Yixuan Wang

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G5 PhD candidate,
Applied + Computational Mathematics,
California Institute of Technology (Caltech)
E-mail: roywang [@] caltech [dot] edu.

About Me

I received a B.S. degree in mathematics summa cum laude from Peking University (PKU), in 2020. My undergraduate supervisor is Prof. Ruo Li.
My graduate supervisor is Prof. Thomas Yizhao Hou. I also work with Prof. Anima Anandkumar and Prof. Andrew Stuart. Check out my candidacy slides.

Research

My research interests broadly lie in

  • Numerical Analysis

  • Partial Differential Equation

  • Applied Probability

  • AI for Science

Actively looking for discussions and possible collaborations on interesting topics.

Find out more

Publications

  1. R. Li, Y Wang and Y. Wang. Approximation to Singular Quadratic Collision Model in Fokker-Planck-Landau Equation,
    SIAM Journal on Scientific Computing, 42(3), 2020, pp. B792-B815. [paper, slides]

  2. Y. Chen, T.Y. Hou and Y. Wang. Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions,
    Multiscale Modeling and Simulation, 19(2), 2021, pp. 980–1010. [paper]

  3. Z. Liu, S. Qian, Y. Wang, Y. Yan and T Yang. Schrödinger Principal-component Analysis: On the Duality between Principal-component Analysis and the Schrödinger Equation,
    Physical Review E, 104(2), 2021, 025307. [paper, slides]

  4. Y. Chen, T.Y. Hou and Y. Wang. Exponentially Convergent Multiscale Methods for 2D High Frequency Heterogeneous Helmholtz Equations,
    Multiscale Modeling and Simulation, 21(3), 2023, pp. 849–883. [paper, slides]

  5. Z. Liu, A. Stuart and Y. Wang. (2022) Second Order Ensemble Langevin Method for Sampling and Inverse Problems,
    [arxiv, slides]

  6. H. Maust, Z. Li, Y. Wang, D. Leibovici, O. Bruno, T.Y. Hou and A. Anandkumar. Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators,
    NeurIPS 2022, 3rd AI for Science workshop. [arxiv, poster]

  7. Y. Chen, T.Y. Hou and Y. Wang. Exponentially Convergent Multiscale Finite Element Method,
    Communications on Applied Mathematics and Computation, 6(2), 2024, 862-878. [paper, slides, poster]

  8. T.Y. Hou and Y. Wang. Blowup Analysis for a Quasi-exact 1D Model of 3D Euler and Navier-Stokes,
    Nonlinearity, 37(3), 2024, 035001. [paper, slides]

  9. T.Y. Hou, V.T. Nguyen and Y. Wang. (2024) L^2-based Stability of Blowup with Log Correction for semilinear Heat Equation,
    [arxiv]

  10. Z. Liu, Y. Wang, S. Vaidya, F. Ruehle, J. Halverson, M. Soljacic, T.Y. Hou and M. Tegmark. (2024) KAN: Kolmogorov-Arnold Networks,
    [arxiv, slides, poster, Scientific American, IEEE Spectrum, Quanta, MIT Technology Review]

  11. J. Chen, T.Y. Hou, V.T. Nguyen and Y. Wang. (2024) On the stability of blowup solutions to the complex Ginzburg-Landau equation in R^d,
    [arxiv, slides]

  12. Z. Liu, P. Ma, Y. Wang, W. Matusik and M. Tegmark. (2024) KAN 2.0: Kolmogorov-Arnold Networks Meet Science,
    [arxiv]

  13. Y. Wang, J.W. Siegel, Z. Liu and T.Y. Hou. (2024) On the expressiveness and spectral bias of KANs,
    [arxiv]

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