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

TL;DR

This paper surveys physics-informed machine learning (PIML) with a focus on physics-informed neural networks (PINNs) applied to subsurface energy systems. It categorizes integration strategies (data/feature engineering, postprocessing, initialization, optimizer design, architecture, loss functions, and hybrids) and details theoretical PINN formulations for solving and discovering governing equations, including PDEs with initial/boundary conditions and coefficient discovery. The review maps applications across geoscience, drilling, reservoir engineering, production forecasting, and carbon storage, highlighting advances such as neural operators, graph neural networks, elastic FWI, and multiphysics PINNs, while addressing failure modes (loss weighting, optimizers, activation functions, sequence learning, curriculum learning) and proposed remedies. It concludes that while PIML will not replace high-fidelity simulators, it offers fast, physics-consistent surrogates to accelerate workflows, guide initial model construction, and support decision-making, with future work focusing on uncertainty quantification, handling sharp fronts, and scalable training in heterogeneous subsurface environments.

Abstract

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.

Figures (11)

• Figure 1: Various modes of physics integration within data-driven models, some examples for each mode, and where they fall on the physical knowledge/data availability spectrum.
• Figure 2: Typical architecture of a physics-informed neural network
• Figure 3: Helmholtz equation solution for a single point source (green dot) with uniform wave propagation velocity. The sinusoidal representation networks (SIREN) provide the most accurate solution when compared against grid solver Sitzmann2020.
• Figure 4: ($a$) Full architecture of Fourier neural network. A neural network $P$ projects the input $u$ into a higher dimension; then the input goes through Fourier layers before being projected to the target dimension using a network $Q$. $u$ is the output. ($b$) is a Fourier layer that takes an input $v$. On top: applies Fourier transform $\mathcal{F}$, filters out the higher Fourier modes using a linear transform $R$, then inverse Fourier transform $\mathcal{F}^{-1}$. On bottom: applies a local linear transform $W$Li2021.
• Figure 5: Seismic data interpolation using PINNs, where (a) is the original seismic data, (b) is PINN output, and (c) is their difference. Red lines denote regions with missing traces Brandolin2022.