Differential Equations Python Packages

torchsde

Differentiable SDE solvers with GPU support and efficient sensitivity analysis.

diffrax

Numerical differential equation solvers in JAX. Autodifferentiable and GPU-capable. https://docs.kidger.site/diffrax/

torchcde

Differentiable controlled differential equation solvers for PyTorch with GPU support and memory-efficient adjoint backpropagation.

brian2

Brian is a free, open source simulator for spiking neural networks.

heyoka

Python library for ODE integration via Taylor's method and LLVM

diffraxtra

Extras for Diffrax: OOP and vectorization

jaxfne

Tensor-Field Neural Equations (TFNE) in JAX

axiomize

Reproducible scientific modeling engine and agent skill pack: versioned Model IR with mandatory units, dimensional and numerical validation, calibration, uncertainty analysis, and portable export (SBML, CellML, Modelica) via CLI, REST and MCP. Install: pip install axiomize.

scientific-computing-system

Pure-Python computational science with zero runtime dependencies: linear algebra, ODE/PDE solvers, quadrature, Monte Carlo, statistics, signal processing, quantum simulation, uncertainty quantification, sensitivity analysis, dimensional analysis, and reproducible workflows.

pydecay

Radioactive decay mathematics for Python: analytical decay, Bateman chains, multi-nuclide inventories, ICRP-107 data, spectra, and Bq/Ci unit conversions

brian2cuda

A brian2 extension to simulate spiking neural networks on GPUs

semiflow-pde

Fast no_std Rust library for evolution equations and PDEs via Chernoff approximation of operator semigroups — heat, Schrödinger, diffusion, graph & manifold operators. Bindings for C, Python, and WebAssembly.

tedeous

Combines power of torch, numerical methods to conquer and solve ALL {O,P}DEs

simframe

Python framework for setting up and running scientific simulations. It comes with a variety of integration schemes and some infrastructure of reading and writing data files.

cognitive-discovery-platform

Pure-Python computational science with zero runtime dependencies: linear algebra, ODE/PDE solvers, quadrature, Monte Carlo, statistics, signal processing, quantum simulation, uncertainty quantification, sensitivity analysis, dimensional analysis, and reproducible workflows.

cognitive-discovery-system

Pure-Python computational science with zero runtime dependencies: linear algebra, ODE/PDE solvers, quadrature, Monte Carlo, statistics, signal processing, quantum simulation, uncertainty quantification, sensitivity analysis, dimensional analysis, and reproducible workflows.

diffeqpy

Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization

neurodiffeq

A library for solving differential equations using neural networks based on PyTorch, used by multiple research groups around the world, including at Harvard IACS.

pydiffgame

PyDiffGame is a Python implementation of a Nash Equilibrium solution to Differential Games, based on a reduction of Game Hamilton-Bellman-Jacobi (GHJB) equations to Game Algebraic and Differential Riccati equations, associated with Multi-Objective Dynamical Control Systems

jax-numerical-operators

Differentiable numerical solvers and scientific machine learning on one JAX substrate; you write the math, it stays differentiable end to end.

arflab

Python library for creating a mathematical environment

torchlaplace

Neural Laplace: Differentiable Laplace Reconstructions for modelling any time observation with O(1) complexity.

scipy-dae

Python implementation of solvers for differential algebraic equation's (DAE's) that should be added to scipy one day.

tensordiffeq

Efficient and Scalable Physics-Informed Deep Learning and Scientific Machine Learning on top of Tensorflow for multi-worker distributed computing