Exploiting Output Coordinates for Efficient Global Sensitivity Analysis of Regional Storm Surge Forecasting via Neural Fields

Abstract Global sensitivity analysis is essential for quantifying how tropical cyclone forecast uncertainties propagate through high-fidelity storm surge models, yet conventional methods face a fundamental trade-off between spatial resolution and computational tractability when outputs span hundreds of thousands of coastal mesh nodes. This paper presents a framework that integrates neural field surrogates into variance-based global sensitivity analysis of high-dimensional spatially distributed outputs. The proposed approach augments the surrogate input space with spatial coordinates, enabling a single neural network to learn a continuous mapping from storm parameters and geographic locations to local surge response. A positional encoding module mitigates the spectral bias of standard neural networks, preserving high-frequency sensitivity patterns near coastlines and storm tracks. Sobol indices are estimated through single-loop Monte Carlo integration over the trained surrogate. The framework is validated on an analytical benchmark with 62,500 output dimensions and then applied to a storm surge simulation of Superstorm Sandy across 100,000 unstructured mesh nodes, with four uncertain tropical cyclone track and intensity parameters as inputs. Results demonstrate that the proposed method reduces first-order and total-effect Sobol’ index estimation errors by 50%–75% compared to alternatives, replacing multiple dimensionality-reduction and surrogate-fitting steps with a single unified model. These improvements enable more reliable identification of the dominant drivers of storm surge risk uncertainty at fine spatial resolution.