Research

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

Publications

2025

  1. J. Zhang, X. Yang, C. Mou, C. Zhou.
    Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problems.
    Journal of Computational Physics, 2025.
    Journal

  2. A. Bacho, A. G. Sorokin, X. Yang, T. Bourdais, E. Calvello, M. Darcy, A. Hsu, B. Hosseini, H. Owhadi.
    Operator Learning at Machine Precision.
    arXiv:2511.19980, 2025.
    arXiv

  3. N. H. Nelsen, H. Owhadi, A. M. Stuart, X. Yang, Z. Zou.
    Bilevel Optimization for Learning Hyperparameters: Application to Solving PDEs and Inverse Problems with Gaussian Processes.
    arXiv:2510.05568, 2025.
    arXiv

  4. X. Yang, J. Zhang.
    Gaussian Process Policy Iteration with Additive Schwarz Acceleration for Forward and Inverse HJB and Mean Field Game Problems.
    arXiv:2505.00909, 2025.
    arXiv

  5. R. Baptista, E. Calvello, M. Darcy, H. Owhadi, A. M. Stuart, X. Yang.
    Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks.
    arXiv:2501.17110, 2025.
    arXiv

2024

  1. 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

  2. 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

  3. 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

2023

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

  2. R. Meng, X. Yang.
    Sparse Gaussian Processes for Solving Nonlinear PDEs.
    Journal of Computational Physics, 2023.
    Journal · arXiv

2022

  1. 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

2020

  1. 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

  2. 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

2016

  1. 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

  2. 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

2014

  1. 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

  • Gaussian Processes for Solving Functional PDEs: Applications to Functional Renormalization Group Equations
    Conference: Scientific Machine Learning: Theory, Algorithms, and Applications, Purdue
    Date: Sep. 2025

  • Data-Driven Methods for PDE Solutions and Model Discovery
    Conference: UQ and Trustworthy AI Algorithms for Complex Systems and Social Good, Chicago
    Date: Mar. 2025

  • Decoding Mean Field Games from Population and Environment Observations by Gaussian Processes
    Conference: SIAM MDS 2024 Minisymposium
    Date: Oct. 2024

  • Decoding Mean Field Games from Population and Environment Observations by Gaussian Processes
    Conference: Workshop on Scientific Computing and Large Data, Department of Mathematics, University of South Carolina
    Date: Dec. 2023

  • Numerical Methods for Mean Field Games Based on Gaussian Processes and Fourier Features
    Conference: DKU–NUSRI Joint Workshop on Pure and Applied Mathematics 2022
    Date: Jan. 2022

  • Hessian Riemannian Flows and Newton’s Method for Effective Hamiltonians and Mather Measures
    Conference: Two–Days Online Workshop on MFG
    Date: Jun. 2020

  • Two-Scale Homogenization of a Stationary Mean-Field Game
    Conference: 32nd Brazilian Math. Colloquium, IMPA, Rio, Brazil
    Date: Jul. 2019

  • Hessian Riemannian Flows and Newton’s Method for Effective Hamiltonians and Mather Measures
    Place: The University of Limoges, France
    Date: Mar. 2019

  • Hessian Riemannian Flows and Newton’s Method for Effective Hamiltonians and Mather Measures
    Place: The University of Padova, Italy
    Date: May. 2018