This paper presents a new algorithm using physics-informed neural networks (PINNs) to track and characterize spatio-temporally varying chemical sources based on time-resolved measurements of chemical concentration, fluid velocity, and pressure. Chemical source emission functions, chemical concentration, fluid velocity and fluid pressure fields are modeled as multi-layer percepterons (MLPs). During the training process, sensors readings of chemical concentratio, fluid velocity, and fluid pressure are matched to the output of the respective MLPs at the given spatio-temporal locations. Simultaneously, the physics of fluid flow and chemical dispersion at an arbitrary number of spatio-temporal locations in the domain of interest are enforced through regularization. Once trained, the constituent MLPs can be evaluated to generate the time resolved maps of source emissions, chemical concentration, fluid velocity and pressure. Extensive numerical simulation validate the method, including scenarios with both static and dynamic sources in complex flow fields. This innovative approach marks a significant advancement in environmental monitoring technologies.