Solving 3D Inverse Groundwater Source History Problems in a LSO Framework Using Physics-Informed Neural Networks and Simulated Annealing in Homogeneous Aquifers

Identifying the source and release history of groundwater contaminants is a crucial task, as removal operations largely depend on these factors. Link Simulation Optimisation (LSO) is a proven method for identifying the history of the source for the groundwater contaminants in inverse problem matrices. In a conventional LSO optimisation algorithm, the simulation algorithm is encapsulated within it. The optimisation algorithm drives the search, whereas the simulation model responds. The main strong point of the LSO is how the tandem optimisation algorithm and simulation model work. However, simulation models often increase the computational burden; as a result, they are replaced with a surrogate model.

Historically, statistical surrogates such as Polynomial Response Surface, Gaussian Process Regression, and radial basis function have been used in the groundwater source release history problem. More recently, machine–learning–based surrogates, such as Artificial Neural Networks, Deep Neural Networks, and Convolutional Neural Networks, have been extensively used in groundwater source release history problems. The main drawbacks of these surrogates are that they don’t consider physics within their training process. As a result, they are heavily dependent on the training data. Outside information beyond their training data often relates to poor performance. Moreover, the source identification of groundwater problems is ill-posed, but surrogates often smooth the objective landscape and provide a false sense of uniqueness. Additionally, a noise level of 1% to 2% in the training data typically results in a significant error in prediction within the LSO framework.

To overcome the aforementioned drawback, we propose a surrogate based on a physics-informed neural network (PINN) in an LSO framework for identifying the source contamination strength in a hypothetical case scenario. The hypothetical scenario is homogeneous and governed by the Dirichlet boundary condition. The proposed PINN learns the spatio-temporal contaminant concentration C(x,y,z,t) by minimising errors in observed data while simultaneously enforcing the 3D advection–dispersion equation, boundary conditions, and initial conditions. The contaminant source is represented as a time-limited mass-loading well (active until 0 to t_on), embedded directly into the governing PDE, ensuring physically consistent transport and mass conservation. Apart from conventional practices, validation is performed during the training process, which provides advantages in avoiding overfitting and retaining the most effective features. This 3D-PINN tested 1000 data points generated using random uniform, Sobol, and Latin hypercube sampling.  Results show that with the correct implementation of the PINN, we can estimate the source strength C(x, y, z, t) with greater accuracy. In this LSO model, we utilise simulated annealing as the optimisation method.