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

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 Avedøre 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).

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

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 Avedøre 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.

STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systems

Most deep learning methods for imputing missing values treat the task as completing patterns within a fixed time window. This assumption often fails in industrial systems, where dynamics are driven by control actions, are highly non-stationary, and can experience long, uninterrupted gaps. We propose STDiff, which reframes imputation as learning how the system evolves from one state to the next. STDiff uses a conditional denoising diffusion model with a causal bias aligned to control theory, generating missing values step-by-step based on the most recent known state and relevant control or environmental inputs. On a public wastewater treatment dataset with simulated missing blocks, STDiff consistently achieves the lowest errors, with its advantage increasing for longer gaps. On a raw industrial dataset with substantial real gaps, it produces trajectories that remain dynamically plausible, in contrast to window-based models that tend to flatten or over-smooth. These results support dynamics-aware, explicitly conditioned imputation as a robust approach for industrial time series, and we discuss computational trade-offs and extensions to broader domains.