Neural Finite Element part I: how to implement MATLAB’s accumarray in PyTorch
The first part among many on how to implement an FEM natively in PyTorch, taking advantages of the auto-diff, natural data structure and functions supporting...
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Crouzeix’s divergence free basis for the Navier-Stokes equation
This is the solution (long read) to a Chapter 11 exercise of the book by Brenner and Scott (Brenner and Scott, 2008). Personally I really like this problem, ...
Amateur mathematician studies Quantum Field Theory part 2: Maxwell equations
In the first part, we reviewed a brief history of the mathematics of the Quantum Field Theory (not exhaustively, but enough to get the idea). In this part, w...
Amateur mathematician studies Quantum Field Theory part I
Translating the language of physicists to the language of mathematicians.
Implementing the hierarchical basis for linear finite elements
This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...
Funny moments of using the GitHub Copilot
My experience of using the GitHub copilot as a computational mathematician.
Shortcut to git commit and push in Visual Studio Code
Use VSCode task to streamline the workflow of building a site and push the changes to GitHub.
Loading a page-specific Javascript Go board in Jekyll
Install wgo.js in the Jekyll blog and load it on demand using a toggle in preamble.
How to use a custom Jekyll plugin on Github pages
GitHub pages allows Jekyll version only to be 3.9, let us find a way around it.
Galerkin Transformer: A One-Shot Experiment at NeurIPS 2021
A newbie’s journey of submitting his first ML paper to a top conference.
MacOS keyboard layout on Linux
Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.
How to undervolt Nvidia GPUs on Linux
Undervolting an NVIDIA RTX GPU, so that the training can run nonstop with controllable thermos.
Use an Nvidia GPU only for CUDA and Intel CPU for display
Configuring Ubuntu Linux to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.
Assembling a budget 3090 deep learning workstation
Assembling of a deep learning workstation with RTX 3090 + 10850k, and how to deal with the bent of the heavy 3090 card.
Build a budget 3090 deep learning workstation Part Zero: random tidbits
A random newbie’s story on building an RTX 3090 workstation.
Vectorization tricks for cell arrays in MATLAB
How to write elegantly fast code to handle cell array with different length vector at each row.
Notes on 130C: Stochastic Processes
This notes contains some of the notes I used in UC Irvine Math 130C course.
Finally switched to Jekyll with Mathjax!
I finally decided to migrate various of my old writing in my faculty website at UC Irvine (deactivated as of Oct 2020) a static website generator Jekyll. App...
Notes on the history of trace theorems on a Lipschitz domain
Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.
MATLAB finally updated its array compatibility to match Python
Matlab finally embraces (partially) the way matrix manipulation should be Starting in MATLAB R2016b with the addition of implicit expansion, some combinatio...
Kaggle比赛记：地震预测
本文前半部分是介绍Kaggle的机器学习比赛，后半则是记录今年3月到6月带领几位University of California, Irvine数学系本科生参加由美国洛斯阿拉莫斯国家实验室在Kaggle上组织的地震预测比赛。
Winter 2019 Math 10 Final Project Kaggle in-class Competition
In the course project, groups of three students will work together to create regression/classifiers for an in-class Kaggle prediction competition. The compet...
Getting ready for Math 10: intro to ML
I created an introductory machine learning class for math undergrad who has no previous exposure to programming back in Winter 2019 quarter. This post will t...
如何在LaTeX中使用TikZ绘图的简明教程
这个简明教程主要是教大家使用强大的LaTeX宏包TikZ来绘制工作生活中需要的一些示意图。
Some constructions related to Helmholtz decomposition
Using Poincare lemma to construct vector field explicitly for Helmholtz decomposition.
Some interesting links
Since Google+ is finally to be shut down by Google as of Feb 1, 2019, aside from migrating G+’s social bookmarking functionality to Medium.com and Pocket app...
Equivalence between Sobolev norm and Sobolev-Slobodeckij norm for integer-order spaces
This short post explores the equivalence between Sobolev norm and Sobolev-Slobodeckij norm for $W^{s,p}(\Omega)$ when $s$ is an integer.
关于《星际穿越》里面的一些物理相关的计算：1小时等于7年的时间差可能吗？etc
这是很久以前在果壳小组写的外行解读帖子，现在果壳小组没有了，把自己以前给果壳写的帖子留个备份。
Deriving the expression of the Lorentz force using the language of a mathematician
This is a continuation of my previous “complaining” post on the language difference of mathematician vs physicists regarding the same thing.
Random notes about physicists’ obsession with Einstein notations
I took a quantum physics class on Coursera this year and I found that the Mathematical language spoken by the two communities, math vs physics, are quite dif...
Several explicit constructions of the Helmholtz decomposition
Here we present two approaches to construct Helmholtz decompositions.
An identity for the continuous integral solution of the conservation law
This is an exercise in Evans, Partial Differential Equations (1st edition), page 164, problem 13.
Kernels of a bounded operator’s extension
This is a post recording my answer to a question on Math StackExchange1 with some references in L. Tartar’s book2. https://math.stackexchange...
Proof of the coercivity for Robin boundary problem
This is an exercise for finite element method most likely. Our question is:
How to impose boundary condition for 2-dimensional curl-curl weak problem
First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...
An example on the limiting case of Sobolev embedding
Sobolev embedding When $p=n$
Use a reverse method of characteristics to get the trajectories equation
This is an exercise in Evans, Partial Differential Equations (2nd edition), Chapter 10 Conservation laws.
Discontinuous Galerkin method for linear advection equation
PDE This was the first project after I switched to a PhD program in computational math. The goal of the project is to study the Discontinuous Galerkin (DG) f...