# Physics-Informed Neural Networks with Skip Connections for Modeling and Control of Gas-Lifted Oil Wells

arXiv: https://arxiv.org/abs/2403.02289 · HTML: https://mlsanity.com/paper/2403.02289/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 4 Mar 2024.

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

- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations](https://mlsanity.com/paper/1907.03507/) (2019)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [Physics Informed Neural Networks for Control Oriented Thermal Modeling of Buildings](https://mlsanity.com/paper/2111.12066/) (2021)
- [Physics-informed Dyna-Style Model-Based Deep Reinforcement Learning for Dynamic Control](https://mlsanity.com/paper/2108.00128/) (2021)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Optimizing the optimizer for data driven deep neural networks and physics informed neural networks](https://mlsanity.com/paper/2205.07430/) (2022)
- [Physics-Informed Deep Learning: A Promising Technique for System Reliability Assessment](https://mlsanity.com/paper/2108.10828/) (2021)

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

- [Solving Differential Equations using Physics-Informed Deep Equilibrium Models](https://mlsanity.com/paper/2406.03472/) (2024)
- [Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control](https://mlsanity.com/paper/2504.20019/) (2025)
- [Physics-Informed Neural Networks for Control of Single-Phase Flow Systems Governed by Partial Differential Equations](https://mlsanity.com/paper/2506.06188/) (2025)
- [Recurrent Neural Networks with Linear Structures for Electricity Price Forecasting](https://mlsanity.com/paper/2512.04690/) (2025)

## Abstract (arXiv)

Neural networks, while powerful, often lack interpretability. Physics-Informed Neural Networks (PINNs) address this limitation by incorporating physics laws into the loss function, making them applicable to solving Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs). The recently introduced PINC framework extends PINNs to control applications, allowing for open-ended long-range prediction and control of dynamic systems. In this work, we enhance PINC for modeling highly nonlinear systems such as gas-lifted oil wells. By introducing skip connections in the PINC network and refining certain terms in the ODE, we achieve more accurate gradients during training, resulting in an effective modeling process for the oil well system. Our proposed improved PINC demonstrates superior performance, reducing the validation prediction error by an average of 67% in the oil well application and significantly enhancing gradient flow through the network layers, increasing its magnitude by four orders of magnitude compared to the original PINC. Furthermore, experiments showcase the efficacy of Model Predictive Control (MPC) in regulating the bottom-hole pressure of the oil well using the improved PINC model, even in the presence of noisy measurements.