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pro vyhledávání: '"Hou, Thomas"'
Kolmogorov-Arnold Networks (KAN) \cite{liu2024kan} were very recently proposed as a potential alternative to the prevalent architectural backbone of many deep learning models, the multi-layer perceptron (MLP). KANs have seen success in various tasks
Externí odkaz:
http://arxiv.org/abs/2410.01803
Building upon the idea in \cite{HNWarXiv24}, we establish stability of the type-I blowup with log correction for the complex Ginzburg-Landau equation. In the amplitude-phase representation, a generalized dynamic rescaling formulation is introduced, w
Externí odkaz:
http://arxiv.org/abs/2407.15812
Autor:
Hou, Thomas Y.
We perform numerical investigation of nearly self-similar blowup of generalized axisymmetric Navier-Stokes equations and Boussinesq system with a time-dependent fractional dimension. The dynamic change of the space dimension is proportional to the ra
Externí odkaz:
http://arxiv.org/abs/2405.10916
Autor:
Liu, Ziming, Wang, Yixuan, Vaidya, Sachin, Ruehle, Fabian, Halverson, James, Soljačić, Marin, Hou, Thomas Y., Tegmark, Max
Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable a
Externí odkaz:
http://arxiv.org/abs/2404.19756
We propose an alternative proof of the classical result of type-I blowup with log correction for the semilinear equation. Compared with previous proofs, we use a novel idea of enforcing stable normalizations for perturbation around the approximate pr
Externí odkaz:
http://arxiv.org/abs/2404.09410
Autor:
Hou, Thomas Y., Wang, Yixuan
We study the singularity formation of a quasi-exact 1D model proposed by Hou-Li in \cite{hou2008dynamic}. This model is based on an approximation of the axisymmetric Navier-Stokes equations in the $r$ direction. The solution of the 1D model can be us
Externí odkaz:
http://arxiv.org/abs/2306.04146
Autor:
Chen, Jiajie, Hou, Thomas Y.
This is Part II of our paper in which we prove finite time blowup of the 2D Boussinesq and 3D axisymmetric Euler equations with smooth initial data of finite energy and boundary. In Part I of our paper [ChenHou2023a], we establish an analytic framewo
Externí odkaz:
http://arxiv.org/abs/2305.05660
Autor:
Hou, Thomas Y., Zhang, Shumao
In Part II of this sequence to our previous paper for the 3-dimensional Euler equations \cite{zhang2022potential}, we investigate potential singularity of the $n$-diemnsional axisymmetric Euler equations with $C^\alpha$ initial vorticity for a large
Externí odkaz:
http://arxiv.org/abs/2212.11924
Autor:
Hou, Thomas Y., Zhang, Shumao
We provide numerical evidence for a potential finite-time self-similar singularity of the 3D axisymmetric Euler equations with no swirl and with $C^\alpha$ initial vorticity for a large range of $\alpha$. We employ a highly effective adaptive mesh me
Externí odkaz:
http://arxiv.org/abs/2212.11912
We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. ExpMsFEM is built on
Externí odkaz:
http://arxiv.org/abs/2212.00823