mlsanityData to 14 Oct 2026

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

arXiv 2505.04263 ↗First posted 7 May 2025cs.LG cs.NA math.NAcited by 0

Not on the map. Why?

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.

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

16 of 58 references.

References · 16

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  2. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  3. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  5. 2020Universal Differential Equations for Scientific Machine Learningcited by 353
  6. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 262
  7. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 135
  8. 2019Physics-Informed Neural Networks for Power Systemscited by 80
  9. 2020Physics informed deep learning for computational elastodynamics without labeled datacited by 80
  10. 2021Scientific Machine Learning Benchmarkscited by 60
  11. 2022Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problemscited by 48
  12. 2019Deep learning observables in computational fluid dynamicscited by 38
4 more
  1. 2018Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Datacited by 36
  2. 2019Constraint-Aware Neural Networks for Riemann Problemscited by 14
  3. 2018An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networkscited by 2
  4. 2022A comparison of PINN approaches for drift-diffusion equations on metric graphscited by 1

Built on by

Not cited yet.