# Explainable Wastewater Digital Twins: Adaptive Context-Conditioned Structured Simulators with Self-Falsifying Decision Support

arXiv: https://arxiv.org/abs/2605.19826 · HTML: https://mlsanity.com/paper/2605.19826/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 56 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 28 of 28)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [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)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [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)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Digital Twin: Values, Challenges and Enablers](https://mlsanity.com/paper/1910.01719/) (2019)
- [Selective Conformal Risk Control](https://mlsanity.com/paper/2512.12844/) (2025)
- [Time Series Dataset for Modeling and Forecasting of N2O in Wastewater Treatment](https://mlsanity.com/paper/2407.05959/) (2024)
- [Safety Monitoring for Learning-Enabled Cyber-Physical Systems in Out-of-Distribution Scenarios](https://mlsanity.com/paper/2504.13478/) (2025)
- [Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification](https://mlsanity.com/paper/2510.24757/) (2025)
- [When Environments Shift: Safe Planning with Generative Priors and Robust Conformal Prediction](https://mlsanity.com/paper/2602.12616/) (2026)
- [Staggered Integral Online Conformal Prediction for Safe Dynamics Adaptation with Multi-Step Coverage Guarantees](https://mlsanity.com/paper/2604.06058/) (2026)
- [SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems](https://mlsanity.com/paper/2604.14879/) (2026)
- [Data-Driven Open-Loop Simulation for Digital-Twin Operator Decision Support in Wastewater Treatment](https://mlsanity.com/paper/2604.20935/) (2026)
- [Identifiable Representation and Model Learning for Latent Dynamic Systems](https://mlsanity.com/paper/2410.17882/) (2024)
- [Machine learning in wastewater treatment: insights from modelling a pilot denitrification reactor](https://mlsanity.com/paper/2412.14030/) (2024)
- [Optimal Control-Based Falsification of Learnt Dynamics via Neural ODEs and Symbolic Regression](https://mlsanity.com/paper/2602.00031/) (2026)
- [End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems](https://mlsanity.com/paper/2605.06315/) (2026)

## Built on by (most cited first, 1 of 1)

- [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)

Operators of safety-critical industrial processes increasingly rely on digital twins to screen control interventions, but such simulators rarely carry certified safety guarantees. Wastewater treatment plants exemplify the gap: operators face a daily safety-efficiency trade-off where aerating too little risks effluent violations and nitrous-oxide (N2O) spikes, and aerating too much wastes energy. We develop an explainable digital twin for aeration and dosing setpoints. CCSS-IX, the simulator, is a bank of interpretable locally linear state-space "experts" adaptively mixed by a context-aware gating network, building on a continuous-time regime-switching scaffold. A runtime decision layer applies conformal risk control to abstain, reopen, or return a falsifying temporal witness for any operator-proposed action that cannot be statistically certified. The artificial-intelligence contribution is twofold: an identifiable, context-conditioned structured surrogate that retains operator-readable dynamics, and a self-falsifying decision rule with finite-sample coverage guarantees. The engineering contribution is a validated, end-to-end decision-support pipeline, tested on a 1000-step slice of the Avedore full-scale plant (42.6% sensor missingness, 2-minute sampling), the Agtrup/BlueKolding full-scale plant in Denmark, and the Benchmark Simulation Model No. 2 (BSM2) international benchmark, under a matched ten-seed protocol. The static structured ensemble lies within 0.78% root-mean-square error of an unconstrained black-box reference, and the adaptive variant within 1.08%. The calibrated reopen rule cuts aggregate two-plant regret by 43.6% at an unsafe-action cost weight of 4 and eliminates unsafe chosen actions on the BSM2 main slice. Event-aligned temporal witnesses prevent 93 of 187 false-safe N2O approvals, about 4.65x the dyadic baseline (paired McNemar p < 1e-21).