Initial condition underdefined in NonlinearProblem

Specific Domains Modelling & Simulations
1

The following works:

using ModelingToolkit, NonlinearSolve

# Define a nonlinear system
@variables x y z
@parameters σ ρ β
eqs = [0 ~ σ * (y - x)
       0 ~ x * (ρ - z) - y
       0 ~ x * y - β * z]
@mtkbuild ns = NonlinearSystem(eqs)

guesses = [x => y, y => 1.0, z => 0.0]
ps = [σ => 10.0, ρ => 26.0, β => 8 / 3]

prob = NonlinearProblem(ns, guesses, ps)
sol = solve(prob, NewtonRaphson())

output:
retcode: Success
u: 2-element Vector{Float64}:
 -2.129924444096732e-29
 -2.398137151871876e-28

While this doesn’t work:

using ModelingToolkit, NonlinearSolve

# Define a nonlinear system
@variables x y z
@parameters σ ρ β
eqs = [0 ~ σ * (y - x)
       0 ~ x * (ρ - z) - y
       0 ~ x * y - β * z]
@mtkbuild ns = NonlinearSystem(eqs)

guesses = [y => 1.0, z => 0.0]
ps = [σ => 10.0, ρ => 26.0, β => 8 / 3]

prob = NonlinearProblem(ns, guesses, ps)
sol = solve(prob, NewtonRaphson())

output:
ERROR: Initial condition underdefined. Some are missing from the variable map.
Please provide a default (`u0`), initialization equation, or guess
for the following variables:

Set(Any[x])

Is there a good reason for this? I would think that if the initial guess for σ and y are known, the program should be able to automatically calculate the initial guess for x using the equation 0 ~ σ * (y - x)

2

What version are you using? @cryptic.ax recently added guess propagation but it must just not hit this case.

3

ModelingToolkit v9.50.0
NonlinearSolve v4.1.0

4

We don’t build initialization systems for NonlinearProblem yet. The unknowns of the simplfied system are x and z, so it complains if you give it y instead of x because it doesn’t know how to solve for the latter from the former.

5

Are you planning to add initialization systems for NonlinearProblem?

6

Yes, it’s in the works

7

Nice!

8

Ahh I see why it’s doing this here. Yeah… okay I’ll do my morning reviews :sweat_smile: . Should come soon.