Numerical simulation of pollutants transport in groundwater using deep neural networks informed by physics

Real-time monitoring of groundwater pollutants is very challenging to implement due to the difficulty and high economic cost. Groundwater numerical modeling is generally used as an alternative to create protection systems and illustrate their effectiveness. Several groundwater simulation software programs are available, however, they are based on numerical methods that require high spatial and temporal meshing, which considerably increases their computational costs and limits their use for optimization process.To solve this problem, a methodology that combines machine learning techniques based on neural networks, flow, and transport equations in underground reservoirs is proposed. This method is known as physics-informed deep neural networks, abbreviated as PINN. In this work, we will show the performance of PINN in predicting the flow and transport of pollutants in an underground reservoir. To evaluate the effectiveness of the PINN, the finite element method with a fine mesh grid is used as a reference solution to validate the PINN results.The results show that PINNS provide very good result in predicting pollutant transport in the reservoir with a relatively low cost.