# ProbabilisticNumericalMethod¶

class probnum.ProbabilisticNumericalMethod(stopping_criterion)

Bases: `abc.ABC`, `Generic`[`probnum._pnmethod._probabilistic_numerical_method.ProblemType`, `probnum._pnmethod._probabilistic_numerical_method.BeliefType`]

Probabilistic numerical methods.

An abstract base class defining the implementation of a probabilistic numerical method 1 2. A PN method solves a numerical problem by treating it as a probabilistic inference task.

Parameters

stopping_criterion (`StoppingCriterion`) – Stopping criterion determining when a desired terminal condition is met.

References

1

Hennig, P., Osborne, Mike A. and Girolami M., Probabilistic numerics and uncertainty in computations. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015.

2

Cockayne, J., Oates, C., Sullivan Tim J. and Girolami M., Bayesian probabilistic numerical methods. SIAM Review, 61(4):756–789, 2019

`ProbabilisticLinearSolver`

Compose a custom probabilistic linear solver.

Notes

All PN methods should subclass this base class. Typically convenience functions (such as `problinsolve()`) will instantiate an object of a derived subclass.

Methods Summary

 `solve`(prior, problem, **kwargs) Solve the given numerical problem.

Methods Documentation

abstract solve(prior, problem, **kwargs)[source]

Solve the given numerical problem.

Parameters
• prior (`TypeVar`(`BeliefType`)) – Prior knowledge about quantities of interest of the numerical problem.

• problem (`TypeVar`(`ProblemType`)) – Numerical problem to be solved.

Return type

`Tuple`[`TypeVar`(`BeliefType`), `TypeVar`(`StateType`)]