# Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management

arXiv: https://arxiv.org/abs/2206.10718 · HTML: https://mlsanity.com/paper/2206.10718/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 89 references that are in the map.
- First posted on arXiv 21 Jun 2022.

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

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Adversarial Uncertainty Quantification in Physics-Informed Neural Networks](https://mlsanity.com/paper/1811.04026/) (2018)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Don't Unroll Adjoint: Differentiating SSA-Form Programs](https://mlsanity.com/paper/1810.07951/) (2018)
- [A Robust Deep Learning Workflow to Predict Multiphase Flow Behavior during Geological CO2 Sequestration Injection and Post-Injection Periods](https://mlsanity.com/paper/2107.07274/) (2021)
- [A Gradient-based Deep Neural Network Model for Simulating Multiphase Flow in Porous Media](https://mlsanity.com/paper/2105.02652/) (2021)
- [A Physics-Constrained Deep Learning Model for Simulating Multiphase Flow in 3D Heterogeneous Porous Media](https://mlsanity.com/paper/2105.09467/) (2021)

## Built on by (most cited first, 7 of 7)

- [What You See is Not What You Get: Neural Partial Differential Equations and The Illusion of Learning](https://mlsanity.com/paper/2411.15101/) (2024)
- [Physics-informed Convolutional Recurrent Surrogate Model for Reservoir Simulation with Well Controls](https://mlsanity.com/paper/2305.09056/) (2023)
- [Model-Agnostic Knowledge Guided Correction for Improved Neural Surrogate Rollout](https://mlsanity.com/paper/2503.10048/) (2025)
- [Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management](https://mlsanity.com/paper/2508.19419/) (2025)
- [Learning to Optimize by Differentiable Programming](https://mlsanity.com/paper/2601.16510/) (2026)
- [Progressive reduced order modeling: empowering data-driven modeling with selective knowledge transfer](https://mlsanity.com/paper/2310.03770/) (2023)
- [Physics-informed reservoir characterization from bulk and extreme pressure events with a differentiable simulator](https://mlsanity.com/paper/2604.13291/) (2026)

## Abstract (arXiv)

Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. The heterogeneity typically requires high-fidelity physics-based models to make predictions on CO2 fate. Furthermore, characterizing the heterogeneity accurately is fraught with parametric uncertainty. Accounting for both, heterogeneity and uncertainty, makes this a computationally-intensive problem challenging for current reservoir simulators. To tackle this, we use differentiable programming with a full-physics model and machine learning to determine the fluid extraction rates that prevent over-pressurization at critical reservoir locations. We use DPFEHM framework, which has trustworthy physics based on the standard two-point flux finite volume discretization and is also automatically differentiable like machine learning models. Our physics-informed machine learning framework uses convolutional neural networks to learn an appropriate extraction rate based on the permeability field. We also perform a hyperparameter search to improve the model's accuracy. Training and testing scenarios are executed to evaluate the feasibility of using physics-informed machine learning to manage reservoir pressures. We constructed and tested a sufficiently accurate simulator that is 400000 times faster than the underlying physics-based simulator, allowing for near real-time analysis and robust uncertainty quantification.