We develop an efficient,adaptive locally weighted projection regression(ALWPR)framework for uncertainty quantification(UQ)of systems governed by ordinary and partial differential equations.The algorithm adaptively sel...We develop an efficient,adaptive locally weighted projection regression(ALWPR)framework for uncertainty quantification(UQ)of systems governed by ordinary and partial differential equations.The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new localmodels.It effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics.The developed methodology provides predictions and confidence intervals at any query input and can dealwithmulti-output cases.Numerical examples are presented to show the accuracy and efficiency of the ALWPR framework including problems with non-smooth local features such as discontinuities in the stochastic space.展开更多
文摘We develop an efficient,adaptive locally weighted projection regression(ALWPR)framework for uncertainty quantification(UQ)of systems governed by ordinary and partial differential equations.The algorithm adaptively selects the new input points with the largest predictive variance and decides when and where to add new localmodels.It effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics.The developed methodology provides predictions and confidence intervals at any query input and can dealwithmulti-output cases.Numerical examples are presented to show the accuracy and efficiency of the ALWPR framework including problems with non-smooth local features such as discontinuities in the stochastic space.
