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Welcome to Π4U

Π4U is a high performance framework for optimization, sampling and Bayesian uncertainty quantification of large scale computational models.

The framework is based on the TORC task-parallel library for clusters, which is designed to provide unified programming and runtime support for computing platforms that range from single-core systems to hybrid multicore-GPU clusters and heterogenous Grid based supercomputers.



What Π4U can do for you

  1. Optimize: given a cost function F(\vartheta) find $$ \vartheta^\star = \mathop{\arg\min}\limits_{\vartheta} F(\vartheta) \,. $$

  2. Sample: given the density of a probability distribution p_{\vartheta} draw samples, $$ \vartheta^{(k)} \sim p_\vartheta, \quad k=1,\ldots,N_s \, . $$

  3. Uncertainty Quantification: given a set of data d, the output of the model f(x;\vartheta) a likelihood function p(d|\vartheta) and a prior probablity density p(\vartheta) sample the posterior distribution, $$ p(\vartheta | d) = \frac{p(d | \vartheta) p(\vartheta)}{p(d)}\, . $$ The model output f depends on a set of input parameters x.

After installing the software have a look at the examples and learn how you can run your cases.







Warning

The software and the documentation page are under continuous development. New pages and new feature will be constantly added.