Predictors

This documentation describes the available predictors. A predictor is used to determine the initial guess in each time step by extrapolating the solution from previous time steps. The predictors differ in the number of previous time steps they take into account and the polynomial degree that is used. Additionally, there is one special type that uses a surrogate model. The formulas in this document, use the index $n$ to refer to the time step, where $n+1$ is the current time step, i.e. the time step for which the initial guess is made. The vector $x$ is the input for the first solver, conform the coupled solvers' documentation.

A predictor is intialized in the coupled solver using an initial solution as determined by the coupled solver. As such, there is at least one previous solution available.

For the polynomial predictors, the predictor dictionary only requires a type (e.g. predictors.linear) in the JSON file, no settings dictionary has to be provided.

Specification of a predictor is mandatory, also for a steady simulation. In that case, however, it does not matter which predictor is chosen as only one "time step" is performed.

Constant

The type for this predictor is predictors.constant. This predictor uses the result from the previous solution as the initial guess in the current time step: $$ x^{n+1}=x^{n}. $$

Linear

The type for this predictor is predictors.linear. This predictor uses the results from the last two time steps to determine the initial guess in the current time step using a linear extrapolation as follows $$ x^{n+1}=2x^{n}-1x^{n-1}. $$ If no two previous solutions are available, the solution from the last time step is used, i.e. the predictor PredictorConstant.

Legacy

The type for this predictor is predictors.legacy. This predictor uses the results from the last three time steps to determine the initial guess in the current time step using a linear extrapolation as follows $$ x^{n+1}=\frac{5}{2}x^{n}-2x^{n-1}+\frac{1}{2}x^{n-2}. $$ If no three previous solutions are available, the predictor PredictorLinear is used. This predictor is called PredictorLegacy as it corresponds to the second order extrapolator in the coupling code Tango, the predecessor of CoCoNuT.

Quadratic

The type for this predictor is predictors.quadratic. This predictor uses the results from the last three time steps to determine the initial guess in the current time step using a quadratic extrapolation as follows $$ x^{n+1}=3x^{n}-3x^{n-1}+1x^{n-2}. $$ If no three previous solutions are available, the predictor PredictorLinear is used.

Cubic

The type for this predictor is predictors.cubic. This predictor uses the results from the last three time steps to determine the initial guess in the current time step using a cubic extrapolation as follows $$ x^{n+1}=4x^{n}-6x^{n-1}+4x^{n-2}-1x^{n-3}. $$ If no four previous solutions are available, the predictor PredictorQuadratic is used.

Surrogate

The type for this predictor is predictors.surrogate.

The following parameters may be included in the settings dictionary.

This predictor requires that a surrogate model is used in the coupled solver CoupledSolverIQNISM (defined in the settings of the coupled solver). Moreover, this surrogate model must provide a surrogate solution, which is used to update the values in this predictor.

There are two options available:

• The surrogate solution can be used directly: $$ x^{n+1}=x_s^{n+1}, $$ where $x_s^{n+1}$ is the surrogate solution of the current time step.
• Or the change in surrogate solution can be used: $$ x^{n+1}=x^{n} + (x_s^{n+1} - x_s^{n}), $$ where $x_s$ is the surrogate solution, and the superscript $n+1$ and $n$ indicate the current and previous time steps, respectively.

The following parameters need to be included in the settings dictionary.

parameter	type	description
predict_change	dict	(optional) Default: true. Indicates it the change in surrogate solution should be used. If false, the surrogate solution serves as prediction directly.

Restart

Upon restart, the predictor may be changed. When changing an extrapolator (Constant, Linear, Quadratic, Legacy and Cubic) to a higher order, the first extrapolation will still be of the original order, but the order will increase with each time step until the new order is reached, just like at the start of a simulation. Changing to a lower order has direct effect.

No information is transferred when switching from or to a surrogate predictor.

Dummy predictor

This dummy predictor can be used in the one-way coupled solvers, which doesn't require a predictor.

If the use of a dummy predictor is allowed, the type (convergence_criteria.dummy_convergence_criterion) can be written explicitly or omitted. No settings are required. Note that the key predictor is still required.