Yixuan Wang

Final year PhD, Computing + Mathematical Sciences, 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.
I am on the job market this year!

Research

My research interests broadly lie in

• Partial Differential Equation

• AI for Science

• Applied Probability

• Numerical Analysis

I develop analytical and computational frameworks for understanding singularity formation in PDEs, motivated by the Clay prize problem on blowup of Navier-Stokes equations. I build systematic proofs inspired by numerics, amenable to computer-assisted verification; design high-precision machine learning tools, including neural networks and neural operators; and pioneer Kolmogorov–Arnold Network (KAN) for broad application to AI. I establish the open problem of nonuniqueness of Leray-Hopf solutions to 3D incompressible NSE.

Citations: 2707 as of Sep 29, 2025

Actively looking for discussions and possible collaborations on interesting topics.

Find out more

Selected Publications

1. 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]

2. 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]

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

4. Z. Liu, Y. Wang, S. Vaidya, F. Ruehle, J. Halverson, M. Soljacic, T.Y. Hou and M. Tegmark. KAN: Kolmogorov-Arnold Networks,
   ICLR 2025 Oral. [paper, slides, poster, Scientific American, IEEE Spectrum, Quanta, MIT Technology Review]

5. 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,
   accepted by Annals of PDE. [arxiv, slides]

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

7. Y. Wang, J.W. Siegel, Z. Liu and T.Y. Hou. On the Expressiveness and Spectral Bias of KANs,
   ICLR 2025. [paper, slides, poster]

8. J. Liu, Y. Wang, and T. Zhou. (2025) Finite Time Blowup for Keller-Segel Equation with Logistic Damping in Three Dimensions,
   [arxiv]

9. Y. Wang, Z. Liu, Z. Li, A. Anandkumar, and T.Y. Hou. (2025) High Precision PINNs in Unbounded Domains: Application to Singularity Formulation in PDEs,
   [arxiv]

10. T.Y. Hou, Y. Wang, and C. Yang. (2025) Nonuniqueness of Leray–Hopf solutions to the unforced incompressible 3D Navier–Stokes Equation,
    [arxiv]

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