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

2025-09-04

AI Summary

Traditional history matching (HM) is limited to scalar outputs and struggles to effectively incorporate functional observational data—such as time series—thereby constraining the accuracy and real-time capability of high-dimensional parameter inversion. To address this, we propose Functional History Matching (FHM), the first HM framework explicitly designed for functional outputs. FHM leverages outer-product surrogate modeling and random projection to efficiently extract infinite-dimensional dynamic features and rigorously quantify uncertainty. It further integrates Gaussian process extension with derivative-based feature extraction to enable model discrepancy correction. Evaluated on an Indian Ocean tsunami early-warning simulation, FHM achieves reliable coastal wave-height prediction directly from buoy time-series observations. Compared to conventional scalar HM, FHM delivers significantly improved accuracy, computational efficiency, and real-time decision support—demonstrating its viability for operational forecasting under stringent latency constraints.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Time-Series/Data Streams
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

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.

Problem

• Extends history matching to functional data like time series
• Enables tsunami wave forecasting using offshore buoy data
• Improves accuracy over scalar methods for early warning systems

Innovation

• Extends History Matching to functional data
• Uses Outer Product Emulator for time series
• Leverages Random Projection for feature extraction