Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.

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

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

OrbitalTrajectories.jl is a modern orbital trajectory design, optimisation, and analysis library for Julia, providing methods and tools for designing spacecraft orbits and transfers via high-performance simulations of astrodynamical models.

Global glacier model using Universal Differential Equations for climate-glacier interactions

Atomic graph models for molecules and crystals in Julia

A suite of tools for solving Nonlinear Schrodinger equations via higher-order algorithms and Darboux transformations.

A Julia package for classical orthogonal polynomials and expansions

A Julia repository for linear algebra with infinite matrices

A Julia package for working with spherical harmonic expansions

A package to calculate ensemble averaged waves in heterogeneous materials. The focus is on wave propagation, scattering, and reflection, from particulate and porous materials.

From Semiconductor to TransistorLevel Modeling in Julia

Supports approximating functions and solving differential equations on various higher dimensional domains such as disks and triangles

N-Point Correlation Functions in Julia

Quantum states for quantum optics.

Plot Wigner function and density matrix generated by QuantumStateBase.jl

A package for representing orthogonal polynomials as quasi arrays

A Julia repository for semiclassical orthogonal polynomials

Distributions for continuous variables

A Julia package for piecewise spectral methods such as p-FEM

A Julia package for computing singular integrals

Differential Inequality Algorithms for Parametric ODEs

Julia library for the computation of Poincaré integral invariants

Gross-Pitaevskii and Bogoliubov-de Gennes in 2D

Bounds and Relaxations of Parametric Differential Equations

Abstraction Layer for Dynamic Bounds

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Valid Discrete-Time Methods for Relaxing pODEs

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Calculate equilibrium measures from potentials