Identifying subsurface contamination is challenging as the sources are not directly perceivable. Aquifer contamination only gets noticed when it is measured in one of the observation wells. As remediation of the contaminated sites is expensive and time-consuming, it is essential to locate sources of contamination for efficient remediation design and water resources management. Simulation-optimization approach is popularly used for identification of contaminant sources. However, the numerous runs required for the simulation model by utilizing the optimization algorithm makes this approach computationally expensive. Alternatively, the simulation model can be substituted by a surrogate model which can significantly reduce the computational cost. In this study, a deep neural network (DNN) based surrogate model is proposed for simulating the transport of a reactive contaminant Tritium in a hypothetical aquifer. The DNN is trained by considering injection rates at possible source locations as inputs and concentration at observation wells simulated by meshfree Radial Point Collocation Method (RPCM) as output. RPCM efficiently handles instabilities associated with advection and reaction dominant problems in comparison to grid/mesh-based methods. The backpropagation approach is used to optimize the weights and biases of the DNN using adaptive moment estimation (ADAM) as an optimizer. The performance evaluation of the surrogate model yields Mean Squared Error (MSE) close to zero and correlation coefficient (R²) of 0.99. An inverse model is developed by linking the DNN surrogate model and Particle Swarm Optimizer (PSO). The application of the inverse model show that the DNN-PSO model can predict the injection rates at possible source locations accurately.