Yixuan Wang
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G5 PhD candidate, |
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.
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. (2022) Second Order Ensemble Langevin Method for Sampling and Inverse Problems,
to appear in Communications in Mathematical Sciences. [arxiv, 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]