GeONet: Geometry-Encoded Operator Network for Predicting Flow in Heterogeneous Porous Media

Abstract

Rapid prediction of pressure-driven flow in microfluidic porous media is important for experimental design, tracer-test interpretation, and digital-twin development for subsurface energy and critical mineral applications. High-fidelity simulations resolve geometry-controlled flow but are computationally expensive across large geometry ensembles. Here, we introduce GeONet, a Geometry-Encoded Operator Network that predicts steady-state pressure fields by jointly representing material properties, spatial coordinates, and solid--void geometry. GeONet extends the Branch--Trunk architecture with a dedicated Leaf Network encoding the binary domain mask through multiscale features. The Branch Network represents porosity and permeability, the Trunk Network combines coordinates with local geometric descriptors and random Fourier features, and a gated DeepMixer integrates these representations to predict pressure. GeONet was trained and evaluated using 5,000 PFLOTRAN simulations of heterogeneous Reduced Complexity Platform domains, comprising nearly 30 TB of data. Comparisons with pore-scale Stokes solutions across three geometries yielded Pearson correlations of 0.987--0.991 and R² values of 0.974--0.982, supporting PFLOTRAN as reference data. Under matched partitions and two-stage hyperparameter optimization, GeONet substantially outperformed a boundary-condition-aware DeepONet baseline. Across three held-out domains, GeONet achieved NRMSE of 0.0381--0.0500, MAPE of 1.76--2.59%, and R² of 0.9673--0.9822, versus 0.1483--0.2040, 7.81--10.45%, and 0.5658--0.7126 for DeepONet, respectively. On three additional unseen geometries, GeONet achieved NRMSE of 0.0448--0.0676 and R² of 0.9511--0.9770. These results demonstrate improved accuracy, pressure-range preservation, and cross-geometry generalization through explicit geometry encoding.

Localization Landscapes as Operator-Induced Geometry for Heterogeneous Systems
Josué García-Ávila
arXiv6 Sep 2026PreprintCC BY-NC-ND 4.0Full textMathematical physics Condensed matterarXiv
SAGE-PINN: A Singularity-free Axisymmetric Geometry-Encoded Physics-Informed Neural Network for Axisymmetric Multiphysics Flow in Cylindrical Coordinates
Raj Maurya, Joyprakash Akhuli, Doyel Pandey
arXiv7 Oct 2026PreprintarXiv licenceFull textFluid dynamicsarXiv
Geometry-Encoded Hidden Orientational Memory
Vladimir A. Baulin
arXiv13 Oct 2026PreprintCC BY-SA 4.0Full textCondensed matterarXiv
GREEN-PRECONDITIONED DYNAMIC GRAPH NEURAL OPERATOR FOR ELECTROMAGNETIC FIELD PREDICTION IN HETEROGENEOUS MEDIA
Gao zhiwei, Zhijie Liu, chengan sun +2
Optics Express22 Oct 2026Peer-reviewedLicence not statedOptics & photonicsCrossref
Quantum Federated Learning Based on Bures--Uhlmann Geometry for Heterogeneous Noisy Clients
Haruki Emori, Masaki Uchihara, Yuuki Tokunaga
arXiv28 Aug 2026PreprintarXiv licenceFull textQuantum physics & quantum informationarXiv

Cite

BibTeX RIS

BibTeX

@misc{mamud2026geonet,
  title = {{GeONet: Geometry-Encoded Operator Network for Predicting Flow in Heterogeneous Porous Media}},
  author = {Md Lal Mamud and Maruti K. Mudunuru and Yucheng Fu and Aramy Troung and Satish Karra and Ivani Patel and Arunima Bhattacharjee and Tamas Varga and Pratanu Roy and Michael Penwarden and Rajesh K. Singh and Arjun Chakrawal and Kalyana B. Nakshatrala and Christof Meile and Erin Rooney and Glenn Hammond},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19493},
  eprint = {2610.19493},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19493},
}

RIS

TY  - UNPB
TI  - GeONet: Geometry-Encoded Operator Network for Predicting Flow in Heterogeneous Porous Media
AU  - Md Lal Mamud
AU  - Maruti K. Mudunuru
AU  - Yucheng Fu
AU  - Aramy Troung
AU  - Satish Karra
AU  - Ivani Patel
AU  - Arunima Bhattacharjee
AU  - Tamas Varga
AU  - Pratanu Roy
AU  - Michael Penwarden
AU  - Rajesh K. Singh
AU  - Arjun Chakrawal
AU  - Kalyana B. Nakshatrala
AU  - Christof Meile
AU  - Erin Rooney
AU  - Glenn Hammond
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19493
UR  - https://arxiv.org/abs/2610.19493
AB  - Rapid prediction of pressure-driven flow in microfluidic porous media is important for experimental design, tracer-test interpretation, and digital-twin development for subsurface energy and critical mineral applications. High-fidelity simulations resolve geometry-controlled flow but are computationally expensive across large geometry ensembles. Here, we introduce GeONet, a Geometry-Encoded Operator Network that predicts steady-state pressure fields by jointly representing material properties, spatial coordinates, and solid--void geometry. GeONet extends the Branch--Trunk architecture with a dedicated Leaf Network encoding the binary domain mask through multiscale features. The Branch Network represents porosity and permeability, the Trunk Network combines coordinates with local geometric descriptors and random Fourier features, and a gated DeepMixer integrates these representations to predict pressure. GeONet was trained and evaluated using 5,000 PFLOTRAN simulations of heterogeneous Reduced Complexity Platform domains, comprising nearly 30 TB of data. Comparisons with pore-scale Stokes solutions across three geometries yielded Pearson correlations of 0.987--0.991 and R^2 values of 0.974--0.982, supporting PFLOTRAN as reference data. Under matched partitions and two-stage hyperparameter optimization, GeONet substantially outperformed a boundary-condition-aware DeepONet baseline. Across three held-out domains, GeONet achieved NRMSE of 0.0381--0.0500, MAPE of 1.76--2.59%, and R^2 of 0.9673--0.9822, versus 0.1483--0.2040, 7.81--10.45%, and 0.5658--0.7126 for DeepONet, respectively. On three additional unseen geometries, GeONet achieved NRMSE of 0.0448--0.0676 and R^2 of 0.9511--0.9770. These results demonstrate improved accuracy, pressure-range preservation, and cross-geometry generalization through explicit geometry encoding.
ER  -

Abstract

Related

Cite