Calibration of the underlying surface parameters for urban flood using latent variables and adjoint equation

TL;DR

This paper presents a Bayesian optimization approach with latent variables and adjoint equations for efficient calibration of urban surface parameters in flood modeling.

Contribution

It introduces a novel calibration method combining latent variables, adjoint equations, and parameter sharing to improve efficiency and uncertainty representation.

Findings

Method converges quickly in simple cases.

Calibrated Manning's coefficient with maximum relative error of 13.88%.

Insensitivity to observation time interval.

Abstract

Calibrating the urban underlying surface parameters is crucial for urban flood simulation. We formulate the parameter calibration problem into an optimization problem within the Bayesian framework using the maximum likelihood principle. We adopt the urban flood dynamical system model as the surrogate model and innovatively introduce latent variables inspired by machine learning to represent more uncertainties, which can also be compatible with common physical parameter calibration. For more efficient optimization, we construct the adjoint equation of the surrogate model to obtain gradient information and propose the parameter sharing technique and the localization technique to reduce the computation complexity of the adjoint equation. A simple case verifies the proposed method can converge quickly and is insensitive to the observation time interval. In the case derived from Test 8A, we calibrate Manning's coefficient of urban roads, with a maximum relative error of 13.88% and a minimum of 1.16%.