Run CheckInit after Initialization and Fix Core1 tests

[DhairyaLGandhi]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

This dispatch does need to be removed, but check CI for failures.

Add any other context about the problem here.

[DhairyaLGandhi]

I think we need to provide w2 => -1. in u0_correct if we want to still check with CheckInit which will cause the initialization to be over determined.

I have marked a copy of the prob such that we have a gt case which has this over determined initialization but does not affect the other test cases which will want to run initialization with a fully determined system specifcally.

Further, there is a bug in the Rodas methods it seems like. The case with the fully determined initialization when solved with NoInit should error since it does not have a value or guess for the algebraic variable. Instead, it produces:

julia> new_sol = solve(prob_correctu0, Rodas5P(); initializealg = NoInit(), sensealg, abstol = 1e-6, reltol = 1e-3)
retcode: Success
Interpolation: specialized 4rd order "free" stiffness-aware interpolation
t: 10-element Vector{Float64}:
   0.0
   1.0e-6
   1.1e-5
   0.00011099999999999999
   0.0011109999999999998
   0.011110999999999996
   0.11111099999999996
   1.1111109999999995
  11.111110999999994
 100.0
u: 10-element Vector{Vector{Float64}}:
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]
 [2.0, 0.0, 0.0, 1.0, 0.0]

[ChrisRackauckas]

I think we need to provide w2 => -1. in u0_correct if we want to still check with CheckInit which will cause the initialization to be over determined.

Not true, if there's a guess that should be used, unless there's still a bug there @AayushSabharwal

[ChrisRackauckas]

Further, there is a bug in the Rodas methods it seems like. The case with the fully determined initialization when solved with NoInit should error since it does not have a value or guess for the algebraic variable. Instead, it produces:

No, that's why I was saying you shouldn't use NoInit here.

[ChrisRackauckas]

I just checked. Guess propagation is working fine on my end:

using OrdinaryDiffEq, ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
@parameters σ ρ β A[1:3]
@variables x(t) y(t) z(t) w(t) w2(t)

eqs = [D(D(x)) ~ σ * (y - x),
    D(y) ~ x * (ρ - z) - y,
    D(z) ~ x * y - β * z,
    w ~ x + y + z + 2 * β,
    0 ~ x^2 + y^2 - w2^2
]

@mtkbuild sys = ODESystem(eqs, t)

u0_incorrect = [D(x) => 2.0,
    x => 1.0,
    y => 0.0,
    z => 0.0]

p = [σ => 28.0,
    ρ => 10.0,
    β => 8 / 3]

tspan = (0.0, 100.0)

u0_correct = [D(x) => 2.0,
    x => 1.0,
    y => 0.0,
    z => 0.0,]
prob_correctu0 = ODEProblem(sys, u0_correct, tspan, p, jac = true, guesses = [w2 => -1.0])
mtkparams_correctu0 = SciMLSensitivity.parameter_values(prob_correctu0)
test_sol = solve(prob_correctu0, Rodas5P(), initializealg = CheckInit(), abstol = 1e-6, reltol = 1e-3)

[ChrisRackauckas]

julia> test_sol = solve(prob_correctu0, Rodas5P(), initializealg = CheckInit(), abstol = 1e-6, reltol = 1e-3)
retcode: Success
Interpolation: specialized 4rd order "free" stiffness-aware interpolation
t: 10232-element Vector{Float64}:
   0.0
   1.0e-6
   4.6676023541089825e-6
   1.406277673596804e-5
   3.278144741397908e-5
   6.419148942107095e-5
   0.00011116456475568178
   0.00017786678081930103
   0.000271133385736624
   ⋮
  99.91687143040015
  99.92926704759054
  99.94166266478094
  99.95539352281644
  99.9646987791528
  99.97400403548916
  99.98330929182552
  99.99261454816188
 100.0
u: 10232-element Vector{Vector{Float64}}:
 [2.0, 0.0, 0.0, 1.0, -1.0]
 [1.9999720001120003, 1.0000004999950436e-5, 5.000003607056631e-12, 1.000001999986, -1.000002000036]
 [1.9998693095741922, 4.6676132468589305e-5, 1.0893293993865827e-10, 1.0000093348997008, -1.0000093359890214]
 [1.9996062644011885, 0.00014062875602951922, 9.888190132121024e-10, 1.0000281227849122, -1.0000281326728617]
 [1.9990822398364054, 0.00032781984549872586, 5.3732513186776715e-9, 1.0000655478514173, -1.0000656015808531]
 [1.9982030998441016, 0.0006419354837430721, 2.0603753564580495e-8, 1.0001283253010556, -1.000128531315339]
 [1.9968887764760062, 0.0011117073667597829, 6.179309726719579e-8, 1.0002221561749574, -1.0002227739846816]
 [1.9950232744291352, 0.0017788257101189419, 1.5820467061650703e-7, 1.0003552908594773, -1.0003568724082876]
 [1.9924165022118636, 0.0027117004285139934, 3.6764346859572156e-7, 1.0005412383294567, -1.0005449129975832]
 ⋮
 [22.451502965977113, 3.5763156602418764, 14.49076032504619, 19.095009873023972, -19.42720577938862]
 [16.825095478698696, 2.4355128410705102, 14.724562457922266, 19.338935013763827, -19.49181125475473]
 [10.72457093433667, 1.2739062770137506, 14.684097844197916, 19.510161047524054, -19.55174035252264]
 [3.4519383074370587, 0.0475040376449663, 14.326813158830632, 19.608073663940203, -19.608065632865248]
 [-1.7464560579732538, -0.7034545257092123, 13.914876060126806, 19.616162583416656, -19.628713340973025]
 [-7.124655444976655, -1.3610934986046739, 13.38588197040998, 19.57501386541934, -19.622205586841815]
 [-12.642627570620036, -1.9057588504443905, 12.762322984740244, 19.48313632696152, -19.576047368186142]
 [-18.255577651189146, -2.323296528666386, 12.06983231985069, 19.339434641524246, -19.47841981533405]
 [-22.746257645129607, -2.558672337734426, 11.489307512570512, 19.188037129458547, -19.357853875055586]

[DhairyaLGandhi]

Core 8 also has a new failure with

  LoadError: Cyclic guesses detected in the system. Symbolic values were found for the following variables/parameters in the map: 
  ampermeter₊n₊v(t)  => capacitor2₊v(t) + input_signal₊output₊u(t)
  In order to resolve this, please provide additional numeric guesses so that the chain can be resolved to assign numeric values to each variable.

Should we add a guess here?

[ChrisRackauckas]

🎉