# An Adaptive Machine Learning Framework for Fluid Flow in Dual-Network Porous Media

arXiv: https://arxiv.org/abs/2603.19561 · HTML: https://mlsanity.com/paper/2603.19561/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 56 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [L-HYDRA: Multi-Head Physics-Informed Neural Networks](https://mlsanity.com/paper/2301.02152/) (2023)
- [Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions](https://mlsanity.com/paper/1705.08883/) (2017)
- [A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model](https://mlsanity.com/paper/1805.01389/) (2018)
- [CoolPINNs: A Physics-informed Neural Network Modeling of Active Cooling in Vascular Systems](https://mlsanity.com/paper/2303.05300/) (2023)
- [Composable block solvers for the four-field double porosity/permeability model](https://mlsanity.com/paper/1808.08328/) (2018)
- [A Machine Learning-Enhanced Hopf-Cole Formulation for Nonlinear Gas Flow in Porous Media](https://mlsanity.com/paper/2603.11250/) (2026)

## Abstract (arXiv)

Porous materials -- natural or engineered -- often exhibit dual pore-network structures that govern processes such as mineral exploration and hydrocarbon recovery from tight shales. Double porosity/permeability (DPP) mathematical models describe incompressible fluid flow through two interacting pore networks with inter-network mass exchange. Despite significant advances in numerical methods, there remains a need for computational frameworks that enable rapid forecasting, data assimilation, and reliable inverse analysis. To address this, we present a physics-informed neural network (PINN) framework for forward and inverse modeling of DPP systems. The proposed approach encodes the governing equations in mixed form, along with boundary conditions, directly into the loss function, with adaptive weighting strategies to balance their contributions. Key features of the framework include adaptive weight tuning, dynamic collocation point selection, and the use of shared trunk neural architectures to efficiently capture the coupled behavior of the dual pore networks. It is inherently mesh-free, making it well-suited for complex geometries typical of porous media. It accurately captures discontinuities in solution fields across layered domains without introducing spurious oscillations commonly observed in classical finite element formulations. Importantly, the framework is well-suited for inverse analysis, enabling robust parameter identification in scenarios where key physical quantities -- such as the mass transfer coefficient in DPP models -- are difficult to measure directly. In addition, a systematic convergence analysis is provided to rigorously assess the stability, accuracy, and reliability of the method. The effectiveness and computational advantages of the approach are demonstrated through a series of representative numerical experiments.