How to save 95% of computational load of numerical modeling in examining the coastal protection decision scenarios

Decision-making in the coastal protection projects often involves assessing a large number of shoreline decision combinations. Examining the impacts of the decisions using large-scale numerical models is time-consuming. For example, the numerical model to produce the result of one run in estimating the sea-level rise (SLR) impact in the San Francisco Bay (CoSMoS) needs at least 24 hours with 28 CPUs for one month of tidal dynamics. The basic binary decision of building a levee or not to protect the shoreline for a system of 9 levees requires 2^9=512 runs. The computational load could easily exceed the budgeted time and cost.

Here we present a sensitivity analysis-based approach to understand the impact of the variation in the shoreline protection strategy. We considered the seawalls’ impact on the hydrodynamics in the San Francisco Bay. To save the computational load to examine the decision making task, three key issues were addressed using the new method called Dimension REduced Surrogate based Sensitivity Analysis (DRESSA): 1) low-dimensional latent outputs were extracted using Principal Component Analysis (PCA), which informs us the pattern embedded in the high-dimensional output data and compresses the data to save data analysis efforts (e.g., time and memory); 2) efficient surrogates were trained using only small number of the numerical simulations and the prediction of the surrogates with acceptable errors were used to complement the simulation pool; and 3) a variance-based sensitivity analysis was performed to estimate the primary and joint sensitivity of all the possible decisions, where the trained surrogates were used to efficiently estimate the relevant covariance matrices in the latent outputs, which were then used to directly establish the sensitivity of the high-dimensional outputs through PCA transformations.

We applied this method to generate sensitivity maps and investigate the impact of different containment strategies on peak water level (PWL) over the entire San Francisco Bay under SLR and found we could save up to 95% of computational load in the task.