Multifidelity Sparse-Grid-Based Uncertainty Quantification for the Hokkaido Nansei-oki Tsunami

With uncertainty quantification, we aim to efficiently propagate the uncertainties in the input parameters of a computer simulation, in order to obtain a probability distribution of its output. In this work, we use multi-fidelity sparse grid interpolation to propagate the uncertainty in the shape of the incoming wave for the Okushiri test-case, which is a wave tank model of a part of the 1993 Hokkaido Nansei-oki tsunami. An important issue with many uncertainty quantification approaches is the ‘curse of dimensionality’: the overall computational cost of the uncertainty propagation increases rapidly when we increase the number of uncertain input parameters. We aim to mitigate the curse of dimensionality by using a multifidelity approach. In the multifidelity approach, we combine results from a small number of accurate and expensive high-fidelity simulations with a large number of less accurate but also less expensive low-fidelity simulations. For the Okushiri test-case, we find an improved scaling when we increase the number of uncertain input parameters. This results in a significant reduction of the overall computational cost. For example, for four uncertain input parameters, accurate uncertainty quantification based on only high-fidelity simulations comes at a normalised cost of 219 high-fidelity simulations; when we use a multifidelity approach, this is reduced to a normalised cost of only 10 high-fidelity simulations.