probnum.diffeq.odefilter.init_routines¶

Initialization routines for ODE filters.

You may use the following (rough) guidelines to choose a suitable strategy for low(ish) dimensional ODEs.

num_derivatives = 1: Stack
num_derivatives = 2: StackWithJacobian if a Jacobian is available, or NonProbabilisticFit if not. If Jax is available, compute the Jacobian and use StackWithJacobian, (or choose ForwardModeJVP altogether).
num_derivatives = 3,4,5: NonProbabilisticFitWithJacobian if the Jacobian of the ODE vector field is available, or NonProbabilisticFit if not.
num_derivatives > 5: TaylorMode. For orders 6 and 7, ForwardModeJVP might work well too. TaylorMode shines for num_derivatives >> 5.

Initialization routines for high-dimensional ODEs are not implemented efficiently yet.

It may also be worth noting:

Only automatic-differentiation-based routines yield the exact initialization. This becomes more desirable, the larger the number of modelled derivatives is.
ForwardModeJVP is generally more efficient than ForwardMode. The jury is still out on the efficiency of ReverseMode.
Stack and StackWithJacobian are the only routines that come essentially for free. The other routines rely on either inference or automatic differentiation.
For stiff ODEs, prefer NonProbabilisticFitWithJacobian with BDF or Radau over NonProbabilisticFit (or use one of the automatic-differentiation-based routines).
Initialization routines can be chained together. For example, build a prior_process with an initrv that is generated by StackWithJacobian, and initialize the ODE filter with NonProbabilisticFitWithJacobian.

Classes¶

`InitializationRoutine`(*, is_exact, requires_jax)	Initialization routines for a filtering-based ODE solver.
`Stack`(*[, scale_cholesky])	Initialization by stacking y0, f(y0).
`StackWithJacobian`(*[, scale_cholesky])	Initialization by stacking y0, f(y0), and df(y0).
`NonProbabilisticFit`(*[, dt, ...])	Fit the prior process to a few steps of a non-probabilistic solver.
`NonProbabilisticFitWithJacobian`(*[, dt, ...])	Fit the prior process to a few steps of a non-probabilistic solver and use Jacobians.
`ForwardMode`()	Initialization via forward-mode automatic differentiation.
`ForwardModeJVP`()	Initialization via Jacobian-vector-product-based automatic differentiation.
`ReverseMode`()	Initialization via reverse-mode automatic differentiation.
`TaylorMode`()	Initialize a probabilistic ODE solver with Taylor-mode automatic differentiation.