Appraisal of data-driven and mechanistic emulators of nonlinear hydrodynamic urban drainage simulators

TL;DR

This paper compares data-driven and mechanistic emulators for nonlinear urban drainage simulators, finding that naive data-driven models often outperform mechanistic ones, with insights into their respective advantages and limitations.

Contribution

It provides a systematic comparison of Gaussian Process-based mechanistic emulators and matrix factorization-based data-driven emulators for urban water system modeling.

Findings

Data-driven emulators often outperform mechanistic ones in urban applications.

Mechanistic emulators may be better for extrapolation and sparse data scenarios.

The paper discusses recent machine learning advances relevant to environmental modeling.

Abstract

Many model based scientific and engineering methodologies, such as system identification, sensitivity analysis, optimization and control, require a large number of model evaluations. In particular, model based real-time control of urban water infrastructures and online flood alarm systems require fast prediction of the network response at different actuation and/or parameter values. General purpose urban drainage simulators are too slow for this application. Fast surrogate models, so-called emulators, provide a solution to this efficiency demand. Emulators are attractive, because they sacrifice unneeded accuracy in favor of speed. However, they have to be fine-tuned to predict the system behavior satisfactorily. Also, some emulators fail to extrapolate the system behavior beyond the training set. Although, there are many strategies for developing emulators, up until now the selection of the emulation strategy remains subjective. In this paper, we therefore compare the performance of two families of emulators for open channel flows in the context of urban drainage simulators. We compare emulators that explicitly use knowledge of the simulator's equations, i.e. mechanistic emulators based on Gaussian Processes, with purely data-driven emulators using matrix factorization. Our results suggest that in many urban applications, naive data-driven emulation outperforms mechanistic emulation. Nevertheless, we discuss scenarios in which we think that mechanistic emulation might be favorable for i) extrapolation in time and ii) dealing with sparse and unevenly sampled data. We also provide many references to advances in the field of Machine Learning that have not yet permeated into the Bayesian environmental science community.