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In this paper, we use a novel combination of probabilistic programming and flowpipe construction to predict bounds on future biogas production for a wastewater treatment plant given operational data from the past. The operation of the anaerobic digester of a wastewater treatment plant is modeled through an Ordinary Differential Equation (ODE) model with unknown parameters and unobservable internal states. We are given data from the plant’s operation that includes the daily measurement of the incoming waste volumes and concentrations along with the volume of biogas produced. We formalize our problem as first estimating the unknown parameters and initial conditions using Bayesian inference, such that the past behavior of the system is “compatible” with the observed data. Next, we propagate those input parameter estimates forward using flowpipe construction. To enable rapid and accurate flowpipe construction, we exploit the monotonicity property of the dynamical model of the plant. The procedure yields an over-approximation of the upper and lower bounds on biogas production, given the inputs. As a result, it can be used to formally bound future predictions that might inform facility operations. We implemented this procedure using a first-order kinetics model of hydrolysis to model the anaerobic digester of a real-world case study facility. We demonstrate how this method constructs realistic bounds for biogas prediction from the historical data that contain the actual ground-truth data 100% of the time. Our approach outperforms the standard approach that computes a posterior predictive distribution from samples both in terms of time and accuracy.

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Using Bayesian Inference and Flowpipe Construction to Bound Predictions of Biogas Production at Wastewater Treatment Plants

  • 会议论文

  • 发表日期：

    2026年

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  • Fletcher Chapin,
  • Ankur Varma,
  • Samuel Akinwande,
  • Meagan Mauter,
  • Sriram Sankaranarayanan

摘要

In this paper, we use a novel combination of probabilistic programming and flowpipe construction to predict bounds on future biogas production for a wastewater treatment plant given operational data from the past. The operation of the anaerobic digester of a wastewater treatment plant is modeled through an Ordinary Differential Equation (ODE) model with unknown parameters and unobservable internal states. We are given data from the plant’s operation that includes the daily measurement of the incoming waste volumes and concentrations along with the volume of biogas produced. We formalize our problem as first estimating the unknown parameters and initial conditions using Bayesian inference, such that the past behavior of the system is “compatible” with the observed data. Next, we propagate those input parameter estimates forward using flowpipe construction. To enable rapid and accurate flowpipe construction, we exploit the monotonicity property of the dynamical model of the plant. The procedure yields an over-approximation of the upper and lower bounds on biogas production, given the inputs. As a result, it can be used to formally bound future predictions that might inform facility operations. We implemented this procedure using a first-order kinetics model of hydrolysis to model the anaerobic digester of a real-world case study facility. We demonstrate how this method constructs realistic bounds for biogas prediction from the historical data that contain the actual ground-truth data 100% of the time. Our approach outperforms the standard approach that computes a posterior predictive distribution from samples both in terms of time and accuracy.