# Physics-Informed Graph Neural Network for Spatial-temporal Production Forecasting

arXiv: https://arxiv.org/abs/2209.11885 · HTML: https://mlsanity.com/paper/2209.11885/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 23 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [A Gradient-based Deep Neural Network Model for Simulating Multiphase Flow in Porous Media](https://mlsanity.com/paper/2105.02652/) (2021)

## Built on by (most cited first, 8 of 8)

- [A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classification](https://mlsanity.com/paper/2410.22377/) (2024)
- [A Critical Review of Physics-Informed Machine Learning Applications in Subsurface Energy Systems](https://mlsanity.com/paper/2308.04457/) (2023)
- [Actionable Interpretability via Causal Hypergraphs: Unravelling Batch Size Effects in Deep Learning](https://mlsanity.com/paper/2506.17826/) (2025)
- [On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition](https://mlsanity.com/paper/2507.08861/) (2025)
- [Beyond Grid Data: Exploring Graph Neural Networks for Earth Observation](https://mlsanity.com/paper/2411.03223/) (2024)
- [FieldFormer: Locality-Aware Transformers for Spatio-Temporal Modeling on Sparse Sensor Networks](https://mlsanity.com/paper/2510.03589/) (2025)
- [TG-PhyNN: An Enhanced Physically-Aware Graph Neural Network framework for forecasting Spatio-Temporal Data](https://mlsanity.com/paper/2408.16379/) (2024)
- [DIFFUMA: High-Fidelity Spatio-Temporal Video Prediction via Dual-Path Mamba and Diffusion Enhancement](https://mlsanity.com/paper/2507.06738/) (2025)

## Abstract (arXiv)

Production forecast based on historical data provides essential value for developing hydrocarbon resources. Classic history matching workflow is often computationally intense and geometry-dependent. Analytical data-driven models like decline curve analysis (DCA) and capacitance resistance models (CRM) provide a grid-free solution with a relatively simple model capable of integrating some degree of physics constraints. However, the analytical solution may ignore subsurface geometries and is appropriate only for specific flow regimes and otherwise may violate physics conditions resulting in degraded model prediction accuracy. Machine learning-based predictive model for time series provides non-parametric, assumption-free solutions for production forecasting, but are prone to model overfit due to training data sparsity; therefore may be accurate over short prediction time intervals. We propose a grid-free, physics-informed graph neural network (PI-GNN) for production forecasting. A customized graph convolution layer aggregates neighborhood information from historical data and has the flexibility to integrate domain expertise into the data-driven model. The proposed method relaxes the dependence on close-form solutions like CRM and honors the given physics-based constraints. Our proposed method is robust, with improved performance and model interpretability relative to the conventional CRM and GNN baseline without physics constraints.