Uncertainty Quantification of Hydro-morphodynamic Models using Probabilistic Surrogate Models

Quantifying uncertainty in complex hydro-morphodynamics models, particularly those governed by the Navier–Stokes partial differential equations (PDE), is a challenging task due to the complex and highly non-linear relationship of high-dimensional inputs and outputs, coupled with inherent computational complexity. Traditional surrogate models, which provide an efficient approximation of the underlying expensive model, exemplified by the Gaussian process (GP), encounter limitations in accurately capturing the non-Gaussian nature inherent in the input/output relationship. Such limitations restrict their applicability to simpler problems. Furthermore, the applicability of newer hybrid surrogates, such as physics-informed neural networks (PINNs), for uncertainty quantification (UQ) is hindered by the significant computational cost of quantifying uncertainty, which requires a large number of parameters to optimise.
This research addresses these challenges by leveraging an efficient non-linear GP model known as the deep Gaussian process (deep GP), which is designed to the complexities of deep learning and modelling high-dimensional complex systems. This model is structured with multiple hidden layers interconnected by non-linear mappings. We explore the applicability of deep Gaussian processes, including their adaptation to replace a complex numerical model that solves the Navier–Stokes equations to model the hydro-morphodynamics around mangrove environments, and development of a novel UQ and uncertainty for deep GP for this high-resolution complex model. The derived findings reveal that the deep GP exhibits remarkable improvements in efficiency, significantly surpassing the baseline UQ method in terms of computational time and accuracy level. Concurrently, it demonstrates an accuracy improvement of over 5 orders of magnitude when contrasted with the standard GP model. Moreover, the deep GP exhibits superior robustness in quantifying uncertainty amidst diverse spatio-temporal complexities compared to its GP counterpart. This research significantly advances the understanding and application of uncertainty quantification in the field of hydro-morphodynamics with significant real-world implications for climate change adaptation and protection mitigation decisions.