Deep probabilistic surrogate modelling for uncertainty quantification in mangrove hydro-morphodynamics

Abstract

Introduction: Mangrove ecosystems are increasingly recognised as essential nature-based solutions for enhancing coastal resilience against sea-level rise and climate-induced extreme events. However, achieving robust uncertainty quantification for hydro-morphodynamic models of mangrove systems remains a critical challenge due to the complexity of physical processes and the high computational cost of solving Navier–Stokes partial differential equations. Conventional uncertainty quantification approaches, including Gaussian Process surrogates and physics-informed neural networks, are limited by their inability to adequately capture non-Gaussian behaviour, high-dimensional interactions, or to scale efficiently to large-scale coastal systems. Methods: To address these limitations, we propose an efficient and scalable probabilistic framework based on Deep Gaussian Processes, which hierarchically stack multiple Gaussian Process layers to represent complex, multi-scale, and non-Gaussian dependencies in hydro-morphodynamic dynamics. The framework is applied to a high-resolution numerical model of mangrove systems and trained using a variational inference approach to enable efficient surrogate modelling and uncertainty propagation. Results: The proposed Deep Gaussian Process model reduces computational cost by more than three orders of magnitude (approximately 1.4 minutes compared to over five days for the full numerical solver), while achieving substantially improved predictive accuracy relative to standard Gaussian Process models. Specifically, a fivefold reduction in error is observed, with an RMSE of 0.0095 m compared to 0.0465 m for conventional Gaussian Processes. The framework enables reliable propagation of uncertainty across complex, nonlinear system dynamics. Discussion: These results demonstrate the potential of Deep Gaussian Processes to provide accurate and computationally efficient uncertainty quantification for hydro-morphodynamic modelling of mangrove ecosystems. The proposed approach supports evidence-based planning for climate adaptation and ecosystem-based coastal resilience, offering a practical pathway for integrating advanced uncertainty quantification into operational decision-making for sustainable coastal management.