Direct Estimation of Electric Field Distribution in Circular ECT Sensors Using Graph Convolutional Networks

The Electrical Capacitance Tomography (ECT) imaging pipeline relies on accurate estimation of electric field distributions to compute electrode capacitances and reconstruct permittivity maps. Traditional ECT forward model methods based on the Finite Element Method (FEM) offer high accuracy but are computationally intensive, limiting their use in real-time applications. In this proof-of-concept study, we investigate the use of Graph Convolutional Networks (GCNs) for direct, one-step prediction of electric field distributions associated with a circular ECT sensor numerical model. The network is trained on FEM-simulated data and outputs of full 2D electric field maps for all excitation patterns. To evaluate physical fidelity, we compute capacitance matrices using both GCN-predicted and FEM-based fields. Our results show strong agreement in both direct field prediction and derived quantities, demonstrating the feasibility of replacing traditional solvers with fast, learned approximators. This approach has significant implications for further real-time ECT imaging and control applications.