Yixuan Wang
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Final year PhD, |
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
Numerical Analysis
Partial Differential Equation
Applied Probability
AI for Science
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 numeric and 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.
Citations: 2081 as of July 20, 2025
Actively looking for discussions and possible collaborations on interesting topics.
Publications
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]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]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]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]Z. Liu, A. Stuart and Y. Wang. Second Order Ensemble Langevin Method for Sampling and Inverse Problems,
Communications in Mathematical Sciences, 23(5), 2025, 1299-1317. [paper, slides]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]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]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]T.Y. Hou, V.T. Nguyen and Y. Wang. (2024) L^2-based Stability of Blowup with Log Correction for Semilinear Heat Equation,
[arxiv]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]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]Z. Liu, P. Ma, Y. Wang, W. Matusik and M. Tegmark. (2024) KAN 2.0: Kolmogorov-Arnold Networks Meet Science,
[arxiv]Y. Wang, J.W. Siegel, Z. Liu and T.Y. Hou. On the Expressiveness and Spectral Bias of KANs,
ICLR 2025. [paper, slides, poster]Z. Li, S. Lanthaler, C. Deng, Y. Wang, K. Azizzadenesheli and A. Anandkumar. Scale-consistent Learning with Neural Operators,
Neurips 2024, Workshop Foundation Models for Science: Progress, Opportunities, and Challenges. [paper]J. Liu, Y. Wang, and T. Zhou. (2025) Finite Time Blowup for Keller-Segel Equation with Logistic Damping in Three Dimensions,
[arxiv]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]