Author(s): Tomoya Naito
  • Organizer: 73rd OMEG-SSANP Workshop "r-process nucleosynthesis and some specific topics for nuclear physics"
  • Int'l Joint Research / Invited
• [Presentation] (一般シンポジウム講演) Phenomenological determination of nuclear equation of state: current status and future (2024)
  • Author(s): Tomoya Naito
  • Organizer: 日本物理学会 2024年春季大会
  • Invited
• [Presentation] To Be Determined: Energy Density Functional and Equation of State (2024)
  • Author(s): Tomoya Naito
  • Organizer: Advancing physics at next RIBF (ADRIB24)
  • Invited
• [Presentation] 原子核構造計算と電荷半径を用いた核力の理解 (2024)
  • Author(s): 内藤智也
  • Organizer: 京都大学化学研究所 粒子ビーム科学研究領域セミナー
  • Invited
• [Presentation] A simple method of multi-body wave function using deep neural network (2023)
  • Author(s): Tomoya Naito
  • Organizer: Computational Approaches to Quantum Many-Body Systems
  • Int'l Joint Research / Invited
• [Presentation] Impact of the isospin symmetry breaking on the nuclear equation of state (2023)
  • Author(s): Tomoya Naito
  • Organizer: 1st IReNA-Ukakuren Joint Workshop "Advancing Professional Development in Nuclear Astrophysics and Beyond"
  • Int'l Joint Research / Invited
• [Presentation] Impact of the isospin symmetry breaking on the neutron-skin thickness and the nuclear equation of state (2023)
  • Author(s): Tomoya Naito, Gianluca Colo, Haozhao Liang, Xavier Roca-Maza, and Hiroyuki Sagawa
  • Organizer: 7th International Conference on Collective Motion in Nuclei under Extreme Conditions (COMEX7)
  • Int'l Joint Research
• [Presentation] Isospin symmetry breaking in nuclear ground state---Phenomenological and QCD sum rule approach--- (2023)
  • Author(s): Tomoya Naito
  • Organizer: High Energy Theory Group Seminar, Institute of Physics, Academia Sinica
  • Int'l Joint Research / Invited
• [Presentation] A simple method of multi-body wave function using deep neural network (2023)
  • Author(s): 内藤智也
  • Organizer: 酒見グループセミナー
  • Invited
• [Presentation] Low-Energy Nuclear Physics---from femtometer to kilometer--- (2023)
  • Author(s): Tomoya Naito
  • Organizer: T30d Group Meeting, Physik-Department, Technische Universiat Munchen
  • Int'l Joint Research / Invited
• [Presentation] 密度汎関数理論入門〜表面吸着の第一原理計算に向けて〜 (2023)
  • Author(s): 内藤智也
  • Organizer: 東京農工大学 畠山研セミナー
  • Invited