# Operator-based machine learning framework for generalizable prediction of unsteady treatment dynamics in stormwater infrastructure

arXiv: https://arxiv.org/abs/2507.04682 · HTML: https://mlsanity.com/paper/2507.04682/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 76 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Revisiting Small Batch Training for Deep Neural Networks](https://mlsanity.com/paper/1804.07612/) (2018)
- [An artificial neural network approach to bifurcating phenomena in computational fluid dynamics](https://mlsanity.com/paper/2109.10765/) (2021)

## Abstract (arXiv)

Stormwater infrastructures are decentralized urban water-management systems that face highly unsteady hydraulic and pollutant loadings from episodic rainfall-runoff events. Accurately evaluating their in-situ treatment performance is essential for cost-effective design and planning. Traditional lumped dynamic models (e.g., continuously stirred tank reactor, CSTR) are computationally efficient but oversimplify transport and reaction processes, limiting predictive accuracy and insight. Computational fluid dynamics (CFD) resolves detailed turbulent transport and pollutant fate physics but incurs prohibitive computational cost for unsteady and long-term simulations. To address these limitations, this study develops a composite operator-based neural network (CPNN) framework that leverages state-of-the-art operator learning to predict the spatial and temporal dynamics of hydraulics and particulate matter (PM) in stormwater treatment. The framework is demonstrated on a hydrodynamic separator (HS), a common urban treatment device. Results indicate that the CPNN achieves R2 > 0.8 for hydraulic predictions in 95.2% of test cases; for PM concentration predictions, R2 > 0.8 in 72.6% of cases and 0.4 < R2 < 0.8 in 22.6%. The analysis identifies challenges in capturing dynamics under extreme low-flow conditions, owing to their lower contribution to the training loss. Exploiting the automatic-differentiation capability of the CPNN, sensitivity analyses quantify the influence of storm event loading on PM transport. Finally, the potential of the CPNN framework for continuous, long-term evaluation of stormwater infrastructure performance is discussed, marking a step toward robust, climate-aware planning and implementation.