Extensibility of the language

DifferentialEquations

A package for solving differential equations, similar to odesolve in Matlab.

Example:

using DifferentialEquations
function lotka_volterra(du,u,p,t)
  x, y = u
  α, β, δ, γ = p
  du[1] = dx = α*x - β*x*y
  du[2] = dy = -δ*y + γ*x*y
end
u0 = [1.0,1.0]
tspan = (0.0,10.0)
p = [1.5,1.0,3.0,1.0]
prob = ODEProblem(lotka_volterra,u0,tspan,p)

sol = solve(prob)
using Plots
plot(sol)

Measurements

A package defining "numbers with precision" and complete algebra on these numbers:

using Measurements

a = 4.5 ± 0.1
b = 3.8 ± 0.4

2a + b
sin(a)/cos(a) - tan(a)

It also defines recipes for Plots.jl how to plot such numbers.

Starting ODE from an interval

using Measurements
u0 = [1.0±0.1,1.0±0.01]

prob = ODEProblem(lotka_volterra,u0,tspan,p)
sol = solve(prob)
plot(sol,denseplot=false)

• all algebraic operations are defined,
• passes all grid refinement techniques
• plot uses the correct plotting for intervals

Integration with other toolkits

Flux: toolkit for modelling Neural Networks. Neural network is a function.

• integration with Measurements,
• Integration with ODE (think of NN as part of the ODE)

Turing: Probabilistic modelling toolkit

• integration with FLux (NN)
• interation with ODE
• using arbitrary bijective transformations, Bijectors.jl