# A novel stacking ensemble model for predicting discharge coefficient of submerged multi parallel radial gates

## TL;DR

This paper introduces a deep learning-based stacking ensemble model to accurately predict the discharge coefficient of radial gates for better water management.

## Contribution

The novel contribution is a dual-layer stacking ensemble model using LSTM with attention for Cd prediction in radial gates.

## Key findings

- The model achieved a root mean square error of 0.0175.
- The ensemble outperformed existing models for Cd prediction.
- The attention mechanism highlighted relevant data patterns effectively.

## Abstract

Enhancing the precision of discharge coefficient (Cd) prediction holds paramount importance for effective Water distribution control. Calculating the Cd for radial gates is often complex, with existing methods frequently depending on intricate procedures and underlying assumptions. This study introduces a deep learning-based stacking ensemble model for Cd prediction. The proposed model comprises a dual-layer structure. Four machine learning algorithms are exploited as baseline models. The Meta model employed long short-term memory (LSTM) with attention mechanism to amalgamate the outputs from the base models and assign sufficient weight to each base model. The spatial attention mechanism effectively highlighted relevant patterns within the data. The proposed model achieved an impressive root mean square error of 0.0175. The ensemble model outperformed existing longstanding models. The proposed system holds substantial strategic importance, enabling optimal water resource management.

The online version contains supplementary material available at 10.1038/s41598-026-38117-2.