py-pde
py-pde: A Python package for solving partial differential equations - Published in JOSS (2020)
Gridap
Gridap: An extensible Finite Element toolbox in Julia - Published in JOSS (2020)
FastVPINNs
FastVPINNs: An efficient tensor-based Python library for solving partial differential equations using hp-Variational Physics Informed Neural Networks - Published in JOSS (2024)
GridapDistributed
GridapDistributed: a massively parallel finite element toolbox in Julia - Published in JOSS (2022)
simpeg
Simulation and Parameter Estimation in Geophysics - A python package for simulation and gradient based parameter estimation in the context of geophysical applications.
pysdc
pySDC is a Python implementation of the spectral deferred correction (SDC) approach and its flavors, esp. the multilevel extension MLSDC and PFASST.
NeuralPDE
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
VoronoiFVM
Solution of nonlinear multiphysics partial differential equation systems using the Voronoi finite volume method
SciMLBenchmarks
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax), MATLAB, R
DiffEqBase
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
LFAToolkit
Local Fourier Analysis for arbitrary order finite element type operators
DiffEqFlux
Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods
SciMLTutorials
Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.
FEniCS
A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language
p4pdes
C and Python examples from my book on using PETSc and Firedrake to solve PDEs
Adapode
Adaptive P/ODE numerics with Grassmann element TensorField assembly
https://github.com/usnistgov/fipy
FiPy is a Finite Volume PDE solver written in Python
financial-models-numerical-methods
Collection of notebooks about quantitative finance, with interactive python code.
FiniteVolumeMethod
Solver for two-dimensional conservation equations using the finite volume method in Julia.
quantpde
A high-performance, open-source, header-only C++(>=11) library for pricing derivatives.
vcnef
Official PyTorch implementation of the Vectorized Conditional Neural Field.
seismic-inversion
Seismic inversion using a neural network regulariser implemented as an ExternalOperator in Firedrake
linpde-gp
Code for the Paper "Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers"
poisson-fast-mc
Fast Monte Carlo estimator for numerically solving a Poisson PDE.
https://github.com/amazon-science/boon
Datasets and code for results presented in the BOON paper
NeuralGraphPDE
Integrating Neural Ordinary Differential Equations, the Method of Lines, and Graph Neural Networks
dumux
DuMux: an open-source simulator for flow and transport processes in porous media (repository mirrored from https://git.iws.uni-stuttgart.de/dumux-repositories/dumux.git)
focallaserablationstudy
Data supporting the findings of a Focal Laser Ablation study.
pinns_mapi-3
Repositorio con el material para el taller sobre PINNs en MAPI-3 2024
AutoPDEx
AutoPDEx: An Automized Partial Differential Equation solver based on JAX - Published in JOSS (2025)