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Choosing a solver¤

Good solvers are problem-dependent. Nevertheless, some guidelines exist:

State-space model factorisation¤

  • If your problem is scalar-valued (shape=()), use a scalar implementation. Of course, you are always welcome to transform your problem into one with shape (1,) and use a vector-valued solver (not all features are implemented for scalar models).
  • If your problem is vector-valued, be aware that different implementation choices imply different modelling choices.

If you don't care about modelling choices:

  • If your problem is high-dimensional, use a blockdiag or isotropic implementation.
  • If your problem is medium-dimensional, use any implementations. isotropic factorisations tend to be the fastest with the worst UQ and worst stability, dense factorisations tend to be the slowest with the best UQ and best stability, blockdiag factorisations are somewhere in between.

Stiffness¤

If your problem is stiff, use a a dense implementation in combination with a correction scheme that employs first-order linearisation; for instance, ts1 or slr1. Zeroth-order approximation and too-aggressive state-space model factorisation will likely fail.

If your problem is stiff and high-dimensional: try first-order linearisation with a block-diagonal factorisation. If that does not work: let me know what you come up with...

Filters vs smoothers¤

Almost always, use a ivpsolvers.strategy_filter strategy for simulate_terminal_values, a ivpsolvers.strategy_smoother strategy for solve_adaptive_save_every_step, and a ivpsolvers.strategy_fixedpoint strategy for solve_adaptive_save_at. Use either a filter (if you must) or a smoother (recommended) for solve_fixed_step. Other combinations are possible, but rather rare (and require some understanding of the underlying statistical concepts).

Calibration¤

Use a solvers.solver_dynamic solver if you expect that the output scale of your IVP solution varies greatly. Otherwise, use an solvers.solver_mle solver. Try a solvers.solver for parameter-estimation.

Miscellaneous¤

If you use a ts0, choose an isotropic factorisation instead of a dense factorisation. They do the same, but the isotropic factorisation is cheaper.

These guidelines are a work in progress and may change soon. If you have any input, let me know!