Research

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

Publications

2026

1. X. Yang, M. Darcy, M. Hudes, F. J. Alexander, G. Eyink, H. Owhadi.
   Solving Functional PDEs with Gaussian Processes and Applications to Functional Renormalization Group Equations.
   Journal of Computational Physics 563, 115085, 2026.
   Journal · arXiv

2. X. Yang, H. Owhadi.
   A Minibatch Method for Solving Nonlinear PDEs with Gaussian Processes.
   SIAM Journal on Scientific Computing 48 (4), C635–C657, 2026.
   Journal · arXiv

3. 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.
   Mathematics of Computation, 2026.
   Journal · arXiv

4. H. Yan, X. Yang, J. Zhang.
   A Globally Convergent Flow for Time-Dependent Mean Field Games and a Solver-Agnostic Framework for Inverse Problems.
   arXiv:2603.10336, 2026.
   arXiv

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 543, 114412, 2025.
   Journal · arXiv

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

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 the Dots.
   Proceedings of the National Academy of Sciences 121 (32), e2403449121, 2024.
   Journal · arXiv

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 508, 112978, 2024.
   Journal · arXiv

3. L. M. Briceño-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), Article 16, 2024.
   Journal · arXiv

2023

1. R. Meng, X. Yang.
   Sparse Gaussian Processes for Solving Nonlinear PDEs.
   Journal of Computational Physics 490, 112340, 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 460, 111188, 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 26, Article 17, 2020.
   Journal · arXiv

2. D. A. Gomes, X. Yang.
   The Hessian Riemannian Flow and Newton’s Method for Effective Hamiltonians and Mather Measures.
   ESAIM: Mathematical Modelling and Numerical Analysis 54 (6), 1883–1915, 2020.
   Journal · arXiv

2017

1. N. Almayouf, E. Bachini, A. Chapouto, R. Ferreira, D. Gomes, D. Jordão, D. Evangelista 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 10 (3), 473–493, 2017.
   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 7 (36), 57671–57678, 2016.
   Journal · PubMed Central

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 33 (6), Article 226, 1–11, 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