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Dynamic simulators model systems evolving over time. Often, it operatesiteratively over fixed number of time-steps. The output of such simulator canbe considered as time series or discrete functional outputs. Metamodeling is ane ective method to approximate demanding computer codes. Numerous metamodelingtechniques are developed for simulators with a single output. Standard approachto model a dynamic simulator uses the same method also for multi-time seriesoutputs: the metamodel is evaluated independently at every time step. This canbe computationally demanding in case of large number of time steps. In somecases, simulator outputs for di erent combinations of input parameters havequite similar behaviour. In this paper, we propose an application of shapeinvariant model approach to model dynamic simulators. This model assumes acommon pattern shape curve and curve-specific di erences in amplitude andtiming are modelled with linear transformations. We provide an e cientalgorithm of transformation parameters estimation and subsequent predictionalgorithm. The method was tested with a CO2 storage reservoir case using anindustrial commercial simulator and compared with a standard single stepapproach. The method provides satisfactory predictivity and it does not dependon the number of involved time steps.

Shape invariant model approach for functional data analysis in uncertainty and sensitivity studies