Physics-informed machine learning for autonomous driving: From perception to control

Batteries, recognized as effective energy storage solutions, are considered the main facilitators of the world-wide transition towards clean and renewable energy sources. Among different types of batteries, lithium-ion (Li-ion) variants offer higher energy densities and relatively longer life spans when compared to other types. Nonetheless, a primary concern with these batteries is their lifetime. Batteries undergo various degradation mechanisms under storage and use, significantly impacting their lifespan. To this end, it is crucial to predict the degradation and lifetime of Li-ion batteries under given conditions.Researchers use three main methodologies to perform battery health diagnostics and to predict the lifetime of batteries. One approach revolves around using mechanistic, first-principle electrochemical models, also known as physics-based models. If equipped with proper thermodynamic theories, such models can show promising capabilities; however, holistic degradation prediction with these models is still challenging due to the computational complexities and the multitude of parameters that need to be fine-tuned in this approach. The other common strategy is to use empirical models to predict battery degradation. These models generally entail fewer parameters to be identified and are computationally less intensive to solve. Nonetheless, empirical models can suffer from the accuracy point-of-view as they are constrained to predict degradation trends introduced by certain degradation modes. Another common technique in battery life prediction is to utilize purely data-driven methods, such as machine learning (ML) algorithms, which also have shown promising results in the literature on rapid health predictions. However, these methods require large volumes of experimental data for training and testing ML models to ensure accuracy. In addition, data-driven methods are likely to extrapolate poorly to conditions beyond their training data and are indifferent towards the underlying degradation mechanisms. Recently, physics-informed machine learning (PI-ML) methods have garnered significant attention. They integrate physics-based or empirical models (developed based on physics) with a data-driven approach and allow one to train ML models on a smaller set of experimental data.To the best of the authors’ knowledge, the performance comparison between first-principle and empirical models when integrated within PI-ML remains unclear. Therefore, in this work, we aim to compare these two models when applied to prognostics (capacity forecasting and remaining useful life prediction) of a set of Li-ion batteries. To perform this study, we generate aging data for 40 Li-ion coin cells cycled under randomized conditions. Each cell undergoes a three-step charging stage followed by a two-step discharge stage. After obtaining the aging data, we will develop two PI-ML models, one equipped with a physics-based model and another with a set of empirical models. Both PI-ML models in this work will follow the sequential integration approach, where the training data for the final PI-ML model come from both experimental and computational data, the latter of which are obtained from the physics-based or empirical models. The parameters for the physics-based and empirical models are identified from another set of experimental data. Finally, the PI-ML models will be tested with experimental data obtained at different cycling conditions. The data flow for the sequential architecture of PI-ML is shown in the attached figure. This comparative study will help identify the performance of physics-based and empirical models when integrated into PI-ML. The main performance metric considered in this work is each model’s ability to extrapolate beyond the experimental training data set, hence aiding the final PI-ML model in generalizing to conditions not covered by its experimental training data set. Figure 1

Physics-based models for permeability prediction are essential for ensuring physically consistent reservoir characterization, yet they often fail to capture the full complexity of real geological systems. This study applies an explainable physics-informed machine learning (PIML) framework for discrepancy modeling to a legacy well dataset from a carbonate formation in southern Iraq. The dataset, originally comprising more than 2,400 samples from 10 wells, was heavily contaminated with incorrectly imputed or interpolated core permeability values. Through a rigorous zonation-based cleaning process, 1,130 high-quality samples were retained for modeling. A baseline physics model, built using well log–derived porosity and a porosity–permeability transform, was combined with a machine learning (ML) discrepancy model trained on three physics-informed features: neutron porosity (NPHI), the gamma ray/ bulk density (GR/RHOB) ratio, and depth. Three ML algorithms, Random Forest, XGBoost, and CatBoost, were evaluated, with five-fold cross-validation employed to ensure robustness. The discrepancy model effectively captured systematic biases in the physical model's predictions. When integrated into the boosted-ML frameworks, it delivered substantially higher permeability prediction performance, reducing root mean squared error (RMSE) by 56% and improving the adjusted coefficient of determination (adjusted R2) from −0.27 to 0.76 compared to the original physical model. These results demonstrate the strong potential of discrepancy-based ML-enhancement methodologies for improving permeability prediction in legacy well datasets. Explainable AI analysis using Shapley additive explanations (SHAP) to determine feature influence identified measured depth as the most influential predictor. Compaction effects not captured by the original physical model, GR/RHOB and NPHI also exerted substantial influence on the PIML permeability predictions. These findings not only improve permeability prediction performance but also reveal missing physics in the baseline model, enabling targeted refinement of physical relationships. This work highlights the feasibility and value of applying discrepancy-based PIML to noisy, incomplete legacy datasets, bridging the gap between empirical ML corrections and physically consistent modeling.

Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO_2 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 CO_2 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 400 000 times faster than the underlying physics-based simulator, allowing for near real-time analysis and robust uncertainty quantification.

Physics-informed machine learning framework for creep-fatigue life prediction of a Ni-based superalloy using ensemble learning

Physics-informed machine learning for battery degradation diagnostics: A comparison of state-of-the-art methods

Abstract. Despite showing great success of applications in many commercial fields, machine learning and data science models generally show limited success in many scientific fields, including hydrology (Karpatne et al., 2017). The approach is often criticized for its lack of interpretability and physical consistency. This has led to the emergence of new modelling paradigms, such as theory-guided data science (TGDS) and physics-informed machine learning. The motivation behind such approaches is to improve the physical meaningfulness of machine learning models by blending existing scientific knowledge with learning algorithms. Following the same principles in our prior work (Chadalawada et al., 2020), a new model induction framework was founded on genetic programming (GP), namely the Machine Learning Rainfall–Runoff Model Induction (ML-RR-MI) toolkit. ML-RR-MI is capable of developing fully fledged lumped conceptual rainfall–runoff models for a watershed of interest using the building blocks of two flexible rainfall–runoff modelling frameworks. In this study, we extend ML-RR-MI towards inducing semi-distributed rainfall–runoff models. The meaningfulness and reliability of hydrological inferences gained from lumped models may tend to deteriorate within large catchments where the spatial heterogeneity of forcing variables and watershed properties is significant. This was the motivation behind developing our machine learning approach for distributed rainfall–runoff modelling titled Machine Induction Knowledge Augmented – System Hydrologique Asiatique (MIKA-SHA). MIKA-SHA captures spatial variabilities and automatically induces rainfall–runoff models for the catchment of interest without any explicit user selections. Currently, MIKA-SHA learns models utilizing the model building components of two flexible modelling frameworks. However, the proposed framework can be coupled with any internally coherent collection of building blocks. MIKA-SHA's model induction capabilities have been tested on the Rappahannock River basin near Fredericksburg, Virginia, USA. MIKA-SHA builds and tests many model configurations using the model building components of the two flexible modelling frameworks and quantitatively identifies the optimal model for the watershed of concern. In this study, MIKA-SHA is utilized to identify two optimal models (one from each flexible modelling framework) to capture the runoff dynamics of the Rappahannock River basin. Both optimal models achieve high-efficiency values in hydrograph predictions (both at catchment and subcatchment outlets) and good visual matches with the observed runoff response of the catchment. Furthermore, the resulting model architectures are compatible with previously reported research findings and fieldwork insights of the watershed and are readily interpretable by hydrologists. MIKA-SHA-induced semi-distributed model performances were compared against existing lumped model performances for the same basin. MIKA-SHA-induced optimal models outperform the lumped models used in this study in terms of efficiency values while benefitting hydrologists with more meaningful hydrological inferences about the runoff dynamics of the Rappahannock River basin.

_ The relentless march of computational intelligence continues to redefine the paradigms of petroleum engineering, offering sophisticated solutions to long- standing challenges in subsurface characterization and operational optimization. A compelling triptych of recent research illuminates this trajectory, showcasing the burgeoning capacity of machine learning (ML) to unlock substantial efficiencies and enhance decision-making across the exploration and production lifecycle. Paper SPE 222299 presents a framework for synthesizing crucial openhole well logs by ingeniously leveraging readily available mud-log and logging-while-drilling data within the complex geological context of the Gulf of Thailand. The authors demonstrate that robust algorithms, particularly random forest and gradient-boosting regressors, can achieve remarkable predictive accuracy. This offers a pragmatic solution to populate data-deficient legacy wells, crucial for informed reservoir management, and promises tangible fiscal benefits by curtailing the necessity for costly conventional logging. Paper SPE 35892 introduces a physics-informed ML framework to elevate permeability prediction in notoriously heterogeneous carbonate reservoirs. By integrating physics-based constraints—specifically, modeling the discrepancy between core and nuclear-magnetic-resonance-derived permeability—this research enhances the predictive power of tree-ensemble algorithms. Physics-informed models transcend purely data-driven methodologies, offering more-robust and generalizable frameworks by embedding domain-specific physical understanding directly into the learning process, thereby bridging the gap between empirical observation and fundamental reservoir physics. Further exemplifying ML’s strategic value, paper SPE 224365 details an intelligent system for optimizing depth selection in formation pressure testing (FPT). An artificial neural network trained on an extensive suite of well logs demonstrates a remarkable 94% specificity in identifying depth intervals likely to yield invalid pressure data. This capability is paramount in minimizing resource expenditure on unproductive tests, particularly in complex reservoir settings. The model provides a data-driven, consistent alternative to traditional, often subjective, FPT planning, underscoring the value of ML in derisking and streamlining critical field operations. Collectively, these contributions signal a mature phase in the application of ML within the oil and gas sector. No longer confined to academic exploration, these techniques are providing robust, field-deployable solutions that enhance subsurface interpretation, improve operational foresight, and potentially drive economic benefits. The continued success of such endeavors will undoubtedly rely on the synergistic fusion of domain expertise, high-quality data, and the ever-evolving sophistication of ML algorithms. Summarized Papers in This August 2025 Issue SPE 222299 - Machine Learning Unlocks Potential of Mud Logs, LWD in the Gulf of Thailand by Sethawut Palviriyachote, Texas A&M University, et al. OTC 35892 - Machine-Learning Approach Optimizes Formation-Pressure Testing in Complex Reservoirs by Ahmed K. Khassaf, Basrah University of Oil and Gas, et al. SPE 224365 - Physics-Informed Machine Learning Enhances Permeability Prediction in Carbonate Reservoirs by Mohammad K. Aljishi, University of Oklahoma, et al. Recommended Additional Reading at OnePetro: www.onepetro.org. SPE 224566 - Applying Machine Learning in Highly Laminated Formation To Differentiate Pay and Nonpay Zones and Resolve Rt for Fit-for-Purpose Azimuthal Resistivity Tool Selection by Armando Vianna, Baker Hughes SPE 223396 - Early Signs of Gas Recognition Based on Machine-Learning Analysis of Passive Acoustics by Y. Maslennikova, TGT Diagnostics, et al.

Landfills are one of the major sources of greenhouse gas emissions worldwide. Over the past few decades, gas collection and energy conversion systems have been increasingly implemented in landfills to enhance sustainability and profitability. Accurate methane (CH4) generation rate estimates are essential for designing and optimizing these systems. However, due to the heterogeneity of waste properties, site-specific conditions, and the complex interrelated thermo-hydro-bio-mechanical processes involved, obtaining precise CH4 generation predictions is challenging. Although laboratory and field monitoring data provide valuable insights, obtaining such data is expensive and is often site-specific and non-generalizable. Process-based numerical models, such as the coupled thermo-hydro-bio-mechanical (CTHBM) model developed at the University of Illinois Chicago, offer reliable estimates but are computationally intensive for optimization tasks. Recent advancements in machine learning (ML) based data-driven modeling show promise in handling complex nonlinear datasets. This study evaluates the effectiveness of several ML models, including random forests (RF), extreme gradient boosting (XGB), multi-layer perceptron (MLP), and linear regression (LR), in predicting landfill CH4 generation rates. The data used to train these ML models is generated using the CTHBM model by varying several waste properties. Results indicate that during the rapid methane generation phase, the MLP model demonstrated excellent performance, while XGB also showed reasonable accuracy. In contrast, RF and LR models did not accurately predict methane generation rates during this phase. This study is a preliminary proof of concept for applying ML techniques in landfill CH4 prediction. Further exploration of advanced techniques, such as physics-informed ML, is recommended for scalable and generalizable predictions.

Physics informed machine learning (PIML) is a recently developed technique that combines knowledge about physical systems with deep learning to produce meshless solvers for partial differential equations. Herein we outline the use and limitations of physics informed neural nets and operator networks for optimization of cathodic protection. Leveraging outputs from Boundary Element Modelling (BEM) to train neural networks allows us to rapidly iterate and optimize the number and distribution of anodes in complex geometries such as heat exchangers and wharves. This technical paper presents a theoretical example of using PIML for optimizing cathodic protection (CP) design.

Machine learning drives a new paradigm in inorganic solid-state electrolytes research

The Interval Control Valve (ICV) tool goes through a rigorous bench-test called the System Integration Test (SIT) to ensure the tool is safe for use before downhole deployment. The data from each sensor is stored in separate streams. Manual analysis of this high-volume stream data (often up to ∼300k data points) is time-consuming and usually involves visual judgement of the traces, which is prone to inconsistency and mistakes. This paper aims to automate anomaly detection and compliance reporting to improve speed, accuracy, and repeatability of SIT validation. A physics-informed ensemble machine learning (ML) system was developed to automate the process of detecting anomalies for the subsurface ICV tool during SIT. An ensemble of 10 models was trained on unlabeled SIT data. This ensemble comprises both Isolation Forest and XGB residuals machine learning models. A web application was built that ingests data directly from the data source in the cloud, displays the analysis on a dashboard interface, and enables one-click PDF report generation. The ensemble achieved high accuracy; the physics-guided feature selection proved successful with the model achieving a mean F1 score of 0.93. Notably, a simple delta Temperature-based Isolation Forest outperformed more complex models in detecting seal leakage (F1 = 0.99), underscoring the value of domain knowledge in anomaly detection. The system demonstrated operational efficiency, batch processing ∼30k datapoints in 58 seconds with only 14 MB memory usage, making it lightweight enough for deployment without GPU resources. Detected anomalies included power drops, jittering choke positions, and temperature divergence, all of which correlate with failure modes identified by engineers. By automating SIT review, the system reduces analysis time from hours to minutes and ensures standardized, auditable documentation. The results highlight how lightweight ML models can accelerate SIT workflows, improve tool qualification, and reduce the risk of faulty tools reaching deployment. This work presents one of the first physics-informed ensemble ML systems applied to SIT of downhole completion tools. Unlike previous studies focusing on production surveillance, this solution targets the qualification stage, bridging anomaly detection with automated reporting.

Big data is one of the most important phenomena of the 21st century, creating unique opportunities and challenges in its processing and interpretation. Machine learning (ML), a subset of artificial intelligence (AI), has become a foundation of data science, which enables applications ranging from computer vision, geoscience, aviation and medicine. ML becomes important when establishing mathematical models that connect explanatory variables to predicted variables is impossible due to complexity. Deep learning (DL), a subset of ML, has revolutionized fields such as speech recognition, email filtering, and time series analysis. However, DL methods face challenges such as high data demand, overfitting, and the “black box” problem.We review least-squares-based deep learning (LSBDL), a framework that combines the interpretability of linear least squares (LS) theory with the flexibility and power of deep learning (DL). LS theory, widely used in engineering and geosciences, provides powerful tools for parameter estimation, quality control, and reliability through linear models. DL, on the other hand, deals with modelling complex nonlinear relationships where the mapping between explanatory and predicted variables is unknown. LSBDL bridges these approaches by formulating DL within the LS framework: training networks to establish a design matrix, an essential element of linear models. Through this integration, LSBDL enhances DL with transparency, statistical inference, and reliability. Gradient descent methods such as steepest descent and Gauss-Newton methods are used to construct an adaptive design matrix. By combining the transparency of LS theory with the data-driven adaptability of DL, LSBDL addresses challenges in different fields including geoscience, aviation, and data science. This approach not only improves the interpretability of DL models, but also extends the applicability of LS theory to nonlinear and complex systems, offering new opportunities for innovation and research.By embedding statistical foundations in the DL workflow, LSBDL offers a three-fold advantage: i) Direct computation of covariance matrices for predicted outcomes allows for quantitative assessment of model uncertainty. ii) Well-established theories of hypothesis testing and outlier detection facilitate the identification of model misspecifications and outlying data, and iii) The covariance matrix of observations can be used to train networks with statistically correlated, inconsistent, or heterogeneous datasets. Incorporating least squares principles increases model explainability, a critical aspect of interpretable and explainable artificial intelligence, and bridges the gap between traditional statistical methods and modern DL techniques. For example, LSBDL can incorporate prior knowledge using soft and hard physics-based constraints, a technique known as physics-informed machine learning (PIML).The approach is illustrated through three illustrative examples: Surface fitting, time series forecasting, and groundwater storage downscaling. Beyond these examples, LSBDL offers opportunities for various applications including geoscience, inverse problems, aviation, data assimilation, sensor fusion, and time series analysis.

Fuzzy machine learning predictions of settling velocity based on fractal aggregate physical features in water treatment

This chapter explores the application of machine learning (ML) techniques as an efficient alternative for permeability estimation, leveraging well log data to model complex nonlinear relationships. Various ML methods are discussed and compared, including artificial neural networks (ANNs) and ensemble techniques such as stochastic gradient boosting (SGB). A case study demonstrates the impact of feature selection, hyperparameter tuning, and model evaluation metrics on permeability prediction performance. The findings emphasize that SGB models offer a strong balance between accuracy and computational efficiency, significantly outperforming conventional techniques. Future research directions are highlighted, focusing on integrating physics-informed ML models, uncertainty quantification, transfer learning, and real-time permeability prediction for enhanced reservoir management and characterization.

Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material – including lecture videos per section, homeworks, data, and code in MATLAB®, Python, Julia, and R – available on databookuw.com.