Dynamic weights enabled Physics-Informed Neural Network for simulating the mobility of Engineered Nano-particles in a contaminated aquifer

Abstract: Numerous polluted groundwater sites across the globe require an active remediation strategy to restore natural environmental conditions and local ecosystem. The Engineered Nano-particles (ENPs) have emerged as an efficient reactive agent for the in-situ degradation of groundwater contaminants. While the performance of these ENPs has been highly promising on the laboratory scale, their application in real field case conditions is still limited. The complex transport and retention mechanisms of ENPs hinder the development of an efficient remediation strategy. Therefore, a predictive tool for understanding the transport and retention behavior of ENPs is highly required. The existing tools in the literature are dominated with numerical simulators, which have limited flexibility and accuracy in the presence of sparse datasets. This work uses a dynamic, weight-enabled Physics-Informed Neural Network (dw-PINN) framework to model the nano-particle behavior within an aquifer. The result from the forward model demonstrates the effective capability of dw-PINN in accurately predicting the ENPs mobility. The model verification step shows that the relative mean square error (MSE) of the predicted ENPs concentration using dw-PINN converges to a minimum value of $1.3{e^{-5}}$. In the subsequent step, the result from the inverse model estimates the governing parameters of ENPs mobility with reasonable accuracy. The research demonstrates the tool's capability to provide predictive insights for developing an efficient groundwater remediation strategy.