# Data-Driven Open-Loop Simulation for Digital-Twin Operator Decision Support in Wastewater Treatment

arXiv: https://arxiv.org/abs/2604.20935 · HTML: https://mlsanity.com/paper/2604.20935/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Builds on (most cited first, 25 of 25)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Log Neural Controlled Differential Equations: The Lie Brackets Make a Difference](https://mlsanity.com/paper/2402.18512/) (2024)
- [Deep-OSG: Deep Learning of Operators in Semigroup](https://mlsanity.com/paper/2302.03358/) (2023)
- [Time Series Dataset for Modeling and Forecasting of N2O in Wastewater Treatment](https://mlsanity.com/paper/2407.05959/) (2024)

## Built on by (most cited first, 2 of 2)

- [Explainable Wastewater Digital Twins: Adaptive Context-Conditioned Structured Simulators with Self-Falsifying Decision Support](https://mlsanity.com/paper/2605.19826/) (2026)
- [Simulator-Grounded Large Language Models for Industrial Causal Reasoning: Tool-Use, Structured Injection, and Plant-Portable Retrieval for Wastewater Treatment Decision Support](https://mlsanity.com/paper/2608.05151/) (2026)

## Abstract (arXiv)

Wastewater treatment plants (WWTPs) need digital-twin-style decision support tools that can simulate plant response under prescribed control plans, tolerate irregular and missing sensing, and remain informative over 12-36 h planning horizons. Meeting these requirements with full-scale plant data remains an open engineering-AI challenge. We present CCSS-RS, a controlled continuous-time state-space model that separates historical state inference from future control and exogenous rollout. The model combines typed context encoding, gain-weighted forcing of prescribed and forecast drivers, semigroup-consistent rollouts, and Student-t plus hurdle outputs for heavy-tailed and zero-inflated WWTP sensor data. On the public Avedore full-scale benchmark, with 906,815 timesteps, 43% missingness, and 1-20 min irregular sampling, CCSS-RS achieves RMSE 0.696 and CRPS 0.349 at H=1000 across 10,000 test windows. This reduces RMSE by 40-46% relative to Neural CDE baselines and by 31-35% relative to simplified internal variants. Four case studies using a frozen checkpoint on test data demonstrate operational value: oxygen-setpoint perturbations shift predicted ammonium by -2.3 to +1.4 over horizons 300-1000; a smoothed setpoint plan ranks first in multi-criterion screening; context-only sensor outages raise monitored-variable RMSE by at most 10%; and ammonium, nitrate, and oxygen remain more accurate than persistence throughout the rollout. These results establish CCSS-RS as a practical learned simulator for offline scenario screening in industrial wastewater treatment, complementary to mechanistic models.