Add new option to DAE solvers to never initialize DAE

[MartinOtter]

Please, add a new option to the DAE solvers, so that initialization is never performed by the DAE solver.

Note, the IDA DAE solver uses the following code in Sundials/src/common_interface/solve.jl:

    f!(rtest, du0, u0, prob.p, t0)
    if any(abs.(rtest) .>= reltol)
        ...
        flag = IDACalcIC(mem, init_type, _t)
    end 

This means that solve first calls the user-suppled function f! = prob.f and then checks whether the absolute values of the returned residuals rtest are small enough. If this is not the case, the IDA initialization IDACalcIC is called. The problem is that this function may easily fail, even if the IDA integrator will integrate the model with the provided u0, du0. Explanation:

Initialization of DAEs is difficult. Good initializers use model information that is not available to a general DAE solver. For example assume that the DAE is initialized in steady state (so du=0) with a homotopy method (because good start values are not available for u0; this is, for example, standard for electric circuit simulators). Good non-linear solvers will not use the absolute values of the residuals as termination conditions, because this is not scale invariant (multiplying a residual equation with any number, will not change the exact mathematical solution). Therefore, it is easily possible that the solver test any(abs.(rtest) .>= reltol) fails, even if initialization is fine and the DAE integrator will integrate the model with the u0, du0 computed by an external initializer.

[ChrisRackauckas]

Indeed I agree this option is necessary.

[ChrisRackauckas]

We will also want it accessible in callbacks so after modifying values you can tell it whether or not to re-run initialization.

[MartinOtter]

I could not figure out what to do (with DifferentialEquations v6.15.0). I tried to call

DifferentialEquations.u_modified!(integrator,false) 

before running a simulation and then get the message

ERROR: LoadError: MethodError: no method matching u_modified!(::Sundials.IDA{:Dense,Nothing,Nothing}, ::Bool)
Closest candidates are:
  u_modified!(::OrdinaryDiffEq.ODEIntegrator, ::Bool) at D:\otter\home\.julia\packages\OrdinaryDiffEq\NsugH\src\integrators\integrator_interface.jl:48
  u_modified!(::StochasticDiffEq.SDEIntegrator, ::Bool) at D:\otter\home\.julia\packages\StochasticDiffEq\BhcRo\src\integrators\integrator_interface.jl:32
  u_modified!(::DelayDiffEq.DDEIntegrator, ::Bool) at D:\otter\home\.julia\packages\DelayDiffEq\BCL4Q\src\integrators\interface.jl:157
  ...

It seems that u_modified! is not supported for a DAE integrator?

Since you closed this issue, it seems to be solved. Can you give more explanations what to do to switch off automatic initialization for DAE problems

[ChrisRackauckas]

Oh, forgot to add it to the docs: https://github.com/SciML/DiffEqDocs.jl/blob/master/docs/src/solvers/dae_solve.md#full-list-of-methodsid-dae_solve_full .

It seems that u_modified! is not supported for a DAE integrator?

It is. https://github.com/SciML/Sundials.jl/blob/master/src/common_interface/integrator_utils.jl#L113-L115 What version of Sundials are you using?

[ChrisRackauckas]

Now that NoInit() is in the docs I'll close this.

(We still need to unify Sundials with the new initialization setup, but for now it's 🤷 )

[MartinOtter]

Still do not manage. I tried:

import DifferentialEquations
DifferentialEquations.solve(<..>, initializealg = DifferentialEquations.NoInit())   

and get then the error

ERROR: LoadError: UndefVarError: NoInit not defined

I also tried to call u_modified! directly before calling solve

import DifferentialEquations
integrator = DifferentialEquations.IDA()
DifferentialEquations.u_modified!(integrator,false)

and get then the error:

ERROR: LoadError: MethodError: no method matching u_modified!(::Sundials.IDA{:Dense,Nothing,Nothing}, ::Bool)
Closest candidates are:
  u_modified!(::OrdinaryDiffEq.ODEIntegrator, ::Bool) at OrdinaryDiffEq\NsugH\src\integrators\integrator_interface.jl:48
  u_modified!(::StochasticDiffEq.SDEIntegrator, ::Bool) at StochasticDiffEq\BhcRo\src\integrators\integrator_interface.jl:32
  u_modified!(::DelayDiffEq.DDEIntegrator, ::Bool) at DelayDiffEq\BCL4Q\src\integrators\interface.jl:157

I use the newest versions:

• Sundials v4.2.5
• DifferentialEquations v6.15.0

[ChrisRackauckas]

It wasn't exported, so I just added a patch that fixes that: SciML/OrdinaryDiffEq.jl@2b3770c Should be registered in about an hour or so.

[MartinOtter]

Now that NoInit() is in the docs I'll close this.

(We still need to unify Sundials with the new initialization setup, but for now it's 🤷 )

I use:

DifferentialEquations.solve(<..>, initializealg = DifferentialEquations.NoInit())   

for DifferentialEquations.IDA() solver. This works for a standard DAE. However, if an event is triggered with conditions!/affect! functions, an error is triggered when the affect! function is left:

ERROR: LoadError: Must supply differential_vars argument to DAEProblem constructor to use IDA initial value solver.

It seems NoInit() is not yet fully implemented for IDA? When supplying the differential_vars argument to DAEproblem, the event is correctly processed (but probably IDA is running its initialization code - which should be switched off).

[ChrisRackauckas]

Yes it's on OrdinaryDiffEq. This is an issue for Sundials.jl then. SciML/Sundials.jl#285