# Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls

arXiv: https://arxiv.org/abs/2310.06319 · HTML: https://mlsanity.com/paper/2310.06319/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 19 of 19)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [U-Net and its variants for medical image segmentation: theory and applications](https://mlsanity.com/paper/2011.01118/) (2020)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems](https://mlsanity.com/paper/1908.05823/) (2019)
- [Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media](https://mlsanity.com/paper/1807.00882/) (2018)
- [Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling](https://mlsanity.com/paper/2109.06407/) (2021)
- [Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification](https://mlsanity.com/paper/1812.09444/) (2018)
- [Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity](https://mlsanity.com/paper/2203.08802/) (2022)
- [Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example](https://mlsanity.com/paper/2007.15580/) (2020)
- [A Gradient-based Deep Neural Network Model for Simulating Multiphase Flow in Porous Media](https://mlsanity.com/paper/2105.02652/) (2021)
- [Deep Learning-Accelerated 3D Carbon Storage Reservoir Pressure Forecasting Based on Data Assimilation Using Surface Displacement from InSAR](https://mlsanity.com/paper/2201.08543/) (2022)
- [Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network](https://mlsanity.com/paper/2110.10080/) (2021)
- [Physics-informed Convolutional Recurrent Surrogate Model for Reservoir Simulation with Well Controls](https://mlsanity.com/paper/2305.09056/) (2023)
- [Physics-Informed Localized Learning for Advection-Diffusion-Reaction Systems](https://mlsanity.com/paper/2305.03774/) (2023)

## Built on by (most cited first, 4 of 4)

- [Evaluating Modern Approaches in 3D Scene Reconstruction: NeRF vs Gaussian-Based Methods](https://mlsanity.com/paper/2408.04268/) (2024)
- [Utilizing Deep Learning to Optimize Software Development Processes](https://mlsanity.com/paper/2404.13630/) (2024)
- [Predict Click-Through Rates with Deep Interest Network Model in E-commerce Advertising](https://mlsanity.com/paper/2406.10239/) (2024)
- [Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning](https://mlsanity.com/paper/2401.02810/) (2024)

## Abstract (arXiv)

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network parameterizes the solution with time-varying controls to establish a control-to-state regression. Firstly, finite volume scheme is adopted to discretize flow equations and formulate loss function that respects mass conservation laws. Neumann boundary conditions are seamlessly incorporated into the semi-discretized equations so no additional loss term is needed. The network architecture comprises two parallel U-Net structures, with network inputs being well controls and outputs being the system states. To capture the time-dependent relationship between inputs and outputs, the network is well designed to mimic discretized state space equations. We train the network progressively for every timestep, enabling it to simultaneously predict oil pressure and water saturation at each timestep. After training the network for one timestep, we leverage transfer learning techniques to expedite the training process for subsequent timestep. The proposed model is used to simulate oil-water porous flow scenarios with varying reservoir gridblocks and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The results underscore the potential of PICNN in effectively simulating systems with numerous grid blocks, as computation time does not scale with model dimensionality. We assess the temporal error using 10 different testing controls with variation in magnitude and another 10 with higher alternation frequency with proposed control-to-state architecture. Our observations suggest the need for a more robust and reliable model when dealing with controls that exhibit significant variations in magnitude or frequency.