In recent years, artificial intelligence (AI), as a rapidly developing and powerful tool to solve practical problems, has attracted much attention and has been widely used in various areas. Owing to their strong learning and accurate prediction abilities, all sorts of AI models have also been applied in wastewater treatment (WWT) to optimize the process, predict the efficiency and evaluate the performance, so as to explore more cost-effective solutions to WWT. In this review, we summarize and analyze various AI models and their applications in WWT. Specifically, we briefly introduce the commonly used AI models and their purposes, advantages and disadvantages, and comprehensively review the inputs, outputs, objectives and major findings of particular AI applications in water quality monitoring, laboratory-scale research and process design. Although AI models have gained great success in WWT-related fields, there are some challenges and limitations that hinder the widespread applications of AI models in real WWT, such as low interpretability, poor model reproducibility and big data demand, as well as a lack of physical significance, mechanism explanation, academic transparency and fair comparison. To overcome these hurdles and successfully apply AI models in WWT, we make recommendations and discuss the future directions of AI applications.

A Review on Applications of Artificial Intelligence in Wastewater Treatment

In this paper, we contemplate the dynamics of an aquatic system consisting of three interacting species, phytoplankton, zooplankton, and fish. We assume that the evading risk of fish predation induces fear in zooplankton species, which affects its growth dynamics radically. On the other hand, zooplankton develop an anti-predator defense by taking temporary refuge. Interestingly, the system potentially exhibits multi-stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including multiple saddle–node and transcritical bifurcations with varying levels of nutrients, strength of phytoplankton toxicity, zooplankton refuge size and the cost of fear imposed by fish population. Further, by adding Gaussian white noise, we have extended the deterministic system to its stochastic version. We find that white noise appears to regulate the survival and extinction of model species. Comprehensive numerical simulations are consistent with mathematical results prognosticated by linear analysis. Overall, our study may provide a new insight into the mechanisms of emergence and mitigation of plankton blooms. 

Nutrient enrichment and phytoplankton toxicity influence a diversity of complex dynamics in a fear-induced plankton-fish model

Dynamical behavior of a nutrient–plankton model with Ornstein–Uhlenbeck process and nutrient recycling

Dynamics of a stochastic nutrient-plankton model with impulsive control strategy

In this paper, we investigate a stochastic nutrient-plankton model with impulsive control of the nutrient concentration and zooplankton population. Analytically, we find that the population size is nonnegative for a sufficiently long time. We derive some sufficient conditions for the existence of stable periodic oscillations, which indicate that the plankton populations will behave periodically. The numerical results show that the plankton system experiences a transition from extinction to the coexistence of species due to the emergence of impulsive control. Additionally, we observe that the nutrient pulse has a stronger relationship with phytoplankton growth than the zooplankton pulse. Although the frequency of impulsive control and appropriate environmental fluctuations can promote the coexistence of plankton populations, an excessive intensity of noise can result in the collapse of the entire ecosystem. Our findings may provide some insights into the relationships among nutrients, phytoplankton and zooplankton in a stochastic environment. 

Investigation of a nutrient-plankton model with stochastic fluctuation and impulsive control

Dynamics of a stochastic nutrient–plankton model with regime switching

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.

Stability switches and chaos induced by delay in a reaction-diffusion nutrient-plankton model.

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Dynamics of a stochastic nutrient–plankton model with regime switching

Dynamics of a stochastic nutrient-plankton model with impulsive control strategy

Stability switches and chaos induced by delay in a reaction-diffusion nutrient-plankton model.