Multi-Step Simulation Improvement for Time Series Using Exogenous State Variables

Accurate simulation of wastewater treatment systems is essential for optimizing control strategies and ensuring efficient operation. This study focuses on enhancing the predictive accuracy of a Long Short-Term Memory (LSTM)-based simulator by incorporating exogenous state variables, such as temperature, flow, and process phases, that are independent of output and control variables. The experimental results demonstrate that including these variables significantly reduces prediction errors, measured by Mean Squared Errors (MSE) and Dynamic Time Warping (DTW) metrics. The improved model, particularly the version that uses actual values of exogenous state variables at each simulation step, showed robust performance across different seasons, reducing MSE by 55% and DTW by 34% compared to the model which didn’t include exogenous state variables. This approach addresses the compounding error issue in multi-step simulations, leading to more reliable predictions and enhanced operational effic iency in wastewater treatment.