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In this paper we focus on comparing machine learning approaches for quantumgraphs, which are metric graphs, i.e., graphs with dedicated edge lengths, andan associated differential operator. In our case the differential equation is adrift-diffusion model. Computational methods for quantum graphs require acareful discretization of the differential operator that also incorporates thenode conditions, in our case Kirchhoff-Neumann conditions. Traditionalnumerical schemes are rather mature but have to be tailored manually when thedifferential equation becomes the constraint in an optimization problem.Recently, physics informed neural networks (PINNs) have emerged as a versatiletool for the solution of partial differential equations from a range ofapplications. They offer flexibility to solve parameter identification oroptimization problems by only slightly changing the problem formulation usedfor the forward simulation. We compare several PINN approaches for solving thedrift-diffusion on the metric graph.

A comparison of PINN approaches for drift-diffusion equations on metric graphs