History matching for functional data and its application to tsunami warnings in the Indian Ocean

Traditional History Matching (HM) identifies implausible regions of the input parameter space by comparing scalar outputs of a computer model to observations. It offers higher computational efficiency than Bayesian calibration, making it suitable for high-dimensional problems. However, in real physical systems, outputs are often functional, such as time series or spatial fields, and conventional HM cannot fully exploit such information. We propose a novel method, Functional History Matching (FHM), which extends HM to handle functional data. FHM incorporates the Outer Product Emulator, an extension of the Gaussian Process emulator designed for time series, to enhance computational efficiency. FHM also leverages Random Projection to extract dynamic features from infinite-dimensional data, including derivatives. FHM supports uncertainty quantification essential for decision-making and naturally accommodates model discrepancies. To demonstrate its practical effectiveness, we apply FHM to a synthetic tsunami forecasting scenario in the Indian Ocean, assuming a realistic event in the Makran subduction zone. Wave elevation time series from offshore buoy data are used to predict wave elevations over the Indian coastline. Our results show that FHM significantly outperforms scalar-based HM in accuracy. FHM enables reliable forecasting from functional data within feasible computational constraints, offering a robust framework for early warning systems and beyond.