*Project Description*

Knowledge of the underlying network structure in a dynamical system is crucial to understanding and predicting its behavior. Unfortunately often the underlying network structure is unknown, thus this structure must often be estimated from data. Granger causality [1] is one way in which such interactions have been estimated. Other methods based on Shannon Entropy [2] have also been developed, including transfer entropy [3] and more recently a generalization of transfer entropy known as causation entropy [4, 5]. In practice causation entropy must be estimated with various joint entropies, and depending upon the distribution of the underlying data (for instance Poisson) must thus be estimated directly from the joint probability distribution. This estimation can be slow, especially in the case of Poisson since the space which must be searched over for calculation is large. This project therefore will focus on utilizing GPU capabilities in order to develop faster methods for calculation of causation entropy.

*References:*

[1] C.W. Granger Journal of the Econometric Society 424-438 (1969). [2] C. E. Shannon The Bell Systems Technical Journal 27, 379-423 (1948).

[3] T. Schreiber Phys. Rev. Lett. 85, 461 (2000).

[4] J. Sun, E. M. Bollt Physica D 267, 49 (2014).

[5] J. Sun, D. Taylor, E. M. Bollt SIAM J. Appl. Dyn. Sys. 14, 73 (2015).