mlsanityData to 14 Oct 2026

Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sources

arXiv 2508.19847 ↗First posted 27 Aug 2025cs.LGcited by 3

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Abstract (arXiv)

We present a hybrid framework that couples finite element methods (FEM) with physics-informed DeepONet to model fluid transport in porous media from sharp, localized Gaussian sources. The governing system consists of a steady-state Darcy flow equation and a time-dependent convection-diffusion equation. Our approach solves the Darcy system using FEM and transfers the resulting velocity field to a physics-informed DeepONet, which learns the mapping from source functions to solute concentration profiles. This modular strategy preserves FEM-level accuracy in the flow field while enabling fast inference for transport dynamics. To handle steep gradients induced by sharp sources, we introduce an adaptive sampling strategy for trunk collocation points. Numerical experiments demonstrate that our method is in good agreement with the reference solutions while offering orders of magnitude speedups over traditional solvers, making it suitable for practical applications in relevant scenarios. Implementation of our proposed method is available at https://github.com/erkara/fem-pi-deeponet.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 24 of its 64 references that are in the map. First posted on arXiv 27 Aug 2025.

Builds on

24 of 64 references.

References · 24

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2015Automatic differentiation in machine learning: a surveycited by 855
  4. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  5. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  6. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  7. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  8. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  9. 2021Improved architectures and training algorithms for deep operator networkscited by 86
  10. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 65
  11. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 58
  12. 2022JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data sciencecited by 41
12 more
  1. 2022JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flowscited by 36
  2. 2022Applications of physics informed neural operatorscited by 33
  3. 2025Neural Chaos: A Spectral Stochastic Neural Operatorcited by 21
  4. 2020Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equationscited by 20
  5. 2024Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solvingcited by 17
  6. 2024Basis-to-Basis Operator Learning Using Function Encoderscited by 17
  7. 2024Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learningcited by 15
  8. 2023A multifidelity approach to continual learning for physical systemscited by 13
  9. 2021A Gradient-based Deep Neural Network Model for Simulating Multiphase Flow in Porous Mediacited by 8
  10. 2022Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networkscited by 6
  11. 2023iPINNs: Incremental learning for Physics-informed neural networkscited by 3
  12. 2024Neural Operator-Based Proxy for Reservoir Simulations Considering Varying Well Settings, Locations, and Permeability Fieldscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2025ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marchingcited by 0
  2. 2026A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous undergroundcited by 0
  3. 2026Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONetscited by 0