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probabilistic numerics toggle navigation about current research code meetings teaching textbooks uncertainty in computation mathematical models used to explain and predict the behaviour of complex systems such as immune cells or the climate rely heavily on numerical methods the exponential growth in available data and computing power has revolutionized the scale of such models in practice however computational resources are limited this introduces uncertainty arising from not running numerical methods to convergence and from observations corrupted by noise probabilistic numerics probabilistic numerics pn aims to quantify uncertainty arising from intractable or incomplete numerical computation and from stochastic input this new paradigm treats a numerical problem as one of statistical inference instead the probabilistic viewpoint provides a principled way to encode structural knowledge about a problem by giving an explicit role to uncertainty from all sources in particular from the computation itself pn gives rise to new applications beyond the scope of classical methods typical numerical tasks to which pn may be applied include optimization integration the solution of ordinary and partial differential equations and the basic tasks of linear algebra e g solution of linear systems and eigenvalue problems linear algebra quadrature optimization odes pdes value of a probabilistic approach as well as offering an enriched reinterpretation of classical methods the pn approach has several concrete practical points of value the probabilistic interpretation of computation allows to build customized methods for specific problems with bespoke priors formalizes the design of adaptive methods using tools from decision theory provides a way of setting parameters of numerical methods via the bayesian formalism expedites the solution of mutually related problems of similar type naturally incorporates sources of stochasticity in the computation can give structural uncertainty via a probability measure compared to an error estimate and finally it offers a principled approach of including numerical error in the propagation of uncertainty through chains of computations open an issue or pull request on github to get in touch or suggest changes to this site copyright 2026 powered by jekyll and the al folio theme hosted on github