The SciML organization is an opinionated collection of tools for scientific machine learning and differential equation modeling. The organization provides well-maintained tools which compose together as a coherent ecosystem. The following are the relevant resources for users interested in the functionality.
These resources cover:
Discrete equations (function maps, discrete stochastic (Gillespie/Markov) simulations)
Ordinary differential equations (ODEs)
Split and Partitioned ODEs (Symplectic integrators, IMEX Methods)
Stochastic ordinary differential equations (SODEs or SDEs)
Random differential equations (RODEs or RDEs)
Differential algebraic equations (DAEs)
Delay differential equations (DDEs)
Mixed discrete and continuous equations (Hybrid Equations, Jump Diffusions)
(Stochastic) partial differential equations ((S)PDEs) (with both finite difference and finite element methods)
Honorable mention to Turing.jl, a probabilistic programming language that composes with the SciML tools.