Physics-Informed Neural Network for monitoring the sulfate ion adsorption process using particle filter.

Fixed-bed columns are a well-established water purification technology. Several models have been constructed over the decades to scale up and predict the breakthrough curve of an adsorption column varying the flow rate, length, and initial concentration of solute. In this work, we proposed using an emerging computational approach of a physic-informed neural network (PINN) that uses artificial intelligence to solve the partial differential equation model of adsorption. The effectiveness of this approach is compared with finite-volume methods and experimental data. We also couple the PINN with a sampling importance resampling particle filter, a Bayesian technique that allows the filter and estimate states of the process, quantifying uncertainties of experimental measurements. The results shows physic-informed neural network capability in solving the proposed model and its uses as an evolution model for sequential estimation.