# Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification

arXiv: https://arxiv.org/abs/2505.04263 · HTML: https://mlsanity.com/paper/2505.04263/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 16 of 16)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [Scientific Machine Learning Benchmarks](https://mlsanity.com/paper/2110.12773/) (2021)
- [Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems](https://mlsanity.com/paper/2203.00003/) (2022)
- [Deep learning observables in computational fluid dynamics](https://mlsanity.com/paper/1903.03040/) (2019)
- [Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data](https://mlsanity.com/paper/1808.04327/) (2018)
- [Constraint-Aware Neural Networks for Riemann Problems](https://mlsanity.com/paper/1904.12794/) (2019)
- [An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networks](https://mlsanity.com/paper/1803.00418/) (2018)
- [A comparison of PINN approaches for drift-diffusion equations on metric graphs](https://mlsanity.com/paper/2205.07195/) (2022)

## Abstract (arXiv)

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.