Unresolved computation and optimal predictions

Alexandre J. Chorin*, Anton P. Kast, Raz Kupferman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


We present methods for predicting the solution of time-dependent partial differential equations when that solution is so complex that it cannot be properly resolved numerically, but when prior statistical information can be found. The sparse numerical data are viewed as constraints on the solution, and the gist of our proposal is a set of methods for advancing the constraints in time so that regression methods can be used to reconstruct the mean future. For linear equations we offer general recipes for advancing the constraints; the methods are generalized to certain classes of nonlinear problems, and the conditions under which strongly nonlinear problems and partial statistical information can be handled are briefly discussed. Our methods are related to certain data acquisition schemes in oceanography and meteorology.

Original languageAmerican English
Pages (from-to)1231-1254
Number of pages24
JournalCommunications on Pure and Applied Mathematics
Issue number10
StatePublished - Oct 1999
Externally publishedYes


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