Differential Equations.

This package defines common dynamical models and probabilistic solvers for differential equations.


logistic(timespan, initrv[, params])

Initial value problem (IVP) based on the logistic ODE.

fitzhughnagumo(timespan, initrv[, params])

Initial value problem (IVP) based on the FitzHugh-Nagumo model.

lotkavolterra(timespan, initrv[, params])

Initial value problem (IVP) based on the Lotka-Volterra model.

seir(timespan, initrv[, params])

Initial value problem (IVP) based on the SEIR model.

lorenz(timespan, initrv[, params])

Initial value problem (IVP) based on the Lorenz system.

probsolve_ivp(f, t0, tmax, y0[, df, method, …])

Solve initial value problem with Gaussian filtering and smoothing.


Propose a suitable first step that can be taken by an ODE solver.

initialize_odefilter_with_rk(f, y0, t0, …)

Initialize an ODE filter by fitting the prior process to a few steps of an approximate ODE solution computed with Scipy’s RK.

initialize_odefilter_with_taylormode(f, y0, …)

Initialize an ODE filter with Taylor-mode automatic differentiation.


ODE(timespan, rhs[, jac, hess, sol])

Ordinary differential equations.

IVP(timespan, initrv, rhs[, jac, hess, sol])

Initial value problems (IVP).

ODESolver(ivp, order)

Interface for ODESolver.

GaussianIVPFilter(ivp, prior, …[, initrv])

ODE solver that uses a Gaussian filter.


(Adaptive) step size rules for ODE solvers.


Constant step size rule for ODE solvers.

AdaptiveSteps(firststep, atol, rtol[, …])

Adaptive step size selection using proportional control.

ODESolution(locations, states[, derivatives])

ODE solution.


Gaussian IVP filtering solution of an ODE problem.

Class Inheritance Diagram

Inheritance diagram of probnum.diffeq.ODE, probnum.diffeq.ode.ivp.IVP, probnum.diffeq.ODESolver, probnum.diffeq.odefiltsmooth.ivpfiltsmooth.GaussianIVPFilter, probnum.diffeq.StepRule, probnum.diffeq.steprule.ConstantSteps, probnum.diffeq.steprule.AdaptiveSteps, probnum.diffeq.odesolution.ODESolution, probnum.diffeq.odefiltsmooth.kalman_odesolution.KalmanODESolution