Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Abstract

et al.. Gaussian process metamodeling of functional-input code for coastal flood hazard assessment. Reliability Engineering and System Safety, Elsevier, 2020, 198, Abstract This paper investigates the construction of a metamodel for coastal flooding early warning at the peninsula of Gâvres, France. The code under study is an hydrodynamic model which receives time-varying maritime conditions as inputs. We concentrate on Gaussian pocess metamodels to emulate the behavior of the code. To model the inputs we make a projection of them onto a space of lower dimension. This setting gives rise to a model selection methodology which we use to calibrate four characteristics of our functional-input metamodel: (i) the family of basis functions to project the inputs; (ii) the projection dimension; (iii) the distance to measure similarity between functional input points; and (iv) the set of functional predictors to keep active. The proposed methodology seeks to optimize these parameters for metamodel predictability, at an affordable computational cost. A comparison to a dimensionality reduction approach based on the projection error of the input functions only showed that the latter may lead to unnecessarily large projection dimensions. We also assessed the adaptability of our methodology to changes in the number of training and validation points. The methodology proved its robustness by finding the optimal solution for most of the instances, while being computationally efficient.

A User-Oriented Local Coastal Flooding Early Warning System Using Metamodelling Techniques

“…A GP-based metamodel is also used for metamodels forced by functional inputs but provide scalar outputs (i.e., Y 7 -Y 18 ). To reduce both the memory and the processing requirements of the metamodel, we implement the B-spline [49] and principal component analysis (PCA) [50] dimension reduction techniques, as thoroughly explained in [23], who tested this method using a simplified flood model (relying on the use of an overtopping formula over a single cross-shore profile). Compared to alternative dimension reduction approaches such as the polynomial or Fourier bases of functions, one advantage is that the basis functions from PCA are orthogonal, and those from B-splines have many zero scalar products, which can be beneficial for least square procedures when the decomposition dimension is large.…”

“…To better explore the potential of metamodelling techniques for coastal flood FEWSs, the ANR RISCOPE project was initiated in 2017 with the aim of establishing a user-centred FEWS by relying on metamodelling techniques. This project led to the development and exploration of metamodels and their ability to predict information regarding inland floods [22][23][24]. Within this project, Ref.…”

A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation

“…commonly called the Lorenz-96 system. Superscripts in parentheses denote components of a vector, l ranges from 1 to n, and (as introduced in [29]) the forcing depends on two parameters 2) .…”

“…Model and truth are integrated between these observation times with five steps of a fourth order Runge-Kutta scheme. At each of these integration steps the true value of θ (1) , θ (2) is drawn from a Gaussian with mean (2, 1) T and variance 0.01I 2 . All DA schemes use fixed parameter estimates between assimilation steps.…”

“…Yet the surrogate DA method employs high-dimensional inputs to the emulator, as the parameter and state vectors are combined and used as design variables. Some recent works [2,18] offer approaches for dimension reduction for statistical emulators that require either significant prior knowledge of the variability of the input space or a significant amount of data to characterize that variability well. For sequential DA, as a matter of course we have this prior knowledge available, but the flavor of appropriate dimension reduction will be problem specific.…”