Researcher Profile and Settings

researchmap

https://researchmap.jp/takashi-furuya

Research funding number

00883696

Research Interests

• Machine Learning
• Inverse Problems
• Partial Differential Equations

Research Areas

• Natural sciences / Mathematical analysis

Research Experience

• Doshisha University, Faculty of Life and Medical Sciences Department of Biomedical Engineering, 助教, 2025/04 - Today
• Shimane University, Head Office for Research and Academic Information Education and Research Center for Mathematical and Data Science, Assistant professor, 2022/08 - 2025/03
• Hokkaido University, Faculty of Science Department of Mathematics, JSPS Fellow, 2021/04 - 2022/07
• Nagoya University, Graduate School of Mathematics, JSPS Fellow, 2019/04 - 2021/03

Education

• Nagoya University, Graduate School of Mathematics, 2016/04 - 2021/03

Association Memberships

• Japan society for industrial and applied mathematics, Apr. 2023, 9999
• Inverse Problems International Association, Jan. 2023, 9999
• The Mathematical Society of Japan, Apr. 2018, 9999

Published Papers

• Quantitative Approximation for Neural Operators in Nonlinear Parabolic Equations.
  Takashi Furuya; Koichi Taniguchi; Satoshi Okuda
  ICLR 2025, 2025, Scientific journal
  

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• Transformers are Universal In-context Learners.
  Takashi Furuya; Maarten V. de Hoop; Gabriel Peyré
  ICLR 2025, 2025, Scientific journal
  

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• Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation
  Jose Antonio Lara Benitez; Takashi Furuya; Florian Faucher; Anastasis Kratsios; Xavier Tricoche; Maarten V. de Hoop
  Journal of Computational Physics, Elsevier BV, 513 113168 - 113168, Sep. 2024
  

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• Convergences for Minimax Optimization Problems over Infinite-Dimensional Spaces Towards Stability in Adversarial Training
  T. Furuya; S. Okuda; K. Suetake; Y. Sawada
  Transactions on Machine Learning Research, 2024, Jun. 2024, Scientific journal
  

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• Consistency of the Bayes method for the inverse scattering problem
  Takashi Furuya; Pu-Zhao Kow; Jenn-Nan Wang
  Inverse Problems, IOP Publishing, 40(5) 055001 - 055001, 18 Mar. 2024
  

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• Can neural operators always be continuously discretized?
  Takashi Furuya; Michael Puthawala; Matti Lassas; Maarten V. de Hoop
  NeurIPS, 2024, International conference proceedings
  

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• Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners
  Maarten V de Hoop; Takashi Furuya; Ching-Lung Lin; Gen Nakamura; Manmohan Vashisth
  Inverse Problems, IOP Publishing, 39(2) 025005 - 025005, 19 Jan. 2023, Scientific journal
  

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• Globally injective and bijective neural operators.
  Takashi Furuya; Michael Puthawala; Matti Lassas; Maarten V. de Hoop
  Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023(NeurIPS), 36 57713 - 57753, Dec. 2023, International conference proceedings
• Inverse medium scattering problems with Kalman filter techniques
  Takashi Furuya; Roland Potthast
  Inverse Problems, IOP Publishing, 38(9) 095003 - 095003, 15 Aug. 2022, Scientific journal
  

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• Spectral Pruning for Recurrent Neural Networks
  Takashi Furuya; Kazuma Suetake; Koichi Taniguchi; Hiroyuki Kusumoto; Ryuji Saiin; Tomohiro Daimon
  Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 151 3458 - 3482, Mar. 2022
  

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• Remarks on the factorization and monotonicity method for inverse acoustic scatterings
  Takashi Furuya
  Inverse Problems, IOP Publishing, 37(6) 065006 - 065006, 01 Jun. 2021, Scientific journal
  

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• Scattering by the local perturbation of an open periodic waveguide in the half plane
  Takashi Furuya
  Journal of Mathematical Analysis and Applications, Elsevier BV, 489(1) 124149 - 124149, Sep. 2020, Scientific journal
  

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• The factorization and monotonicity method for the defect in an open periodic waveguide
  Takashi Furuya
  Journal of Inverse and Ill-posed Problems, Walter de Gruyter GmbH, 28(6) 783 - 796, 11 Jun. 2020, Scientific journal
  

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• The direct and inverse scattering problem for the semilinear Schrödinger equation
  Takashi Furuya
  Nonlinear Differential Equations and Applications NoDEA, Springer Science and Business Media LLC, 27(3), 07 Apr. 2020, Scientific journal
  

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• The monotonicity method for the inverse crack scattering problem
  Tomohiro Daimon; Takashi Furuya; Ryuji Saiin
  Inverse Problems in Science and Engineering, Informa UK Limited, 28(11) 1570 - 1581, 09 Mar. 2020, Scientific journal
  

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• A modification of the factorization method for scatterers with different physical properties
  Takashi Furuya
  Mathematical Methods in the Applied Sciences, Wiley, 42(11) 4017 - 4030, 21 Apr. 2019, Scientific journal
  

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• Hermite expansions of some tempered distributions
  Hiroyuki Chihara; Takashi Furuya; Takumi Koshikawa
  Journal of Pseudo-Differential Operators and Applications, Springer Science and Business Media LLC, 9(1) 105 - 124, 16 May 2017, Scientific journal
  

  DOI URL

Research Projects

• 偏微分方程式の逆問題に対する作用素近似の研究
  古屋 貴士
  日本学術振興会, 科学研究費助成事業, 2024/04 -2027/03, Principal investigator, 若手研究, 島根大学
• 深層学習を用いた偏微分方程式の不良設定逆問題における近似解の研究
  古屋貴士
  住友財団基礎科学研究助成, 2023/12 -2024/11
• Reconstruction Methods for inverse scattering problems including uncertainty
  古屋 貴士
  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 2021/04 -2024/03, Grant-in-Aid for JSPS Fellows, Hokkaido University
• 深層学習を活用した偏微分方程式の逆問題における再構成法
  古屋貴士
  山梨県若手研究者奨励事業費補助金, 2022/08 -2023/03, Principal investigator
• 散乱逆問題におけるサンプリング法の統一について
  古屋 貴士
  研究対象は、サンプリング法である。サンプリング法とは、散乱逆問題において観測データから未知領域を推定するための手法であり、特にFactorization Methodと呼ばれる手法に着目している。Factorization Methodは唯一、観測データから未知領域を推定する議論が抽象的な一般論としてまとめられており、この点から、Factorization Methodはサンプリング法を統一する理論の基軸になると考えている。 2020年度の大きな研究成果は、Factorization Methodの考え方に沿って、Monotonicity Methodの関数解析の枠組みによる一般論の整備を行うことに成功したことである。そのおかげで、一般論上でFactorization MethodとMonotonicity Methodの2つの比較を行える環境が整った。その比較によって、Monotonicity MethodはFactorization Methodよりも先天的仮定が少ない下で未知領域の再構成公式を与えることができることを確認した。しかし、Monotonicity Methodは、未知領域を点でテストするFactorization Methodとは異なり、領域でテストするため、特定の問題において(例えば、それぞれ異なる性質を持つ物体が混在している複雑な未知領域同定問題)は、数値実験がうまく運ばず、視覚的に未知領域を確認できないことがあった。こういったMonotonicity Methodの領域テストの数値実験部分については、今後改善すべき課題である。, 日本学術振興会, 科学研究費助成事業, 2019/04 -2021/03, 特別研究員奨励費, 名古屋大学

Teaching Experience

• Applied mathematics
  Doshisha University
• Linear algebra
  Doshisha University
• Calculus
  Doshisha University
• Data science basics, AI basic
  Shimane University
• Open data analysis
  Shimane University
• Linear algebra II
  Hokkaido University