# A Critical Review of Physics-Informed Machine Learning Applications in Subsurface Energy Systems

arXiv: https://arxiv.org/abs/2308.04457 · HTML: https://mlsanity.com/paper/2308.04457/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 183 references that are in the map.
- First posted on arXiv 6 Aug 2023.

## Builds on (most cited first, 30 of 43)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [UNet 3+: A Full-Scale Connected UNet for Medical Image Segmentation](https://mlsanity.com/paper/2004.08790/) (2020)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Physical Inertial Poser (PIP): Physics-aware Real-time Human Motion Tracking from Sparse Inertial Sensors](https://mlsanity.com/paper/2203.08528/) (2022)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Descending through a Crowded Valley - Benchmarking Deep Learning Optimizers](https://mlsanity.com/paper/2007.01547/) (2020)
- [Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport](https://mlsanity.com/paper/1912.02968/) (2019)
- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [Seismic wave propagation and inversion with Neural Operators](https://mlsanity.com/paper/2108.05421/) (2021)
- [Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions](https://mlsanity.com/paper/2105.09513/) (2021)
- [Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration](https://mlsanity.com/paper/2303.04778/) (2023)
- [A Progressive Batching L-BFGS Method for Machine Learning](https://mlsanity.com/paper/1802.05374/) (2018)
- [Visual Attention Methods in Deep Learning: An In-Depth Survey](https://mlsanity.com/paper/2204.07756/) (2022)
- [A Multi-Batch L-BFGS Method for Machine Learning](https://mlsanity.com/paper/1605.06049/) (2016)
- [Physics-Guided Architecture (PGA) of Neural Networks for Quantifying Uncertainty in Lake Temperature Modeling](https://mlsanity.com/paper/1911.02682/) (2019)
- [Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training](https://mlsanity.com/paper/2110.03049/) (2021)
- [Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity](https://mlsanity.com/paper/2203.08802/) (2022)

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

- [The Transparent Earth: A Multimodal Foundation Model for the Earth's Subsurface](https://mlsanity.com/paper/2509.02783/) (2025)
- [Evaluating the Stability of Deep Learning Latent Feature Spaces](https://mlsanity.com/paper/2402.11404/) (2024)
- [Unlocking the Invisible Urban Traffic Dynamics under Extreme Weather: A New Physics-Constrained Hamiltonian Learning Algorithm](https://mlsanity.com/paper/2512.03744/) (2025)
- [Toward Artificial Intelligence Enabled Earth System Coupling](https://mlsanity.com/paper/2604.03289/) (2026)

## Abstract (arXiv)

Machine learning has emerged as a powerful tool in various fields, including computer vision, natural language processing, and speech recognition. It can unravel hidden patterns within large data sets and reveal unparalleled insights, revolutionizing many industries and disciplines. However, machine and deep learning models lack interpretability and limited domain-specific knowledge, especially in applications such as physics and engineering. Alternatively, physics-informed machine learning (PIML) techniques integrate physics principles into data-driven models. By combining deep learning with domain knowledge, PIML improves the generalization of the model, abidance by the governing physical laws, and interpretability. This paper comprehensively reviews PIML applications related to subsurface energy systems, mainly in the oil and gas industry. The review highlights the successful utilization of PIML for tasks such as seismic applications, reservoir simulation, hydrocarbons production forecasting, and intelligent decision-making in the exploration and production stages. Additionally, it demonstrates PIML's capabilities to revolutionize the oil and gas industry and other emerging areas of interest, such as carbon and hydrogen storage; and geothermal systems by providing more accurate and reliable predictions for resource management and operational efficiency.