MathEpiDeepLearning

See Website of MathEpiDeepLearning

Note that at this time packages are all listed in Readme. Now I am gradually classifying them and move them to docs (with the name Resources) in Website of MathEpiDeepLearning. See details in Resources/Tools for AI4Science.

Guides on contributions:

Open issues to add source links
Fork and pull requests

Also see its twin repo MathEpiDeepLearningTutorial: Tutorials on math epidemiology and epidemiology informed deep learning methods.

Contents:

Introduction
0. Epidemic Model
1. Data Preprocessing
2. Basic Statistics and Data Visualization
3. Differential Programing and Data Mining
4. Theoretical Analysis
5. Writings, Blog and Web

Introduction

Julia and Python resources on mathematical epidemiology and epidemiology informed deep learning methods. Most about package information. Main Topics include

Data Preprocessing
Basic Statistics and Data Visualization
Differential Programing and Data Mining such as bayesian inference, deep learning, scientific machine learning computation
Theoretical Analysis such as calculus, bifurcation analysis
Writings, Blog and Web

[TOC]

Julia:

epirecipes/sir-julia: Various implementations of the classical SIR model in Julia

jangevaare/Pathogen.jl: Simulation, visualization, and inference tools for modelling the spread of infectious diseases with Julia

Mobilityjtmatamalas/MMCAcovid19.jl: Microscopic Markov Chain Approach to model the spreading of COVID-19

jpfairbanks/SemanticModels.jl: A julia package for representing and manipulating model semantics

cambridge-mlg/Covid19

affans/covid19abm.jl: Agent Based Model for COVID 19 transmission dynamics

Python:

ryansmcgee/seirsplus: Models of SEIRS epidemic dynamics with extensions, including network-structured populations, testing, contact tracing, and social distancing.

pyro.contrib.epidemiology.models — Pyro documentation

Modelling Human Mobility scikit-mobility/scikit-mobility: scikit-mobility: mobility analysis in Python

Matlab:

JDureau/AllScripts

1. Data Preprocessing

1.1. Data Science

Julia:

JuliaData/CSV.jl: Utility library for working with CSV and other delimited files in the Julia programming language

JuliaData/DataFrames.jl: In-memory tabular data in Julia

JuliaStats/TimeSeries.jl: Time series toolkit for Julia

Queryverse

JuliaDatabases

Python:

Numpy

Pandas

Smoothing

PumasAI/DataInterpolations.jl: A library of data interpolation and smoothing functions

viraltux/Smoothers.jl: Collection of basic smoothers and smoothing related applications

Expotential Smoothing:

LAMPSPUC/StateSpaceModels.jl: StateSpaceModels.jl is a Julia package for time-series analysis using state-space models.

miguelraz/StagedFilters.jl

JuliaDSP/DSP.jl: Filter design, periodograms, window functions, and other digital signal processing functionality

konkam/FeynmanKacParticleFilters.jl: Particle filtering using the Feynman-Kac formalism

mschauer/Kalman.jl: Flexible filtering and smoothing in Julia

JuliaStats/Loess.jl: Local regression, so smooooth!

CliMA/EnsembleKalmanProcesses.jl: Implements Optimization and approximate uncertainty quantification algorithms, Ensemble Kalman Inversion, and Ensemble Kalman Processes.

Outlier Detection

Surveyrob-med/awesome-TS-anomaly-detection: List of tools & datasets for anomaly detection on time-series data.

Julia:

OutlierDetectionJL

baggepinnen/MatrixProfile.jl: Time-series analysis using the Matrix profile in Julia

jbytecode/LinRegOutliers: Direct and robust methods for outlier detection in linear regression

Python:

yzhao062/pyod: A Python Toolbox for Scalable Outlier Detection (Anomaly Detection)

cerlymarco/tsmoothie: A python library for time-series smoothing and outlier detection in a vectorized way.

DHI/tsod: Anomaly Detection for time series data

2. Basic Statistics and Data Visualization

2.1. Statistics

Julia Statistics

gragusa (Giuseppe Ragusa)

cscherrer/MeasureTheory.jl: "Distributions" that might not add to one.

2.2. (Deep Learning based) Time Series Analysis

Julia: (few)

JuliaStats/TimeSeries.jl: Time series toolkit for Julia

JuliaDynamics/ARFIMA.jl: Simulate stochastic timeseries that follow ARFIMA, ARMA, ARIMA, AR, etc. processes

Python:

SurveyMaxBenChrist/awesome_time_series_in_python: This curated list contains python packages for time series analysis

Introduction — statsmodels

unit8co/darts: A python library for easy manipulation and forecasting of time series.

jdb78/pytorch-forecasting: Time series forecasting with PyTorch

AIStream-Peelout/flow-forecast: Deep learning PyTorch library for time series forecasting, classification, and anomaly detection (originally for flood forecasting).

timeseriesAI/tsai: Time series Timeseries Deep Learning Machine Learning Pytorch fastai | State-of-the-art Deep Learning library for Time Series and Sequences in Pytorch / fastai

tslearn-team/tslearn: A machine learning toolkit dedicated to time-series data

salesforce/Merlion: Merlion: A Machine Learning Framework for Time Series Intelligence

ourownstory/neural_prophet: NeuralProphet: A simple forecasting package

alan-turing-institute/sktime: A unified framework for machine learning with time series

sktime/sktime-dl: sktime companion package for deep learning based on TensorFlow

IBM/TSML.jl: A package for time series data processing, classification, clustering, and prediction.

alkaline-ml/pmdarima: A statistical library designed to fill the void in Python's time series analysis capabilities, including the equivalent of R's auto.arima function.

zhouhaoyi/Informer2020: The GitHub repository for the paper "Informer" accepted by AAAI 2021.

blue-yonder/tsfresh: Automatic extraction of relevant features from time series:

microsoft/forecasting: Time Series Forecasting Best Practices & Examples

TDAmeritrade/stumpy: STUMPY is a powerful and scalable Python library for modern time series analysis

databrickslabs/tempo: API for manipulating time series on top of Apache Spark: lagged time values, rolling statistics (mean, avg, sum, count, etc), AS OF joins, downsampling, and interpolation

2.3. Survival Analysis

Julia:

Python:

Deep Learning for Survival Analysis

sebp/scikit-survival: Survival analysis built on top of scikit-learn

havakv/pycox: Survival analysis with PyTorch

CamDavidsonPilon/lifelines: Survival analysis in Python

chl8856/DeepHit: DeepHit: A Deep Learning Approach to Survival Analysis with Competing Risks

jaredleekatzman/DeepSurv: DeepSurv is a deep learning approach to survival analysis.

square/pysurvival: Open source package for Survival Analysis modeling

2.4. Data Visualization

Julia:

GiovineItalia/Gadfly.jl: Crafty statistical graphics for Julia.

queryverse/VegaLite.jl: Julia bindings to Vega-Lite

JuliaPlots/UnicodePlots.jl: Unicode-based scientific plotting for working in the terminal

Colors and Color schemes

JuliaGraphics/Colors.jl: Color manipulation utilities for Julia

JuliaGraphics/ColorSchemes.jl: colorschemes, colormaps, gradients, and palettes

Interactive

GenieFramework/Stipple.jl: The reactive UI library for interactive data applications with pure Julia.

theogf/Turkie.jl: Turing + Makie = Turkie

Python:

Matplotlib

rougier/scientific-visualization-book: An open access book on scientific visualization using python and matplotlib

R:

Color themes:

Venn Diagrams

R:

yanlinlin82/ggvenn: Venn Diagram by ggplot2, with really easy-to-use API.

gaospecial/ggVennDiagram: A 'ggplot2' implement of Venn Diagram.

Python:

konstantint/matplotlib-venn: Area-weighted venn-diagrams for Python/matplotlib

Julia:

JuliaPlots/VennEuler.jl: Venn/Euler Diagrams for Julia

2.5. GLM

bambinos/bambi: BAyesian Model-Building Interface (Bambi) in Python.

3. Differential Programing and Data Mining

3.1. Differentiation, Quadrature and Tensor computation

3.1.1. Auto Differentiation

SciML/DiffEqSensitivity.jl: A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, and more for ODEs, SDEs, DDEs, DAEs, etc.

Julia:

FluxML/Zygote.jl: Intimate Affection Auditor

JuliaDiffEqFlux organization

JuliaDiff/ForwardDiff.jl: Forward Mode Automatic Differentiation for Julia

JuliaDiff/ReverseDiff.jl: Reverse Mode Automatic Differentiation for Julia

JuliaDiff/AbstractDifferentiation.jl: An abstract interface for automatic differentiation.

JuliaDiff/TaylorSeries.jl: A julia package for Taylor polynomial expansions in one and several independent variables.

kailaix/ADCME.jl: Automatic Differentiation Library for Computational and Mathematical Engineering

chakravala/Leibniz.jl: Tensor algebra utility library

briochemc/F1Method.jl: F-1 method

Python:

google/jax: Composable transformations of Python+NumPy programs: differentiate, vectorize, JIT to GPU/TPU, and more

pytorch/pytorch: Tensors and Dynamic neural networks in Python with strong GPU acceleration

tensorflow/tensorflow: An Open Source Machine Learning Framework for Everyone

AMICI-dev/AMICI: Advanced Multilanguage Interface to CVODES and IDAS

Auto Difference

Julia:

SciML/DiffEqOperators.jl: Linear operators for discretizations of differential equations and scientific machine learning (SciML)

QuantEcon/SimpleDifferentialOperators.jl: Library for simple upwind finite differences

Python:

maroba/findiff: Python package for numerical derivatives and partial differential equations in any number of dimensions.

3.1.2. Quadrature

Learn One equals learn many

SciML/Quadrature.jl: A common interface for quadrature and numerical integration for the SciML scientific machine learning organization

SciML/QuasiMonteCarlo.jl: Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)

SciML/SymbolicNumericIntegration.jl

Julia:

JuliaMath/QuadGK.jl: adaptive 1d numerical Gauss–Kronrod integration in Julia

JuliaMath/HCubature.jl: pure-Julia multidimensional h-adaptive integration

JuliaMath/Cubature.jl: One- and multi-dimensional adaptive integration routines for the Julia language

giordano/Cuba.jl: Library for multidimensional numerical integration with four independent algorithms: Vegas, Suave, Divonne, and Cuhre.

JuliaApproximation/FastGaussQuadrature.jl: Julia package for Gaussian quadrature

JuliaApproximation/ApproxFun.jl: Julia package for function approximation

machakann/DoubleExponentialFormulas.jl: One-dimensional numerical integration using the double exponential formula

JuliaApproximation/SingularIntegralEquations.jl: Julia package for solving singular integral equations

JuliaGNI/GeometricIntegrators.jl: Geometric Numerical Integration in Julia

Bayesian Methods

Julia:

ranjanan/MonteCarloIntegration.jl: A package for multi-dimensional integration using monte carlo methods

theogf/BayesianQuadrature.jl: Is there anything we can't make Bayesian?

s-baumann/BayesianIntegral.jl: Bayesian Integration of functions

theogf/BayesianQuadrature.jl: Is there anything we can't make Bayesian?

Expectations calculation

QuantEcon/Expectations.jl: Expectation operators for Distributions.jl objects

3.1.3. Matrix and Tensor computation

Matrix organization

JuliaLinearAlgebra

JuliaSparse

JuliaLang/SparseArrays.jl: SparseArrays.jl is a Julia stdlib

SciML/LabelledArrays.jl: Arrays which also have a label for each element for easy scientific machine learning (SciML)

SciML/RecursiveArrayTools.jl: Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications

Python:

numpy

numba

scikit-hep/awkward-1.0: Manipulate JSON-like data with NumPy-like idioms.

Special Matrix and Arrays

JuliaMatrices/SpecialMatrices.jl: Julia package for working with special matrix types.

SciML/LabelledArrays.jl: Arrays which also have a label for each element for easy scientific machine learning (SciML)

Computation

BLAS and LAPACKJuliaLinearAlgebra/MKL.jl: Intel MKL linear algebra backend for Julia

mcabbott/Tullio.jl: ⅀

JuliaLinearAlgebra/Octavian.jl: Multi-threaded BLAS-like library that provides pure Julia matrix multiplication

JuliaGPU/GemmKernels.jl: Flexible and performant GEMM kernels in Julia

MasonProtter/Gaius.jl: Divide and Conquer Linear Algebra

Eigenvalues and Solvers

Eignep-pack/NonlinearEigenproblems.jl: Nonlinear eigenvalue problems in Julia: Iterative methods and benchmarks

SolverSciML/LinearSolve.jl: LinearSolve.jl: High-Performance Unified Linear Solvers

Julia:

Eig: JuliaLinearAlgebra/Arpack.jl: Julia Wrappers for the arpack-ng Fortran library

JuliaLinearAlgebra/ArnoldiMethod.jl: Implicitly Restarted Arnoldi Method, natively in Julia

Jutho/KrylovKit.jl: Krylov methods for linear problems, eigenvalues, singular values and matrix functions

pablosanjose/QuadEig.jl: Julia implementation of the quadeig algorithm for the solution of quadratic matrix pencils

JuliaApproximation/SpectralMeasures.jl: Julia package for finding the spectral measure of structured self adjoint operators

Solver:

JuliaInv/KrylovMethods.jl: Simple and fast Julia implementation of Krylov subspace methods for linear systems.

JuliaSmoothOptimizers/Krylov.jl: A Julia Basket of Hand-Picked Krylov Methods

Eig TooJuliaLinearAlgebra/IterativeSolvers.jl: Iterative algorithms for solving linear systems, eigensystems, and singular value problems

tjdiamandis/RandomizedPreconditioners.jl

JuliaLinearAlgebra/RecursiveFactorization.jl

Spectral methods

JuliaApproximation/SpectralMeasures.jl: Julia package for finding the spectral measure of structured self adjoint operators

tpapp/SpectralKit.jl: Building blocks of spectral methods for Julia.

Spasrse Slover

SparseJuliaSparse/Pardiso.jl: Calling the PARDISO library from Julia

SparseJuliaSparse/MKLSparse.jl: Make available to Julia the sparse functionality in MKL

SparseJuliaLang/SuiteSparse.jl: Development of SuiteSparse.jl, which ships as part of the Julia standard library.

Python:

scipy.sparse.linalg.eigs — SciPy v1.7.1 Manual

Maps and Operators

Jutho/LinearMaps.jl: A Julia package for defining and working with linear maps, also known as linear transformations or linear operators acting on vectors. The only requirement for a LinearMap is that it can act on a vector (by multiplication) efficiently.

emmt/LazyAlgebra.jl: A Julia package to extend the notion of vectors and matrices

JuliaSmoothOptimizers/LinearOperators.jl: Linear Operators for Julia

kul-optec/AbstractOperators.jl: Abstract operators for large scale optimization in Julia

matthieugomez/InfinitesimalGenerators.jl: A set of tools to work with Markov Processes

ranocha/SummationByPartsOperators.jl: A Julia library of summation-by-parts (SBP) operators used in finite difference, Fourier pseudospectral, continuous Galerkin, and discontinuous Galerkin methods to get provably stable semidiscretizations, paying special attention to boundary conditions.

hakkelt/FunctionOperators.jl: Julia package that allows writing code close to mathematical notation memory-efficiently.

JuliaApproximation/ApproxFun.jl: Julia package for function approximation

Matrxi Equations

andreasvarga/MatrixEquations.jl: Solution of Lyapunov, Sylvester and Riccati matrix equations using Julia

Kronecker-based algebra

MichielStock/Kronecker.jl: A general-purpose toolbox for efficient Kronecker-based algebra.

3.1.4.Platforms, CPU, GPU and TPU

Julia GPU organization

Python:

tonybaloney/Pyjion: Pyjion - A JIT for Python based upon CoreCLR

numba/numba: NumPy aware dynamic Python compiler using LLVM

3.2. Optimization

An "learn one equals learn all" Julia Package

SciML/GalacticOptim.jl: Local, global, and beyond optimization for scientific machine learning (SciML)

Opt Organization:

Process Systems and Operations Research Laboratory

JuliaNLSolvers/Optim.jl: Optimization functions for Julia

JuliaOpt/NLopt.jl: Package to call the NLopt nonlinear-optimization library from the Julia language

robertfeldt/BlackBoxOptim.jl: Black-box optimization for Julia

jump-dev/MathOptInterface.jl: An abstraction layer for mathematical optimization solvers.

tpapp/MultistartOptimization.jl: Multistart optimization methods in Julia.

bbopt/NOMAD.jl: Julia interface to the NOMAD blackbox optimization software

JuliaFirstOrder

NicolasL-S/SpeedMapping.jl: General fixed point mapping acceleration and optimization in Julia

JuliaManifolds/Manopt.jl: Optimization on Manifolds in Julia

3.2.1. Metaheuristic

Julia:

jmejia8/Metaheuristics.jl: High performance metaheuristics for optimization purely coded in Julia.

ac-tuwien/MHLib.jl: MHLib.jl - A Toolbox for Metaheuristics and Hybrid Optimization Methods in Julia

Python:

guofei9987/scikit-opt: Genetic Algorithm, Particle Swarm Optimization, Simulated Annealing, Ant Colony Optimization Algorithm,Immune Algorithm, Artificial Fish Swarm Algorithm, Differential Evolution and TSP(Traveling salesman)

scikit-optimize/scikit-optimize: Sequential model-based optimization with a scipy.optimize interface

ac-tuwien/pymhlib: pymhlib - A Toolbox for Metaheuristics and Hybrid Optimization Methods

cvxpy/cvxpy: A Python-embedded modeling language for convex optimization problems.

coin-or/pulp: A python Linear Programming API

3.2.2. Evolution Stragegy

Julia:

wildart/Evolutionary.jl: Evolutionary & genetic algorithms for Julia

d9w/Cambrian.jl: An Evolutionary Computation framework

jbrea/CMAEvolutionStrategy.jl

AStupidBear/GCMAES.jl: Gradient-based Covariance Matrix Adaptation Evolutionary Strategy for Real Blackbox Optimization

itsdfish/DifferentialEvolutionMCMC.jl: A Julia package for Differential Evolution MCMC

3.2.3. Genetic Algorithms

Julia:

d9w/CartesianGeneticProgramming.jl: Cartesian Genetic Programming for Julia

WestleyArgentum/GeneticAlgorithms.jl: A lightweight framework for writing genetic algorithms in Julia

Python:

trevorstephens/gplearn: Genetic Programming in Python, with a scikit-learn inspired API

3.2.4. Nonconvex

Julia:

JuliaNonconvex/Nonconvex.jl: Toolbox for non-convex constrained optimization.

3.2.5. First Order Methods

Proximal OPTEC

kul-optec/CIAOAlgorithms.jl: Coordinate and Incremental Aggregated Optimization Algorithms

3.3. Optimal Control

eleurent/phd-bibliography: References on Optimal Control, Reinforcement Learning and Motion Planning

Julia: Jump + InfiniteOpt

Jump is powerfull!!!

jump-dev/JuMP.jl: Modeling language for Mathematical Optimization (linear, mixed-integer, conic, semidefinite, nonlinear)

InfiniteOpt is powerfull!!!

pulsipher/InfiniteOpt.jl: An intuitive modeling interface for infinite-dimensional optimization problems.

GAMS unified softwareGAMS Documentation Center

GAMS-dev/gams.jl: A MathOptInterface Optimizer to solve JuMP models using GAMS

Matlab: Yalmip unifiedYALMIP

Python: unifiedPyomo/pyomo: An object-oriented algebraic modeling language in Python for structured optimization problems.

Julia:

martinbiel/StochasticPrograms.jl: Julia package for formulating and analyzing stochastic recourse models.

odow/SDDP.jl: Stochastic Dual Dynamic Programming in Julia

PSORLab/EAGO.jl: A development environment for robust and global optimization

JuliaSmoothOptimizers/PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints

JuliaMPC/NLOptControl.jl: nonlinear control optimization tool

Python:

casadi is powerful!

python-control/python-control: The Python Control Systems Library is a Python module that implements basic operations for analysis and design of feedback control systems.

Shunichi09/PythonLinearNonlinearControl: PythonLinearNonLinearControl is a library implementing the linear and nonlinear control theories in python.

Matlab:

OpenOCL/OpenOCL: Open Optimal Control Library for Matlab. Trajectory Optimization and non-linear Model Predictive Control (MPC) toolbox.

jkoendev/optimal-control-literature-software: List of literature and software for optimal control and numerical optimization.

3.4. Bayesian Inference

StatisticalRethinkingJulia

Julia:

The Turing Language

cscherrer/Soss.jl: Probabilistic programming via source rewriting

probcomp/Gen.jl: A general-purpose probabilistic programming system with programmable inference

Laboratory of Applied Mathematical Programming and Statistics

StatisticalRethinkingJulia/StatisticalRethinking.jl: Julia package with selected functions in the R package rethinking. Used in the SR2... projects.

Python:

pymc-devs/pymc: Probabilistic Programming in Python: Bayesian Modeling and Probabilistic Machine Learning with Aesara

pints-team/pints: Probabilistic Inference on Noisy Time Series

pyro-ppl/pyro: Deep universal probabilistic programming with Python and PyTorch

tensorflow/probability: Probabilistic reasoning and statistical analysis in TensorFlow

thu-ml/zhusuan: A probabilistic programming library for Bayesian deep learning, generative models, based on Tensorflow

jmschrei/pomegranate: Fast, flexible and easy to use probabilistic modelling in Python.

3.4.1. MCMC

Methods like HMC, SGLD are Covered by above-mentioned packages.

Julia:

mauro3/KissMCMC.jl: Keep it simple, stupid, MCMC

BigBayes/SGMCMC.jl: Stochastic Gradient Markov Chain Monte Carlo and Optimisation

tpapp/DynamicHMC.jl: Implementation of robust dynamic Hamiltonian Monte Carlo methods (NUTS) in Julia.

emceemadsjulia/AffineInvariantMCMC.jl: Affine Invariant Markov Chain Monte Carlo (MCMC) Ensemble sampler

TuringLang/EllipticalSliceSampling.jl: Julia implementation of elliptical slice sampling.

Nested SamplingTuringLang/NestedSamplers.jl: Implementations of single and multi-ellipsoid nested sampling

bat/UltraNest.jl: Julia wrapper for UltraNest: advanced nested sampling for model comparison and parameter estimation

Python:

AdamCobb/hamiltorch: PyTorch-based library for Riemannian Manifold Hamiltonian Monte Carlo (RMHMC) and inference in Bayesian neural networks

jeremiecoullon/SGMCMCJax: Lightweight library of stochastic gradient MCMC algorithms written in JAX.

Nested Samplingjoshspeagle/dynesty: Dynamic Nested Sampling package for computing Bayesian posteriors and evidences

JohannesBuchner/UltraNest: Fit and compare complex models reliably and rapidly. Advanced nested sampling.

dfm/emcee: The Python ensemble sampling toolkit for affine-invariant MCMC

joshspeagle/dynesty: Dynamic Nested Sampling package for computing Bayesian posteriors and evidences

3.4.2. Approximate Bayesian Computation (ABC)

Also called likelihood free or simulation based methods

Julia: (few)

tanhevg/GpABC.jl

marcjwilliams1/ApproxBayes.jl: Approximate Bayesian Computation (ABC) algorithms for likelihood free inference in julia

francescoalemanno/KissABC.jl: Pure julia implementation of Multiple Affine Invariant Sampling for efficient Approximate Bayesian Computation

Python:

sbi-benchmark/sbibm: Simulation-based inference benchmark

elfi-dev/elfi: ELFI - Engine for Likelihood-Free Inference

eth-cscs/abcpy: ABCpy package

pints-team/pints: Probabilistic Inference on Noisy Time Series

mackelab/sbi: Simulation-based inference in PyTorch

ICB-DCM/pyABC: distributed, likelihood-free inference

3.4.3. Data Assimilation (SMC, particles filter)

Julia:

Alexander-Barth/DataAssim.jl: Implementation of various ensemble Kalman Filter data assimilation methods in Julia

baggepinnen/LowLevelParticleFilters.jl: Simple particle/kalman filtering, smoothing and parameter estimation

JuliaGNSS/KalmanFilters.jl: Various Kalman Filters: KF, UKF, AUKF and their Square root variant

CliMA/EnsembleKalmanProcesses.jl: Implements Optimization and approximate uncertainty quantification algorithms, Ensemble Kalman Inversion, and Ensemble Kalman Processes.

FRBNY-DSGE/StateSpaceRoutines.jl: Package implementing common state-space routines.

simsurace/FeedbackParticleFilters.jl: A Julia package that provides (feedback) particle filters for nonlinear stochastic filtering and data assimilation problems

mjb3/DiscretePOMP.jl: Bayesian inference for Discrete state-space Partially Observed Markov Processes in Julia. See the docs:

Python:

nchopin/particles: Sequential Monte Carlo in python

rlabbe/filterpy: Python Kalman filtering and optimal estimation library. Implements Kalman filter, particle filter, Extended Kalman filter, Unscented Kalman filter, g-h (alpha-beta), least squares, H Infinity, smoothers, and more. Has companion book 'Kalman and Bayesian Filters in Python'.

tingiskhan/pyfilter: Particle filtering and sequential parameter inference in Python

3.4.4. Variational Inference

Julia:

bat/MGVI.jl: Metric Gaussian Variational Inference

TuringLang/AdvancedVI.jl: A library for variational Bayesian methods in Julia

ngiann/ApproximateVI.jl: Approximate variational inference in Julia

Python:

3.4.5. Gaussion, non-Gaussion and Kernel

Julia:

Gaussian Processes for Machine Learning in Julia

Laboratory of Applied Mathematical Programming and Statistics

JuliaStats/KernelDensity.jl: Kernel density estimators for Julia

JuliaRobotics/KernelDensityEstimate.jl: Kernel Density Estimate with product approximation using multiscale Gibbs sampling

theogf/AugmentedGaussianProcesses.jl: Gaussian Process package based on data augmentation, sparsity and natural gradients

JuliaGaussianProcesses/TemporalGPs.jl: Fast inference for Gaussian processes in problems involving time

aterenin/SparseGaussianProcesses.jl: A Julia implementation of sparse Gaussian processes via path-wise doubly stochastic variational inference.

PieterjanRobbe/GaussianRandomFields.jl: A package for Gaussian random field generation in Julia

JuliaGaussianProcesses/Stheno.jl: Probabilistic Programming with Gaussian processes in Julia

STOR-i/GaussianProcesses.jl: A Julia package for Gaussian Processes

Python:

cornellius-gp/gpytorch: A highly efficient and modular implementation of Gaussian Processes in PyTorch

GPflow/GPflow: Gaussian processes in TensorFlow

SheffieldML/GPy: Gaussian processes framework in python

3.4.6. Bayesian Optimization

Julia:

SciML/Surrogates.jl: Surrogate modeling and optimization for scientific machine learning (SciML)

jbrea/BayesianOptimization.jl: Bayesian optimization for Julia

baggepinnen/Hyperopt.jl: Hyperparameter optimization in Julia.

Python:

fmfn/BayesianOptimization: A Python implementation of global optimization with gaussian processes.

pytorch/botorch: Bayesian optimization in PyTorch

optuna/optuna: A hyperparameter optimization framework

huawei-noah/HEBO: Bayesian optimisation library developped by Huawei Noah's Ark Library

3.4.7. Information theory

Julia: entropy and kldivengence for distributions or vectors can be seen in Distributions.jl

KL divergence for functionsRafaelArutjunjan/InformationGeometry.jl: Methods for computational information geometry

not maintainedkzahedi/Shannon.jl: Entropy, Mutual Information, KL-Divergence related to Shannon's information theory and functions to binarize data

gragusa/Divergences.jl: A Julia package for evaluation of divergences between distributions

Tchanders/InformationMeasures.jl: Entropy, mutual information and higher order measures from information theory, with various estimators and discretisation methods.

JuliaDynamics/TransferEntropy.jl: Transfer entropy (conditional mutual information) estimators for the Julia language

cynddl/Discreet.jl: A Julia package to estimate discrete entropy and mutual information

3.4.8. Uncertanty

Julia:

uncertainty-toolbox/uncertainty-toolbox: A python toolbox for predictive uncertainty quantification, calibration, metrics, and visualization

JuliaPhysics/Measurements.jl: Error propagation calculator and library for physical measurements. It supports real and complex numbers with uncertainty, arbitrary precision calculations, operations with arrays, and numerical integration.

3.4.9. Casual

zenna/Omega.jl: Causal, Higher-Order, Probabilistic Programming

mschauer/CausalInference.jl: Causal inference, graphical models and structure learning with the PC algorithm.

JuliaDynamics/CausalityTools.jl: Algorithms for causal inference and the detection of dynamical coupling from time series, and for approximation of the transfer operator and invariant measures.

python

Review: rguo12/awesome-causality-algorithms: An index of algorithms for learning causality with data

3.4.10. Sampling

MrUrq/LatinHypercubeSampling.jl: Julia package for the creation of optimised Latin Hypercube Sampling Plans

SciML/QuasiMonteCarlo.jl: Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)

3.5. Machine Learning and Deep Learning

Python:

Survey ritchieng/the-incredible-pytorch at pythonrepo.com

3.5.1. Machine Learning

Julia: MLJ is enough

alan-turing-institute/MLJ.jl: A Julia machine learning framework

Evovest/EvoTrees.jl: Boosted trees in Julia

Dimention Reduction:madeleineudell/LowRankModels.jl: LowRankModels.jl is a julia package for modeling and fitting generalized low rank models.

Linear RegressionJuliaAI/MLJLinearModels.jl: Generalized Linear Regressions Models (penalized regressions, robust regressions, ...)

gerdm/pknn.jl: Probabilistic k-nearest neighbours

IBM/AutoMLPipeline.jl: A package that makes it trivial to create and evaluate machine learning pipeline architectures.

Python:

scikit-learn: machine learning in Python — scikit-learn 1.0.1 documentation

automl/auto-sklearn: Automated Machine Learning with scikit-learn

h2oai/h2o-3: H2O is an Open Source, Distributed, Fast & Scalable Machine Learning Platform: Deep Learning, Gradient Boosting (GBM) & XGBoost, Random Forest, Generalized Linear Modeling (GLM with Elastic Net), K-Means, PCA, Generalized Additive Models (GAM), RuleFit, Support Vector Machine (SVM), Stacked Ensembles, Automatic Machine Learning (AutoML), etc.

pycaret/pycaret: An open-source, low-code machine learning library in Python

nubank/fklearn: fklearn: Functional Machine Learning

wecarsoniv/augmented-pca: Repository for the AugmentedPCA Python package.

Data Generation

snorkel-team/snorkel: A system for quickly generating training data with weak supervision

lk-geimfari/mimesis: Mimesis is a high-performance fake data generator for Python, which provides data for a variety of purposes in a variety of languages.

3.5.2. Deep Learning

Julia: Flux and Knet

FluxML/Flux.jl: Relax! Flux is the ML library that doesn't make you tensor

sdobber/FluxArchitectures.jl: Complex neural network examples for Flux.jl

denizyuret/Knet.jl: Koç University deep learning framework.

Python: Jax, Pytorch, Tensorflow

google/jax: Composable transformations of Python+NumPy programs: differentiate, vectorize, JIT to GPU/TPU, and more

pytorch/pytorch: Tensors and Dynamic neural networks in Python with strong GPU acceleration

tensorflow/tensorflow: An Open Source Machine Learning Framework for Everyone

catalyst-team/catalyst: Accelerated deep learning R&D

murufeng/awesome_lightweight_networks: MobileNetV1-V2，MobileNeXt，GhostNet，AdderNet，ShuffleNetV1-V2，Mobile+ViT etc. ⭐⭐⭐⭐⭐

3.5.3. Reinforce Learning

Julia:

JuliaReinforcementLearning

Python:

ray-project/ray: An open source framework that provides a simple, universal API for building distributed applications. Ray is packaged with RLlib, a scalable reinforcement learning library, and Tune, a scalable hyperparameter tuning library.

tensorlayer/tensorlayer: Deep Learning and Reinforcement Learning Library for Scientists and Engineers 🔥

pfnet/pfrl: PFRL: a PyTorch-based deep reinforcement learning library

3.5.4. GNN

Julia:

CarloLucibello/GraphNeuralNetworks.jl: Graph Neural Networks in Julia

FluxML/GeometricFlux.jl: Geometric Deep Learning for Flux

Python:

pyg-team/pytorch_geometric: Graph Neural Network Library for PyTorch

benedekrozemberczki/pytorch_geometric_temporal: PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models (CIKM 2021)

dmlc/dgl: Python package built to ease deep learning on graph, on top of existing DL frameworks.

THUDM/cogdl: CogDL: An Extensive Toolkit for Deep Learning on Graphs

3.5.5. Transformer

Julia:

chengchingwen/Transformers.jl: Julia Implementation of Transformer models

Python:

huggingface/transformers: 🤗 Transformers: State-of-the-art Natural Language Processing for Pytorch, TensorFlow, and JAX.

3.5.6. Transfer Learning

Surveyjindongwang/transferlearning: Transfer learning / domain adaptation / domain generalization / multi-task learning etc. papers, codes. datasets, applications, tutorials.-迁移学习

3.5.7. Neural Tangent

Python:

google/neural-tangents: Fast and Easy Infinite Neural Networks in Python

3.5.8. Visulization

Python:

ashishpatel26/Tools-to-Design-or-Visualize-Architecture-of-Neural-Network: Tools to Design or Visualize Architecture of Neural Network

julrog/nn_vis: A project for processing neural networks and rendering to gain insights on the architecture and parameters of a model through a decluttered representation.

PowerPointsdair-ai/ml-visuals: 🎨 ML Visuals contains figures and templates which you can reuse and customize to improve your scientific writing.

Semi-supervised Learning

Python:

TorchSSL/TorchSSL: A PyTorch-based library for semi-supervised learning (NeurIPS'21)

3.6. Probablistic Machine Learning and Deep Learning

Julia:

mcosovic/FactorGraph.jl: The FactorGraph package provides the set of different functions to perform inference over the factor graph with continuous or discrete random variables using the belief propagation algorithm.

stefan-m-lenz/BoltzmannMachines.jl: A Julia package for training and evaluating multimodal deep Boltzmann machines

biaslab/ReactiveMP.jl: Julia package for automatic Bayesian inference on a factor graph with reactive message passing

Python:

Probabilistic machine learning

thu-ml/zhusuan: A probabilistic programming library for Bayesian deep learning, generative models, based on Tensorflow

OATML/bdl-benchmarks: Bayesian Deep Learning Benchmarks

pgmpy/pgmpy: Python Library for learning (Structure and Parameter) and inference (Probabilistic and Causal) in Bayesian Networks.

scikit-learn-contrib/imbalanced-learn: A Python Package to Tackle the Curse of Imbalanced Datasets in Machine Learning

3.6.1. GAN

Julia:

Python:

torchgan/torchgan: Research Framework for easy and efficient training of GANs based on Pytorch

kwotsin/mimicry: [CVPR 2020 Workshop] A PyTorch GAN library that reproduces research results for popular GANs.

3.6.2. Normilization Flows

Julia:

TuringLang/Bijectors.jl: Implementation of normalising flows and constrained random variable transformations

slimgroup/InvertibleNetworks.jl: A Julia framework for invertible neural networks

FFJord is impleted in DiffEqFlux.jl

Python:

Surveyjanosh/awesome-normalizing-flows: A list of awesome resources on normalizing flows.

RameenAbdal/StyleFlow: StyleFlow: Attribute-conditioned Exploration of StyleGAN-generated Images using Conditional Continuous Normalizing Flows (ACM TOG 2021)

3.6.3. VAE

Julia:

Python:

Variational Autoencoders — Pyro Tutorials 1.7.0 documentation

AntixK/PyTorch-VAE: A Collection of Variational Autoencoders (VAE) in PyTorch.

timsainb/tensorflow2-generative-models: Implementations of a number of generative models in Tensorflow 2. GAN, VAE, Seq2Seq, VAEGAN, GAIA, Spectrogram Inversion. Everything is self contained in a jupyter notebook for easy export to colab.

altosaar/variational-autoencoder: Variational autoencoder implemented in tensorflow and pytorch (including inverse autoregressive flow)

subinium/Pytorch-AutoEncoders at pythonrepo.com

Ritvik19/pyradox-generative at pythonrepo.com

3.6.4 BNN

JavierAntoran/Bayesian-Neural-Networks: Pytorch implementations of Bayes By Backprop, MC Dropout, SGLD, the Local Reparametrization Trick, KF-Laplace, SG-HMC and more

RajDandekar/MSML21_BayesianNODE

bayesian-neural-networks · GitHub Topics

3.7. Differential Equations and Scientific Computation

Julia:

All you need is the following organization (My Idol Prof. Christopher Rackauckas):

SciML Open Source Scientific Machine Learning

Including agent based models JuliaDynamics

nathanaelbosch/ProbNumDiffEq.jl: Probabilistic ODE Solvers via Bayesian Filtering and Smoothing

PerezHz/TaylorIntegration.jl: ODE integration using Taylor's method, and more, in Julia

gideonsimpson/BasicMD.jl: A collection of basic routines for Molecular Dynamics simulations implemented in Julia

Probablistic Numerical Methods:

Julia:

nathanaelbosch/ProbNumDiffEq.jl: Probabilistic ODE Solvers via Bayesian Filtering and Smoothing

Python:

ProbNum — probnum 0.1 documentation

3.7.1. Partial differential equation

SurveyJuliaPDE/SurveyofPDEPackages: Survey of the packages of the Julia ecosystem for solving partial differential equations

SciML/DiffEqOperators.jl: Linear operators for discretizations of differential equations and scientific machine learning (SciML)

vavrines/Kinetic.jl: Universal modeling and simulation of fluid dynamics upon machine learning

kailaix/AdFem.jl: Innovative, efficient, and computational-graph-based finite element simulator for inverse modeling

SciML/ExponentialUtilities.jl: Utility functions for exponential integrators for the SciML scientific machine learning ecosystem

trixi-framework/Trixi.jl: Trixi.jl: Adaptive high-order numerical simulations of hyperbolic PDEs in Julia

JuliaIBPM

ranocha/SummationByPartsOperators.jl: A Julia library of summation-by-parts (SBP) operators used in finite difference, Fourier pseudospectral, continuous Galerkin, and discontinuous Galerkin methods to get provably stable semidiscretizations, paying special attention to boundary conditions.

Ferrite-FEM/Ferrite.jl: Finite element toolbox for Julia

Python：

DedalusProject/dedalus: A flexible framework for solving PDEs with modern spectral methods.

3.7.2 Fractional Differential and Calculus

Julia

SciFracX/FractionalDiffEq.jl: FractionalDiffEq.jl: A Julia package aiming at solving Fractional Differential Equations using high performance numerical methods

SciFracX/FractionalSystems.jl: Fractional order modeling and analysis in Julia.

SciFracX/FractionalCalculus.jl: FractionalCalculus.jl: A Julia package for high performance, fast convergence and high precision numerical fractional calculus computing.

SciFracX/FractionalTransforms.jl: FractionalTransforms.jl: A Julia package aiming at providing fractional order transforms with high performance.

3.8. Scientific Machine Learning (Differential Equation and ML)

Zymrael/awesome-neural-ode: A collection of resources regarding the interplay between differential equations, deep learning, dynamical systems, control and numerical methods.

massastrello/awesome-implicit-neural-models

3.8.1. Universal Differential Equations. (Neural differential equations)

Julia:

SciML/DiffEqFlux.jl: Universal neural differential equations with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

avik-pal/FastDEQ.jl: Deep Equilibrium Networks (but faster!!!)

UDE with Gaussion ProcessCrown421/GPDiffEq.jl

Python:

DiffEqML/torchdyn: A PyTorch based library for all things neural differential equations and implicit neural models.

rtqichen/torchdiffeq: Differentiable ODE solvers with full GPU support and O(1)-memory backpropagation.

patrick-kidger/diffrax at zzun.app

3.8.2. Physical Informed Neural Netwworks

Predictive Intelligence Lab

Julia:

SciML/NeuralPDE.jl: Physics-Informed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Python:

lululxvi/deepxde: Deep learning library for solving differential equations and more

sciann/sciann: Deep learning for Engineers - Physics Informed Deep Learning

3.8.3. Neural Operator

Julia:

foldfelis/NeuralOperators.jl: learning the solution operator for partial differential equations in pure Julia.

CliMA/OperatorFlux.jl: Operator layers for Flux.jl

brekmeuris/DrMZ.jl: Deep renormalized Mori-Zwanzig (DrMZ) Julia package.

3.9. Data Driven Methods (Equation Searching Methods)

Julia package including SINDy, Symbolic Regression, DMD

SciML/DataDrivenDiffEq.jl: Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

nmheim/NeuralArithmetic.jl: Collection of layers that can perform arithmetic operations

3.9.1. Symbolic Regression

cavalab/srbench: A living benchmark framework for symbolic regression

Python:

trevorstephens/gplearn: Genetic Programming in Python, with a scikit-learn inspired API

MilesCranmer/PySR: Simple, fast, and parallelized symbolic regression in Python/Julia via regularized evolution and simulated annealing

Julia:

MilesCranmer/SymbolicRegression.jl: Distributed High-Performance symbolic regression in Julia

sisl/ExprOptimization.jl: Algorithms for optimization of Julia expressions

3.9.2. SINDy (Sparse Identification of Nonlinear Dynamics from Data)

dynamicslab/pysindy: A package for the sparse identification of nonlinear dynamical systems from data

dynamicslab/modified-SINDy: Example code for paper: Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data

3.9.3. DMD (Dynamic Mode Decomposition)

mathLab/PyDMD: Python Dynamic Mode Decomposition

foldfelis/NeuralOperators.jl: learning the solution operator for partial differential equations in pure Julia.

3.10. Model Evaluation

3.10.1. Structure Idendification

Julia:

SciML/StructuralIdentifiability.jl

alexeyovchinnikov/SIAN-Julia: Implementation of SIAN in Julia

3.10.2. Global Sensitivity Anylysis

Julia:

lrennels/GlobalSensitivityAnalysis.jl: Julia implementations of global sensitivity analysis methods.

SciML/GlobalSensitivity.jl

SciML/DiffEqSensitivity.jl: A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, and more for ODEs, SDEs, DDEs, DAEs, etc.

Python:

SALib/SALib: Sensitivity Analysis Library in Python. Contains Sobol, Morris, FAST, and other methods.

R:

sensitivity

fast

sensobol

3.11. Optimal Transportation

Julia:

Optimal transport in Julia

JuliaOptimalTransport/OptimalTransport.jl: Optimal transport algorithms for Julia

JuliaOptimalTransport/ExactOptimalTransport.jl: Solving unregularized optimal transport problems with Julia

Python:

PythonOT/POT: POT : Python Optimal Transport

3.12. Agents, Graph and Networks

Computational Modeling Software Frameworks

Julia:

JuliaDynamics/Agents.jl: Agent-based modeling framework in Julia

Python:

projectmesa/mesa: Mesa is an agent-based modeling framework in Python

Network

briatte/awesome-network-analysis: A curated list of awesome network analysis resources.

Python:

networkx/networkx: Network Analysis in Python

GiulioRossetti/ndlib: Network Diffusion Library - (for NetworkX and iGraph)

Welcome to Epidemics on Networks’s documentation! — Epidemics on Networks 1.2rc1 documentation

寻找人类传播行为的基因 — 计算传播学

4. Theoretical Analysis

Julia:

JuliaApproximation

Python:

sympy/sympy: A computer algebra system written in pure Python

4.0. Special Functions

Julia:

JuliaMath/SpecialFunctions.jl: Special mathematical functions in Julia

InverseFunction JuliaMath/InverseFunctions.jl: Interface for function inversion in Julia

JuliaStats/StatsFuns.jl: Mathematical functions related to statistics.

JuliaStats/LogExpFunctions.jl: Julia package for various special functions based on log and exp.

Readme · LambertW.jl

scheinerman/Permutations.jl: Permutations class for Julia.

4.1. Symbolic Computation

Julia:

JuliaSymbolics/Symbolics.jl: A fast and modern CAS for a fast and modern language.

JuliaPy/SymPy.jl: Julia interface to SymPy via PyCall

jlapeyre/Symata.jl: language for symbolic mathematics

wbhart/AbstractAlgebra.jl: Generic abstract algebra functionality in pure Julia (no C dependencies)

rjrosati/SymbolicTensors.jl: Manipulate tensors symbolically in Julia! Currently needs a SymPy dependency, but work is ongoing to change the backend to SymbolicUtils.jl

Python:

sympy/sympy: A computer algebra system written in pure Python

4.3. Roots, Intepolations

4.3.1. Roots

Julia:

AllSciML/NonlinearSolve.jl: High-performance and differentiation-enabled nonlinear solvers

SciML/SciMLNLSolve.jl: Nonlinear solver bindings for the SciML Interface

JuliaMath/Roots.jl: Root finding functions for Julia

PolynomialRoots · Julia Packages

JuliaNLSolvers/NLsolve.jl: Julia solvers for systems of nonlinear equations and mixed complementarity problems

sglyon/MINPACK.jl: Wrapper for cminpack multivariate root finding routines

4.3.2. Interpolations and Approximations

Julia:

ApproxFun.jl

PumasAI/DataInterpolations.jl: A library of data interpolation and smoothing functions

JuliaMath/Interpolations.jl: Fast, continuous interpolation of discrete datasets in Julia

kbarbary/Dierckx.jl: Julia package for 1-d and 2-d splines

sisl/GridInterpolations.jl: Multidimensional grid interpolation in arbitrary dimensions

floswald/ApproXD.jl: B-splines and linear approximators in multiple dimensions for Julia

sostock/BSplines.jl: A Julia package for working with B-splines

stevengj/FastChebInterp.jl: fast multidimensional Chebyshev interpolation and regression in Julia

jipolanco/BSplineKit.jl: A collection of B-spline tools in Julia

NFFT/ANOVAapprox.jl: Approximation Package for High-Dimensional Functions in Julia

4.2. Bifurcation

rveltz/BifurcationKit.jl: A Julia package to perform Bifurcation Analysis

4.4 Polynomials

JuliaMath/Polynomials.jl: Polynomial manipulations in Julia

5. Writings, Blog and Web

JuliaDocs/Documenter.jl: A documentation generator for Julia.

chriskiehl/Gooey: Turn (almost) any Python command line program into a full GUI application with one line

Latex:

Detexify LaTeX handwritten symbol recognition

Display Julia Unicode in Latex

mossr/julia-mono-listings: LaTeX listings style for Julia and Unicode support for the JuliaMono font

wg030/jlcode: A latex package for displaying Julia code using the listings package. The package supports pdftex, luatex and xetex for compilation.

davibarreira/NotebookToLaTeX.jl: A Julia package for converting your Pluto and Jupyter Notebooks into beautiful Latex.

Web:

facebook/docusaurus: Easy to maintain open source documentation websites.

Hexo

Jekyll • Simple, blog-aware, static sites | Transform your plain text into static websites and blogs

tlienart/Franklin.jl: (yet another) static site generator. Simple, customisable, fast, maths with KaTeX, code evaluation, optional pre-rendering, in Julia.

一个傻瓜式构建可视化 web的 Python 神器 -- streamlit

streamlit/streamlit: Streamlit — The fastest way to build data apps in Python

gradio-app/gradio: Create UIs for your machine learning model in Python in 3 minutes

GitHub Profile Settings:

abhisheknaiidu/awesome-github-profile-readme: 😎 A curated list of awesome GitHub Profile READMEs 📝

Shields.io: Quality metadata badges for open source projects

ButterAndButterfly/GithubTools: 目标是创建会刷新的ReadMe首页！在这里，你可以得到Github star/fork总数图标, 项目star历史曲线，star数最多的前N个Repo信息...

常用anuraghazra/github-readme-stats: Dynamically generated stats for your github readmes

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