Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification
This work addresses simulation and parameter identification for drift-diffusion models on metric graphs, which is incremental as it adapts existing DeepONet methods to a specific domain.
The authors tackled the problem of solving nonlinear drift-diffusion equations on metric graphs, which are important for applications like biological transport and crowd motion, by developing a physics-informed deep learning approach using DeepONets, achieving accurate evaluation and suitability for optimization or inverse problems.
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport in biological cells to the motion of human crowds. While traditional numerical schemes require a large amount of tailoring, especially in the case of model design or parameter identification problems, physics informed deep operator networks (DeepONet) have emerged as a versatile tool for the solution of partial differential equations with the particular advantage that they easily incorporate parameter identification questions. We here present an approach where we first learn three DeepONet models for representative inflow, inner and outflow edges, resp., and then subsequently couple these models for the solution of the drift-diffusion metric graph problem by relying on an edge-based domain decomposition approach. We illustrate that our framework is applicable for the accurate evaluation of graph-coupled physics models and is well suited for solving optimization or inverse problems on these coupled networks.