CODEWITHSUNDEEP
modelicadymola
Jack
Jack

Reputation: 1242

What is the non-linear solver used in Dymola initialization process?

I often meet the initialization problem shown below, it says that some kind of non-linear solver will attempt to handle this problem. As I know it, Dymola uses Newton Method to solve the equation after getting the BLT form of the original DAE system, so what is this nonlinear solver exactly?

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Upvotes: 4

Views: 454

Answers (1)

Atiyah Elsheikh
Atiyah Elsheikh

Reputation: 578

In general, a Modelica simulation environment needs to do something more than just relying on a known solver that is based on a derivative-based optimization algorithm. It could be based on already known solvers with adaptive capabilities to switch between solvers (line-search or trust-region approaches) and attempting different solvers parameters. Moreover, in advanced instances of the initialization problem, global optimization strategies are needed to avoid local optima of bad quality or divergence.

Reasoning: There are serious obstacles that may hinder identifying a semi-optimal and not necessarily the optimal solution of the initialization problem:

  • The need of good initial guesses in order to converge to a correct optimum with a residual cost function numerically near to zero

  • The Jacobian (or the Hessian) computed for the underlying optimization cost function would be usually singular. Here pseudo inversion is rather used (not necessarily provided by common solvers)

  • Due to the potentially large-scale nature of the underlying problem, values of different variables and initial conditions would lie within a large numerical range of values. This would cause numerical instability of known standard solvers. Here, scaling techniques are followed (which converts all optimization variables under consideration to the value 1 or smaller range of values by logarithmic scaling techniques). Such techniques are usually not provided by common solvers and need to be externally applied to the formulation of the cost function.

  • The provided initial conditions by the modeler might be incomplete and inconsistent and the simulation environment needs to implement rigorous heuristics for guessing a good start values for the solver.

References:

F. Casella and B. Bachmann, On the choice of initial guesses for the Newton-Raphson algorithm, App. Math. & Comp. 2021

Upvotes: 3

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