Author(s): Rijurekha Dasgupta; Subhasish Das; Gourab Banerjee

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Keywords: Physics-informed neural network; Stage-discharge rating curve; Symbolic regression

Abstract: Stage-discharge relationship is a widely researched topic for the estimation of river flow with economically reasonable means and also useful for prediction in ungauged rivers and hydrodynamic modeling. Conventional stage-discharge relationship often fails to meet desired accuracy due to its static nature and unable to capture the hysteretic pattern of the observed dataset. This study is an attempt to derive novel mathematical model of stage-discharge relationship incorporating both of the dynamic nature and hysteretic pattern of the stage-discharge relationship. The well-known Jones formula has been attempted to modify with the novel application of PySR module as an interpretation framework of Physics Informed Neural Network (PINN)-based stage-discharge rating curve (RC). The R2 of the prediction has been improved with PINN-RC to 0.98 from 0.65 for Jones formula at the tested gauging station. The ability to capture hysteretic pattern of both these models have been measured with four individual metrics combined in a sum of products form with equal weights. This overall hysteretic error has been reduced to 1.59 for the PINN-RC from 5.06 for Jones formula. This study concludes the superiority of PINN-RC and presents a universally applicable methodology to modify Jones formula at any geographic location for improved discharge measurement.

DOI: https://doi.org/10.64697/iahr.proc.hic2026.256

Year: 2026