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<p>To meet the demand for managing sustainably water resources as hydrological processes become more complex and the climate continues to change, it is imperative to forecast with increasing accuracy the streamflow of all rivers. Traditional models that are based on physics provide detailed information but do not have the ability to scale well with increasing amounts of data or for large areas; whereas machine learning methods that are based purely on data can capture any nonlinear behaviour, they cannot accurately predict streamflow because they are not based on any physics. To remedy these two opposite shortcomings, this research presents PIDeepONet, a hybrid method that employs both a Physics-Guided Loss (PGL) framework and Bayesian Optimisation (BO) to facilitate the accurate prediction of streamflows from only streamflow observations. The methodology is designed to produce streamflow predictions that will be both physically plausible and accurate, utilising either a small amount of data (limited dataset) or a large amount of data (extreme dataset) to predict flash floods and fires. By embedding hydrological constraints at a neural operator level using soft PGL, BO optimally balances data fidelity and physical plausibility using the optimal hyperparameters found by Bayesian optimisation. Two tributaries of the Cauvery River basin in India, Hemavathi and Kabini Rivers will be utilized to build the framework testing a combination of random and strict temporal data splits to simulate forecasting scenarios in the real world. The combination of a BO–PGL PIDeepONet model and the independent BO model had better accuracy than either model being optimized separately. Therefore, almost perfect predictive accuracy for Hemavathi (R<sup>2</sup> = 0.99976 and RMSE = 0.711) and Kabini (R<sup>2</sup> = 0.99988 and RMSE = 1.926) was achieved through the use of random split. Additionally, even with temporal splits, the generalisation of predicted values is still very good, with R<sup>2</sup> = 0.94715 and R<sup>2</sup> = 0.95914 for Hemavathi and Kabini. The outcomes of this research show the strength, extensibility, and appropriateness of the framework for real-time streamflow forecasting in changing and poorly monitored hydrological domains.</p>

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Physics-Guided Deep Learning with Bayesian Optimization for Enhanced River Streamflow Prediction

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • D. Suresh,
  • M. Sahaya Sheela,
  • Pamarthi Sunitha,
  • S. Gopalakrishnan

摘要

To meet the demand for managing sustainably water resources as hydrological processes become more complex and the climate continues to change, it is imperative to forecast with increasing accuracy the streamflow of all rivers. Traditional models that are based on physics provide detailed information but do not have the ability to scale well with increasing amounts of data or for large areas; whereas machine learning methods that are based purely on data can capture any nonlinear behaviour, they cannot accurately predict streamflow because they are not based on any physics. To remedy these two opposite shortcomings, this research presents PIDeepONet, a hybrid method that employs both a Physics-Guided Loss (PGL) framework and Bayesian Optimisation (BO) to facilitate the accurate prediction of streamflows from only streamflow observations. The methodology is designed to produce streamflow predictions that will be both physically plausible and accurate, utilising either a small amount of data (limited dataset) or a large amount of data (extreme dataset) to predict flash floods and fires. By embedding hydrological constraints at a neural operator level using soft PGL, BO optimally balances data fidelity and physical plausibility using the optimal hyperparameters found by Bayesian optimisation. Two tributaries of the Cauvery River basin in India, Hemavathi and Kabini Rivers will be utilized to build the framework testing a combination of random and strict temporal data splits to simulate forecasting scenarios in the real world. The combination of a BO–PGL PIDeepONet model and the independent BO model had better accuracy than either model being optimized separately. Therefore, almost perfect predictive accuracy for Hemavathi (R2 = 0.99976 and RMSE = 0.711) and Kabini (R2 = 0.99988 and RMSE = 1.926) was achieved through the use of random split. Additionally, even with temporal splits, the generalisation of predicted values is still very good, with R2 = 0.94715 and R2 = 0.95914 for Hemavathi and Kabini. The outcomes of this research show the strength, extensibility, and appropriateness of the framework for real-time streamflow forecasting in changing and poorly monitored hydrological domains.