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4. A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions

Author

Ma, Yingbo, Dixit, Vaibhav, Innes, Mike, Guo, Xingjian, and Rackauckas, Christopher

Subjects
Mathematics - Numerical Analysis
Abstract

Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be difficult for practitioners to understand which method is likely to be the most effective on their particular application. In this manuscript we investigate the performance characteristics of Discrete Local Sensitivity Analysis implemented via Automatic Differentiation (DSAAD) against continuous adjoint sensitivity analysis. Non-stiff and stiff biological and pharmacometric models, including a PDE discretization, are used to quantify the performance of sensitivity analysis methods. Our benchmarks show that on small systems of ODEs (approximately $<100$ parameters+ODEs), forward-mode DSAAD is more efficient than both reverse-mode and continuous forward/adjoint sensitivity analysis. The scalability of continuous adjoint methods is shown to be more efficient than discrete adjoints and forward methods after crossing this size range. These comparative studies demonstrate a trade-off between memory usage and performance in the continuous adjoint methods that should be considered when choosing the technique, while numerically unstable backsolve techniques from the machine learning literature are demonstrated as unsuitable for most scientific models. The performance of adjoint methods is shown to be heavily tied to the reverse-mode AD method, with tape-based AD methods shown to be 2 orders of magnitude slower on nonlinear partial differential equations than static AD techniques. These results also demonstrate the applicability of DSAAD to differential-algebraic equations, delay differential equations, and hybrid differential equation systems, showcasing an ease of implementation advantage for DSAAD approaches., Comment: 13 pages, 3 figures, 2 tables

Published
2018

8. Modeling of Suspended Particulate Matter Concentration in an Extremely Turbid River Based on Multispectral Remote Sensing from an Unmanned Aerial Vehicle (UAV).

Author

Zhai, Yinghui, Zhong, Pu, Duan, Hongtao, Zhang, Dan, Chen, Xin, and Guo, Xingjian

Subjects
DRONE aircraft, REMOTE sensing, PARTICULATE matter, OCEAN color, STANDARD deviations, BODIES of water, SEDIMENT transport
Abstract

Following consecutive years of governance efforts, there has been a substantial reduction in sediment transport in the Yellow River, resulting in significant changes in its water–sediment dynamics. This necessitates precise monitoring of sediment-bearing tributary inflows, a crucial requirement for effective governance strategies on the Loess Plateau's current developmental stage. While satellite remote sensing technology has been widely used to estimate suspended particulate matter concentration (CSPM) in open water bodies like oceans and lakes, its application in narrow rivers presents challenges related to hybrid pixel and proximity effects. As a result, the effectiveness and competence of satellite remote sensing in monitoring CSPM in such confined river environments are reduced. This study attempted to use unmanned aerial vehicle (UAV) remote sensing with multispectral technology to invert CSPM in the Wuding River, a sediment-bearing Yellow River tributary. A novel CSPM concentration inversion model was introduced for highly turbid river settings. The results showed that the accuracy of the new band ratio model in this study is significantly improved compared with the existing models. The validation dataset had a coefficient of determination (R2) of 0.83, a root mean square error (RMSE) of 3.73 g/L, and a mean absolute percentage error (MAPE) of 44.95% (MAPE is 40.68% at 1–20 g/L, and 12.37% at >20 g/L). On this basis, the UAV also monitored the impacts of heavy rainfall on the CSPM, resulting in a rapid rise and fall in CSPM over a period of ten hours. This study demonstrated the potential of UAV remote sensing for CSPM monitoring in extremely turbid narrow rivers (tens to tens of meters), especially before and after rainfall sediment production events, which can provide technical support for accurate sediment management and source identification in the main tributaries of the Yellow River and help realize the goal of high-quality development of the Yellow River Basin. [ABSTRACT FROM AUTHOR]

Published
2023
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