Combining mechanistic and data-driven techniques for predictive modelling of wastewater treatment plants

Mechanistic models are widely used for modelling of wastewater treatment plants. However, as they are based on simplified and incomplete domain knowledge, they often lack accurate predictive capabilities. In contrast, data-driven models are able to make accurate predictions, but only in the operational regions that are sufficiently described by the dataset used. We investigate an alternative hybrid model, combining mechanistic and data-driven techniques. We show that the hybrid approach combines the strengths of both modelling paradigms. It allows for accurate predictions out of the training dataset without the need for complete domain knowledge. Moreover, this approach is not limited to wastewater treatment plants and can potentially be applied wherever mechanistic models are used

Incorporating unmodeled dynamics into first-principles models through machine learning

First-principles modeling of dynamical systems is a cornerstone of science and engineering and has enabled rapid development and improvement of key technologies such as chemical reactors, electrical circuits, and communication networks. In various disciplines, scientists structure the available domain knowledge into a system of differential equations. When designed, calibrated, and validated appropriately, these equations are used to analyze and predict the dynamics of the system. However, perfect knowledge is usually not accessible in real-world problems. The incorporated knowledge thus is a simplification of the real system and is limited by the underlying assumptions. This limits the extent to which the model reflects reality. The resulting lack of predictive power severely hampers the application potential of such models. Here we introduce a framework that incorporates machine learning into existing first-principles modeling. The machine learning model fills in the knowledge gaps of the first-principles model, capturing the unmodeled dynamics and thus improving the representativeness of the model. Moreover, we show that this approach lowers the data requirements, both in quantity and quality, and improves the generalization ability in comparison with a purely data-driven approach. This approach can be applied to any first-principles model with sufficient data available and has tremendous potential in many fields

Lattice-based versus lattice-free individual-based models : impact on coexistence in competitive communities

Individual-based modelling is an increasingly popular framework for modelling biological systems. Many of these models represent space as a lattice, thus imposing unrealistic limitations on the movement of the modelled individuals. We adapt an existing model of three competing species by using a lattice-free approach, thereby improving the realism of the spatial dynamics. We retrieve the same qualitative dynamics as the lattice-based approach. However, by facilitating a higher spatial heterogeneity and allowing for small spatial refuges to form and persist, the maintenance of coexistence is promoted, in correspondence with experimental results. We also implement a directed movement mechanism allowing individuals of different species to pursue or flee from each other. Simulations show that the effects on coexistence depend on the level of aggregation in the community: a high level of aggregation is advantageous for maintaining coexistence, whereas a low level of aggregation is disadvantageous. This agrees with experimental results, where pursuing and escaping behaviour has been observed to be advantageous only in certain circumstances

Hybrid differential equations : integrating mechanistic and data-driven techniques for modelling of water systems

Mathematical modelling is increasingly used to improve the design, understanding, and operation of water systems. Two modelling paradigms, i.e., mechanistic and data-driven modelling, are dominant in the water sector, both with their advantages and drawbacks. Hybrid modelling aims to combine the strengths of both paradigms. Here, we introduce a novel framework that incorporates a data-driven component into an existing activated sludge model of a water resource recovery facility. In contrast to previous efforts, we tightly integrate both models by incorporating a neural differential equation into an existing mechanistic ODE model. This machine learning component fills in the knowledge gaps of the mechanistic model. We show that this approach improves the predictive capabilities of the mechanistic model and is able to extrapolate to unseen conditions, a problematic task for data-driven models. This approach holds tremendous potential for systems that are difficult to model using the mechanistic paradigm only

Coupling mechanistic and data-driven models by means of neural differential equations to incorporate unmodeled dynamics

Good predictive models are essential in modern chemical industry for control and optimization. Mechanistic models, incorporating physical and empirical knowledge, are dominant. However, the incorporated knowledge is inherently a simplification of reality, resulting in model structure uncertainty. Moreover, gathering the necessary knowledge is time-consuming and might be unfeasible for complex poorly-understood processes. With an ever-increasing amount of data available, data-driven methods are becoming more attractive. In these models, the structure is not explicitly specified, but rather determined by searching for relationships in the available data. Given sufficient and representative data, these models can make highly accurate predictions, unconstrained by any assumptions made. Therefore, they are particularly powerful for learning complex and poorly understood dynamics. The downside is their complete lack of interpretability. Moreover, as representative data is needed, they fail to extrapolate into regions not seen before

A hybrid modelling approach for reverse osmosis processes including fouling

A novel hybrid modelling approach, combining the strengths of a mechanistic reverse osmosis (RO) model and a data-driven fouling model, is developed on a unique long-term dataset from a full-scale RO installation to predict its performance. The mechanistic solution-diffusion model describes well understood phenomena in RO such as concentration polarisation, osmotic pressure and solutes transport throughout the membrane. This solution -diffusion model is combined with a data-driven model to cover the gaps in knowledge related to fouling phe-nomena. Several fouling models are tested to predict the membrane resistance over time and a thorough analysis of important input features was performed. A non-linear recurrent neural network with long short-term memor