TY - JOUR
T1 - Unresolved computation and optimal predictions
AU - Chorin, Alexandre J.
AU - Kast, Anton P.
AU - Kupferman, Raz
PY - 1999/10
Y1 - 1999/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0033459243&partnerID=8YFLogxK
U2 - 10.1002/(SICI)1097-0312(199910)52:10<1231::AID-CPA3>3.0.CO;2-C
DO - 10.1002/(SICI)1097-0312(199910)52:10<1231::AID-CPA3>3.0.CO;2-C
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AN - SCOPUS:0033459243
SN - 0010-3640
VL - 52
SP - 1231
EP - 1254
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 10
ER -