# Physics-informed Convolutional Recurrent Surrogate Model for Reservoir Simulation with Well Controls

arXiv: https://arxiv.org/abs/2305.09056 · HTML: https://mlsanity.com/paper/2305.09056/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 15 May 2023.

## Builds on (most cited first, 9 of 9)

- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems](https://mlsanity.com/paper/1908.05823/) (2019)
- [Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data](https://mlsanity.com/paper/2109.12482/) (2021)
- [Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling](https://mlsanity.com/paper/2202.07022/) (2022)
- [Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management](https://mlsanity.com/paper/2206.10718/) (2022)
- [An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator](https://mlsanity.com/paper/2210.12177/) (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)

## 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)
- [Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls](https://mlsanity.com/paper/2310.06319/) (2023)
- [Multi-Step Embed to Control: A Novel Deep Learning-based Approach for Surrogate Modelling in Reservoir Simulation](https://mlsanity.com/paper/2409.09920/) (2024)

## Abstract (arXiv)

This paper presents a novel surrogate model for modeling subsurface fluid flow with well controls using a physics-informed convolutional recurrent neural network (PICRNN). The model uses a convolutional long-short term memory (ConvLSTM) to capture the spatiotemporal dependencies of the state evolution dynamics in the porous flow. The ConvLSTM is linked to the state space equations, enabling the incorporation of a discrete-time sequence of well control. The model requires initial state condition and a sequence of well controls as inputs, and predicts the state variables of the system, such as pressure, as output. By minimizing the residuals of reservoir flow state-space equations, the network is trained without the need for labeled data. The model is designed to serve as a surrogate model for predicting future reservoir states based on the initial reservoir state and input engineering controls. Boundary conditions are enforced into the state-space equations so no additional loss term is needed. Three numerical cases are studied, demonstrating the model's effectiveness in predicting reservoir dynamics based on future well/system controls. The proposed model provides a new approach for efficient and accurate prediction of subsurface fluid flow, with potential applications in optimal control design for reservoir engineering.