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Computer models play a key role in many scientific and engineering problems.One major source of uncertainty in computer model experiment is input parameteruncertainty. Computer model calibration is a formal statistical procedure toinfer input parameters by combining information from model runs andobservational data. The existing standard calibration framework suffers frominferential issues when the model output and observational data arehigh-dimensional dependent data such as large time series due to the difficultyin building an emulator and the non-identifiability between effects from inputparameters and data-model discrepancy. To overcome these challenges we proposea new calibration framework based on a deep neural network (DNN) withlong-short term memory layers that directly emulates the inverse relationshipbetween the model output and input parameters. Adopting the 'learning withnoise' idea we train our DNN model to filter out the effects from data modeldiscrepancy on input parameter inference. We also formulate a new way toconstruct interval predictions for DNN using quantile regression to quantifythe uncertainty in input parameter estimates. Through a simulation study andreal data application with WRF-hydro model we show that our approach can yieldaccurate point estimates and well calibrated interval estimates for inputparameters.

Computer Model Calibration with Time Series Data using Deep Learning and Quantile Regression