Numerical Bric-a-Brac

Collections of numerical techniques with Python and standard computational packages (Numpy, SciPy, Numba, Matplotlib ...).

Differential Equations

Differential Equations describe many physical systems

Notebooks

GitHub	Implementation of Baraff's "Large steps in cloth simulation."
	Analytic solution to damped spring
	Diffusion problem
	Laplace inpainting to restore an image

Optimizations

Those notebooks are the core algorithms for supervised and unsupervised learning in Machine learning.

Machine Learning Notebooks

Supervised Learning
	Linear regression from scratch
	Polynomial regression from scratch
	Logistic regression from scratch
	Multiclass Classification with Scikit-learn
	Support Vector Machine (SVM) with Scikit-learn
Unsupervised Learning
	K-means clustering from scratch

Other Notebooks

Multivariable Optimizations (Gradient Descent and Newton's methods)

Linear Algebra

Standard linear algebra algorithms

Notebooks

	Inverse kinematics using least square methods to solve the ill-posed problem
	Interpolation with Radial Basis Functions (RBFs)

Graph Theory

Part of discrete mathematics, graph theory is the study of graphs, a structures used to model pairwise relations between objects. Graph theory includes problems such as the travelling salesman problem and the spectral analysis of graph.

Notebooks

	List matrices describing a finite graph.
	Greedy algorithm for graph coloring.
	Find the shortest paths between nodes in a graph.
	Spectral Graph Thoery - PLACEHOLDER (WIP).

Neural Network

Artificial neural networks are composed of artificial neurons organized into layers. Neural networks are employed for regression analysis (function approximation) and classification problems.

Notebooks

ConvNets
	Facial keypoints detection
	Image classification on CIFAR-10 using CNN
	Image classification on CIFAR-10 using ResNet
Generative Models
	Autoencoder on Fashion MNIST
	Variational autoencoder on MNIST

Stencil Codes

Stencil codes are at the heart of many numerical solvers and physical simulation codes. They are of particular interest in scientific computing research for solving partial differential equations, image processing, cellular automata, etc. The Finite Difference Method (FDM) is closely related to stencil codes.

Notebooks

	Diffusion problem
	Laplace inpainting to restore an image
	Image processing with convolution kernels
	Cellular automata with Conway's game of life rules

Dimensionality Reduction

Dimensionality reduction is the process of converting data from a high-dimensional space to a low-dimensional space (subspace). A lower dimension representation aids in comprehending meaningful properties (such as latent variables), compressing the data, and removing noise from the original data.

Notebooks

	Optimal transformation of a point cloud with PCA
	Image compression with Singular Value Decomposition
	Autoencoder on Fashion MNIST
	Eigenfaces for face recognition on Olivetti faces dataset

Miscellaneous

Random notebooks about dynamic programming and monte carlo methods

Notebooks

	Example of ML pipeline with Snakemake
	Dynamic programming Examples
	Examples of Monte Carlo integrations
	Skeletal Subspace Deformation
GitHub	Monte Carlo Path Tracing
	Generate authors names from the Collection of Poems from Poetry Foundation