Research

My research interests include mean field games, partial differential equations, numerical analysis, optimization, operator learning, inverse problems, Gaussian processes and kernel methods.

Publications

  • T.Bourdais, P. Batlle, X. Yang, R. Baptista, N. Rouquette, H. Owhadi. Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting dots. Proceedings of the National Academy of Sciences 121 (32), e2403449121. 2024. [Journal]

  • J.Guo, C. Mou, X. Yang, C. Zhou. Decoding Mean Field Games from Population and Environment Observations By Gaussian Processes. Journal of Computational Physics, 2024. [Journal][Arxiv]

  • L. M Briceno-Arias, F. J. Silva, X. Yang. Forward-backward algorithm for functions with locally Lipschitz gradient: applications to mean field games, Set-Valued and Variational Analysis 32 (2), 1-22, 2024. [Journal]

  • X. Yang, H. Owhadi. A Mini-Batch Method for Solving Nonlinear PDEs with Gaussian Processes, arXiv:2306.00307, 2023. [Arxiv]

  • R. Meng, X. Yang. Sparse Gaussian processes for solving nonlinear PDEs. Journal of Computational Physics, 2023. [Journal][Arxiv]

  • C. Mou, X. Yang, C. Zhou. Numerical methods for Mean field Games based on Gaussian Processes and Fourier Features. Journal of Computational Physics, 2022. [Journal][Arxiv]

  • R. Ferreira, D. Gomes, X. Yang. Two-scale homogenization of a stationary mean-field game. ESAIM: Control Optimisation and Calculus of Variations, 2020. [Journal][Arxiv]

  • D. A. Gomes, X. Yang. Hessian Riemannian flows and Newton’s method for Effective Hamiltonians and Mather measures. ESAIM: Mathematical Modelling and Numerical Analysis, 2020. [Journal][Arxiv]

  • X Yang, E Debonneuil, A Zhavoronkov, B. Mishra. Cancer megafunds with in silico and in vitro validation: Accelerating Cancer Drug Discovery via Financial Engineering without Financial Crisis. Oncotarget, 2016. [Journal]

  • N. Almayouf, E. Bachini, A. Chapouto, R. Ferreira, D. Gomes, D. Jordão, D. E. Junior, A. Karagulyan, J. Monasterio, L. Nurbekyan, G. Pagliar, M. Piccirilli, S. Pratapsi, M. Prazeres, J. Reis, A. Rodrigues, O. Romero, M. Sargsyan, T. Seneci, C. Song, K. Terai, R. Tomisaki, H. Velasco-Perez, V. Voskanyan, X. Yang. Existence of positive solutions for an approximation of stationary mean-field games. Involve, a Journal of Mathematics, 2016. [Arxiv]

  • R. Wang, X. Yang, Y. Yuan, W. Chen, K. Bala, H. Bao, Automatic shader simplification using surface signal approximation. ACM Transactions on Graphics, Proceedings of ACM SIGGRAPH ASIA, 2014. [Journal]

Invited Talks

  • Decoding mean field games from population and environment observations by Gaussian Processes Oct.2024
    • Conference: SIAM MDS 2024 Minisymposium
  • Decoding mean field games from population and environment observations by Gaussian Processes Dec.2023
    • Conference: Workshop on Scientific Computing and Large Data
    • Department of Mathematics, University of South Carolina
  • Numerical methods for Mean field Games based on Gaussian Processes and Fourier Features, Jan. 2022
    • Conference: DKU-NUSRI Joint Workshop on Pure and Applied Mathematics 2022
  • Hessian Riemannian flows and Newton’s method for Effective Hamiltonians and Mather measures, Jun. 2020
    • Conference: Two-Days online workshop on MFG
  • Two-scale homogenization of a stationary mean-field game, Jul. 2019
    • Conference: 32nd Brazilian Math. Colloquium
    • Place: IMPA, Rio, Brazil
  • Hessian Riemannian flows and Newton’s method for Effective Hamiltonians and Mather measures, Mar. 2019
    • Place: The University of Limoges, France
  • Hessian Riemannian flows and Newton’s method for Effective Hamiltonians and Mather measures, May. 2018
    • Place: The University of Padova, Italy

Talks

  • Two-scale homogenization of a stationary mean-field game, Sep. 2019
    • Conference: Mean-field games and related topics-5
    • Place: Levico, Terme, Italy
  • Hessian Riemannian flows and Newton’s method for Effective Hamiltonians and Mather measures, Jun. 2018
    • Poster session
    • Graduate Summer School: Mean Field Games and Applications
    • Place: Institute for pure and applied mathematics, UCLA, Los Angeles, California