Publications

Preprints

• Senwei Liang, Shixiao W. Jiang, John Harlim, and Haizhao Yang,
  Solving PDEs On Unknown Manifolds With Machine Learning,
  arxiv.

Journal Publications

• Shixiao W. Jiang, Rongji Li, Qile Yan, John Harlim,
  Generalized Finite Difference Method on unknown manifolds,
  Journal of Computational Physics (2024).   arxiv.   Download codes here.

• John Harlim, Shixiao W. Jiang, John Wilson Peoples,
  Radial basis approximation of tensor fields on manifolds: From operator estimation to manifold learning,
  Journal of Machine Learning Research, 24(345):1−85, (2023).   arxiv.   Download paper here.

• Qile Yan, Shixiao W. Jiang, John Harlim,
  Spectral methods for solving elliptic PDEs on unknown manifolds,
  Journal of Computational Physics, 486, 112132 (2023).   arXiv.

• Qile Yan, Shixiao W. Jiang* and John Harlim,
  Kernel-based methods for Solving Time-Dependent Advection-Diffusion Equations on Manifolds,
  Journal of Scientific Computing (2022).   arXiv.

• John Harlim, Shixiao Jiang, Hwanwoo Kim, and Daniel Sanz-Alonso,
  Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries,
  Inverse Problems (2021).   arxiv.

• Shixiao W. Jiang and John Harlim,
  Ghost Point Diffusion Maps for solving elliptic PDE’s on Manifolds with Classical Boundary Conditions,
  Communications on Pure and Applied Mathematics (2021).   arXiv..

• John Harlim, Shixiao W. Jiang, Senwei Liang, and Haizhao Yang,
  Machine Learning for Prediction with Missing Dynamics,
  Journal of Computational Physics, 428, 109922 (2021).   arxiv.

• Shixiao W. Jiang and John Harlim,
  Modeling of Missing Dynamical Systems: Deriving Parametric Models using a Nonparametric Framework,
  Research in the Mathematical Sciences, 7(3), 1-25 (2020).   arxiv.

• Shixiao W. Jiang, Gregor Kovacic, Douglas Zhou, and David Cai,
  Asymmetric Behavior of Surface Waves Induced by an Underlying Interfacial Wave,
  Communications in Mathematical Sciences 17(5), 1333-1351 (2019).   arxiv.

• Shixiao W. Jiang*, Gregor Kovacic, Douglas Zhou, and David Cai,
  Modulation-resonance mechanism for surface waves in a two-layer fluid system,
  J. Fluid Mech. 875, 807-841 (2019).   arxiv.

• Shixiao W. Jiang and John Harlim,
  Parameter estimation with data-driven nonparametric likelihood functions,
  Entropy, 21(6), 559 (2019).   arxiv.

• Shixiao W. Jiang, Hai-Hao Lu, Douglas Zhou, and David Cai,
  Stochastic linearization of turbulent dynamics of dispersive waves in equilibrium and non-equilibrium state,
  New J. Phys. 18, 083028 (2016).   researchgate.

• Shixiao W. Jiang, Hai-Hao Lu, Douglas Zhou, and David Cai,
  Renormalized dispersion relations of β-Fermi-Pasta-Ulam chains in equilibrium and nonequilibrium states,
  Phys. Rev. E 90, 032925 (2014).   researchgate.