Awesome GitHub RepositoriesDifferential Equation Solvers

SciPy is a scientific computing library for Python that provides a comprehensive collection of mathematical algorithms and numerical tools for research and engineering. It functions as a high-performance numerical analysis framework, bridging high-level Python code with compiled C and Fortran routines to execute complex computations at hardware speeds. The library is built upon array-based data structures that utilize strided memory layouts to enable efficient data manipulation and slicing. By employing vectorized operation dispatch and linking to optimized hardware-specific linear algebra li

PyMC is a Bayesian probabilistic programming framework used for building probabilistic models and performing Bayesian inference. It provides a probabilistic graphical model library for specifying random variables, priors, and likelihood functions, supported by an MCMC sampling engine and variational inference tools to estimate posterior distributions. The framework features a GPU-accelerated inference backend that compiles models into machine code to increase execution speed. It utilizes a backend-agnostic tensor execution model and just-in-time graph compilation to optimize the computation o

jetson-inference is a set of libraries and tools for executing optimized deep learning models on embedded GPU hardware. Its primary purpose is to enable real-time computer vision and AI inference at the edge with low latency and high throughput. The project distinguishes itself through high-performance streaming analytics and the ability to execute concurrent AI pipelines on auto-grade silicon. It provides specialized support for multi-sensor stream processing, utilizing zero-copy data transport to load camera frames directly into GPU memory. The codebase covers a broad surface of capabiliti

This project is a collection of reference implementations for algorithms, mathematics, cryptography, compression, and machine learning written in C#. It serves as an educational library providing standard implementations of sorting, searching, and graph theory algorithms. The repository covers a wide range of computational domains, including combinatorial optimization for constraint satisfaction and scheduling, as well as symmetric and classical cryptographic ciphers. It also provides reference code for lossless data compression techniques and fundamental machine learning primitives such as r

This project is a quantitative finance library providing implementations of numerical methods for financial engineering. It focuses on derivative pricing, portfolio optimization, stochastic simulation, and volatility calibration. The library includes tools for calculating option values using Monte Carlo simulations, binomial trees, and Fourier inversion. It provides a framework for fitting volatility smiles to market data and a simulation engine for generating asset price paths via geometric Brownian motion and jump-diffusion models. The codebase covers broader numerical analysis capabilitie

torchdiffeq 是一个 PyTorch ODE（常微分方程）求解器库，专为解决初值问题和构建神经 ODE 框架而设计。它提供了一个可微分的 ODE 积分器，允许深度学习模型通过随时间积分动力学函数来模拟连续深度。 该库具有用于内存高效反向传播的伴随法梯度计算器。通过在时间上反向求解增广伴随系统，它可以在不存储每个中间求解器状态的情况下计算参数梯度。 该项目涵盖了具有自适应和固定步长求解器的数值积分，并结合了误差控制和多项式状态插值。它还支持可微分事件管理，以便在特定标量函数触发时终止求解器，并沿事件时间传播梯度。 该框架常用于连续归一化流以及通过学习连续时间常微分方程进行概率分布转换等应用。

The TensorFlow Cookbook is a collection of code examples and recipes for building, training, and deploying machine learning models using TensorFlow. It covers the full model lifecycle, from constructing neural networks and training them with configurable parameters to packaging trained models for production deployment with unit tests and multi-device support. The project also integrates TensorBoard for logging and visualizing computational graphs, scalar summaries, and histograms during training. The cookbook demonstrates a wide range of machine learning techniques, including convolutional ne

这是一个构建在 TensorFlow 之上的量化金融库，用于金融工程、资产定价和风险管理。它作为金融衍生品定价引擎、模型校准工具和用于数值任务的硬件加速数学库。 该库提供了使用标准模型和美式期权逻辑对金融资产进行定价的专业功能，以及通过局部波动率将定价模型校准到市场数据的工具。它包括通过自举算法（bootstrapping）和单调凸插值构建收益率曲线的工具。 该框架涵盖了广泛的量化建模任务，包括随机过程模拟、从 Copula 采样以建模依赖结构，以及求解常微分方程和偏微分方程。它还提供用于求根和数学优化的数值分析工具。

PhysX 是一个物理引擎 SDK，旨在计算虚拟应用中的实时刚体动力学、流体模拟和环境交互。它包括一个 GPU 加速的物理求解器，用于计算复杂的粒子流体和燃烧模型；一个用于实时气体、火和烟雾的体素流体模拟器；以及一个用于模拟网格断裂的破坏模拟框架。 该 SDK 具有专门的机器学习物理张量接口，能够使用通用张量格式与机器学习框架交换模拟数据。它还实现了一个破坏系统，根据物理冲击和结构应力将物体破碎成层级碎片。 该项目涵盖了广泛的模拟功能，包括流体动力学计算、刚体断裂模拟和实时物理计算。它为破坏资产创作、结构应力计算以及模拟资产的平台无关二进制序列化提供了配套工具。 该系统通过异步执行跟踪管理硬件资源，并利用基于反射的参数映射系统来更新模拟变量。

这是一个基于 PyTorch 的生成模型框架，旨在通过学习向量场和概率路径将噪声转换为复杂的数据分布。它作为一个多模态生成工具包，通过学习到的概率流来生成合成文本和图像。 该库的独特之处在于支持连续、离散和黎曼流形（Riemannian manifold）集成。这使得该框架能够处理多种数据类型，包括通过离散状态流匹配处理分类数据，以及通过黎曼流形集成处理非欧几里得空间。 该工具包涵盖了完整的生成流水线，包括概率路径定义、向量场回归以及用于数据采样的微分方程求解器。这些功能使得训练和推理能够跨多种模态生成合成内容的生成模型成为可能。

CFDPython 是一个用于计算流体动力学（CFD）和数值分析的教育资源。它提供了一个结构化的课程，通过实现 Navier-Stokes 方程和偏微分方程的数值解来学习流体流动物理学。 该项目组织为一系列通过 Jupyter Notebook 交付的渐进式编码练习。用户构建线性对流、扩散和 Poisson 方程的一维和二维数学模型，以理解收敛性、稳定性和数值扩散等概念。 其实现利用 NumPy 进行向量化，利用 Matplotlib 进行可视化分析，包括生成热力图和等高线图。技术涵盖了有限差分离散化以及通过 Courant-Friedrichs-Lewy 条件进行的稳定性监控。

DeepXDE is a scientific machine learning library and deep learning PDE solver used to compute solutions for forward and inverse ordinary, partial, and integro-differential equations. It functions as a physics-informed neural network library that embeds physical laws and boundary conditions directly into the neural network loss function. The project provides a deep operator network framework for learning operator mappings that approximate relationships between functions in multiphysics problems. It is implemented as a multi-backend tensor library, allowing the system to switch between differen

Neuraloperator is a library for learning mappings between infinite-dimensional function spaces, serving as a tool to accelerate physics simulations and partial differential equation solving. It implements resolution-invariant models and spectral neural networks that can produce consistent predictions regardless of the input grid resolution or spatial discretization. The framework incorporates physics-informed neural networks that enforce physical constraints and differential equations through specialized loss functions. It utilizes Fourier transforms and spectral projections to process multid

This project is a numerical computing library designed for scientific and engineering mathematical operations. It functions as a comprehensive linear algebra framework, a statistical analysis library, and a toolkit for mathematical optimization and numerical integration. The library is distinguished by its provider-based native acceleration, which allows managed code to be swapped for platform-native binary libraries to increase the performance of computationally intensive routines. It also supports a hybrid approach to matrix storage, implementing separate strategies for dense and sparse mat

MNE-Python is an open-source Python library for processing, visualizing, and analyzing human neurophysiological data, including MEG, EEG, sEEG, ECoG, and NIRS recordings. It provides a comprehensive framework for loading data from over 30 proprietary file formats into a common hierarchical FIF data structure, and represents all time-series data as NumPy arrays for seamless integration with the scientific Python ecosystem. The library is built around object-oriented data containers that encapsulate raw, epoched, evoked, and source data with built-in preprocessing and visualization methods. The

DifferentialEquations.jl is a comprehensive numerical library designed for solving ordinary, stochastic, delay, and algebraic differential equations. It functions as a high-performance solver suite that integrates scientific machine learning, probabilistic programming, and automated differentiation into a unified framework. By leveraging multiple dispatch and symbolic-numeric integration, the library provides a flexible environment for complex mathematical modeling and simulation. The project distinguishes itself through its ability to bridge traditional numerical analysis with modern machine

This project is a parallel simulation engine and molecular dynamics simulator designed to model the physical movements of atoms and molecules. It functions as an interatomic potential framework for calculating forces between particles and a materials analysis tool for computing thermodynamic, structural, and transport properties of solids and fluids. The engine is distinguished by its high-performance computing capabilities, utilizing spatial-domain decomposition and message-passing interface communication to distribute workloads across processors. It supports multi-backend GPU acceleration v

Chrono is a multi-physics simulation suite that functions as a multibody dynamics simulator, a finite element analysis tool, and a robotics simulation framework. It provides specialized solvers for fluid-solid interaction and distributed physics engines capable of synchronizing multiple agents across a network. The project features a dedicated pipeline for converting CAD assemblies into simulation-ready formats and integrates directly with robot operating systems to validate autonomous control logic and sensors. It differentiates itself through the use of WebAssembly for portable browser-base

ModelingToolkit.jl is a symbolic modeling framework and computer algebra system designed for the definition and simulation of complex mathematical systems. It provides a foundational environment for constructing multi-domain physical models and differential equation systems, enabling users to represent scientific problems through symbolic graphs that facilitate automated analysis and transformation. The framework distinguishes itself through its acausal component composition, which allows for the assembly of large-scale models by connecting modular elements rather than defining explicit data

Symbolics.jl is a foundational framework for symbolic mathematics, automated differentiation, and scientific compilation within the Julia programming language. It provides a comprehensive system for algebraic manipulation, expression simplification, and the construction of mathematical models, enabling users to represent complex physical and chemical systems as symbolic equations. The library distinguishes itself through a source-to-source compilation engine that translates high-level symbolic representations directly into optimized, parallelized, and hardware-specific numerical code. By util