Computer Model Calibration with Time Series Data using Deep Learning and Quantile Regression
This addresses uncertainty in input parameters for scientific and engineering models, offering a solution for high-dimensional dependent data, though it is incremental as it builds on existing calibration methods.
The paper tackles the challenge of calibrating computer models with high-dimensional time series data by proposing a new framework using deep neural networks with LSTM layers and quantile regression, demonstrating accurate point estimates and well-calibrated interval estimates in simulations and a real-world application.
Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data such as large time series due to the difficulty in building an emulator and the non-identifiability between effects from input parameters and data-model discrepancy. To overcome these challenges we propose a new calibration framework based on a deep neural network (DNN) with long-short term memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the 'learning with noise' idea we train our DNN model to filter out the effects from data model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with WRF-hydro model we show that our approach can yield accurate point estimates and well calibrated interval estimates for input parameters.