Advancing Structural Failure Analysis with Physics-Informed Machine Learning in Engineering Applications

Advanced material models and material characterization of soft biological tissues play an essential role in pre-surgical planning for vascular surgeries and transcatheter interventions. Recent advances in heart valve engineering, medical device and patch design are built upon these models. Furthermore, understanding vascular growth and remodeling in native and tissue-engineered vascular biomaterials, as well as designing and testing drugs on soft tissue, are crucial aspects of predictive regenerative medicine. Traditional nonlinear optimization methods and finite element (FE) simulations have served as biomaterial characterization tools combined with soft tissue mechanics and tensile testing for decades. However, results obtained through nonlinear optimization methods are reliable only to a certain extent due to mathematical limitations, and FE simulations may require substantial computing time and resources, which might not be justified for patient-specific simulations. To a significant extent, machine learning (ML) techniques have gained increasing prominence in the field of soft tissue mechanics in recent years, offering notable advantages over conventional methods. This review article presents an in-depth examination of emerging ML algorithms utilized for estimating the mechanical characteristics of soft biological tissues and biomaterials. These algorithms are employed to analyze crucial properties such as stress-strain curves and pressure-volume loops. The focus of the review is on applications in cardiovascular engineering, and the fundamental mathematical basis of each approach is also discussed. The review effort employed two strategies. First, the recent studies of major research groups actively engaged in cardiovascular soft tissue mechanics are compiled, and research papers utilizing ML and deep learning (DL) techniques were included in our review. The second strategy involved a standard keyword search across major databases. This approach provided 11 relevant ML articles, meticulously selected from reputable sources including ScienceDirect, Springer, PubMed, and Google Scholar. The selection process involved using specific keywords such as "machine learning" or "deep learning" in conjunction with "soft biological tissues", "cardiovascular", "patient-specific," "strain energy", "vascular" or "biomaterials". Initially, a total of 25 articles were selected. However, 14 of these articles were excluded as they did not align with the criteria of focusing on biomaterials specifically employed for soft tissue repair and regeneration. As a result, the remaining 11 articles were categorized based on the ML techniques employed and the training data utilized. ML techniques utilized for assessing the mechanical characteristics of soft biological tissues and biomaterials are broadly classified into two categories: standard ML algorithms and physics-informed ML algorithms. The standard ML models are then organized based on their tasks, being grouped into Regression and Classification subcategories. Within these categories, studies employ various supervised learning models, including support vector machines (SVMs), bagged decision trees (BDTs), artificial neural networks (ANNs) or deep neural networks (DNNs), and convolutional neural networks (CNNs). Additionally, the utilization of unsupervised learning approaches, such as autoencoders incorporating principal component analysis (PCA) and/or low-rank approximation (LRA), is based on the specific characteristics of the training data. The training data predominantly consists of three types: experimental mechanical data, including uniaxial or biaxial stress-strain data; synthetic mechanical data generated through non-linear fitting and/or FE simulations; and image data such as 3D second harmonic generation (SHG) images or computed tomography (CT) images. The evaluation of performance for physics-informed ML models primarily relies on the coefficient of determination . In contrast, various metrics and error measures are utilized to assess the performance of standard ML models. Furthermore, our review includes an extensive examination of prevalent biomaterial models that can serve as physical laws for physics-informed ML models. ML models offer an accurate, fast, and reliable approach for evaluating the mechanical characteristics of diseased soft tissue segments and selecting optimal biomaterials for time-critical soft tissue surgeries. Among the various ML models examined in this review, physics-informed neural network models exhibit the capability to forecast the mechanical response of soft biological tissues accurately, even with limited training samples. These models achieve high values ranging from 0.90 to 1.00. This is particularly significant considering the challenges associated with obtaining a large number of living tissue samples for experimental purposes, which can be time-consuming and impractical. Additionally, the review not only discusses the advantages identified in the current literature but also sheds light on the limitations and offers insights into future perspectives.

This video provides a brief recap of this introductory series on Physics Informed Machine Learning. We revisit the five stages of machine learning, and how physics may be incorporated into these stages. We also discuss architectures, symmetries, the digital twin, applications in engineering, and the importance of dynamical systems and controls benchmarks.

The issue focuses on physics-informed machine learning and its applications for structural integrity and safety assessment of engineering systems/facilities. Data science and data mining are fields in fast development with a high potential in several engineering research communities; in particular, advances in machine learning (ML) are undoubtedly enabling significant breakthroughs. However, purely ML models do not necessarily carry physical meaning, nor do they generalize well to scenarios on which they have not been trained on. This is an emerging field of research that potentially will raise a huge impact in the future for designing new materials and structures, and then for their proper final assessment. This issue aims to update the current research state of the art, incorporating physics into ML models, and providing tools when dealing with material science, fatigue and fracture, including new and sophisticated algorithms based on ML techniques to treat data in real-time with high accuracy and productivity. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Physics-informed machine learning: A comprehensive review on applications in anomaly detection and condition monitoring

Integrating physics-informed machine learning with resonance effect for structural dynamic performance modeling

Physics-informed machine learning (PIML), the combination of prior physics knowledge with data-driven machine learning models, has emerged as an effective means of mitigating a shortage of training data, increasing model generalizability, and ensuring physical plausibility of results. In this paper, we survey a wide variety of recent works in PIML and summarize them from three key aspects: 1) motivations of PIML, 2) physics knowledge in PIML, and 3) methods of physics knowledge integration in PIML. We additionally discuss current challenges and corresponding research opportunities in PIML.

Medical imaging is a cornerstone of modern healthcare, enabling precise diagnosis, treatment planning, and disease monitoring. Traditional machine learning (ML) approaches have significantly improved medical image analysis, yet they face challenges such as data scarcity, lack of interpretability, and variability in imaging protocols. Physics-Informed Machine Learning (PIML) offers a transformative solution by integrating fundamental physical laws, usually in partial differential equations and boundary conditions, into data-driven ML models. PIML constrains the solution space, enhances interpretability, and reduces the dependency on large, annotated datasets. This review provides an overview of the principles, methodologies, and applications of PIML in medical imaging, with a focus on imaging modalities such as MRI, CT, and ultrasound. We discuss the taxonomy of PIML approaches based on observational, inductive, and learning biases, showing their roles in enhancing model accuracy and generalization. Additionally, we explore the impact of PIML on image reconstruction, segmentation, enhancement, and anomaly detection, demonstrating its effectiveness in addressing noise, resolution, and diagnostic accuracy challenges. Despite its advantages, PIML faces challenges in the accurate representation of complex physiological processes, computational efficiency, and the integration of physics-based priors across diverse applications. This review points out future research directions including the development of hybrid models that combine PIML with deep learning techniques and large foundation models, improved benchmark datasets, and scalable algorithms for real-time applications. The findings of this review highlight PIML as a pivotal approach for advancing medical imaging, bridging the gap between theoretical models and practical implementation in clinical settings.

The development of machine learning (ML) provides a promising solution to guarantee the structural integrity of critical components during service period. However, considering the lack of respect for the underlying physical laws, the data hungry nature and poor extrapolation performance, the further application of pure data-driven methods in structural integrity is challenged. An emerging ML paradigm, physics-informed machine learning (PIML), attempts to overcome these limitations by embedding physical information into ML models. This paper discusses different ways of embedding physical information into ML and reviews the developments of PIML in structural integrity including failure mechanism modelling and prognostic and health management (PHM). The exploration of the application of PIML to structural integrity demonstrates the potential of PIML for improving consistency with prior knowledge, extrapolation performance, prediction accuracy, interpretability and computational efficiency and reducing dependence on training data. The analysis and findings of this work outline the limitations at this stage and provide some potential research direction of PIML to develop advanced PIML for ensuring structural integrity of engineering systems/facilities. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

As an emerging research field, physics-informed machine learning and its structural integrity applications may bring new opportunities to the intelligent solution of engineering problems. Pure data-driven approaches have some limitations when solving engineering problems due to lack of interpretability and data hungry applications. Therefore, further unlocking the potential of machine learning will be an important research direction in the future. Knowledge-driven machine learning methods may have a profound impact on future engineering research. The theme of this special issue focuses on more specific physics-informed machine learning methods and case studies. This issue presents a series of practical ideas to demonstrate the huge potential of physics-informed machine learning for solving engineering problems with high precision and efficiency.This article is part of the theme issue ‘Physics-informed machine learning and its structural integrity applications (Part 2)’.

Physics-informed machine learning (PIML) has gained significant attention in various scientific fields and is now emerging in the area of tribology. By integrating physics-based knowledge into machine learning models, PIML offers a powerful tool for understanding and optimizing phenomena related to friction, wear, and lubrication. Traditional machine learning approaches often rely solely on data-driven techniques, lacking the incorporation of fundamental physics. However, PIML approaches, for example, Physics-Informed Neural Networks (PINNs), leverage the known physical laws and equations to guide the learning process, leading to more accurate, interpretable and transferable models. PIML can be applied to various tribological tasks, such as the prediction of lubrication conditions in hydrodynamic contacts or the prediction of wear or damages in tribo-technical systems. This review primarily aims to introduce and highlight some of the recent advances of employing PIML in tribological research, thus providing a foundation and inspiration for researchers and R&D engineers in the search of artificial intelligence (AI) and machine learning (ML) approaches and strategies for their respective problems and challenges. Furthermore, we consider this review to be of interest for data scientists and AI/ML experts seeking potential areas of applications for their novel and cutting-edge approaches and methods.

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

A critical review of physics-informed machine learning applications in subsurface energy systems

Physics-informed machine learning model for battery state of health prognostics using partial charging segments

Discrete-time nonlinear feedback linearization via physics-informed machine learning

Performing initial orbit determination (IOD) using angles-only observations of cislunar objects is intractable via traditional methods due to a reliance on two-body gravitational assumptions. Recent research has suggested that physics-informed machine learning (PIML) IOD algorithms can address this gap via utilization of a regularization term that captures the known differential equations of three-body dynamics. While research has shown that such PIML algorithms can converge on high-accuracy trajectory estimates from a randomized initial state, a detailed study on the operational utility of the trajectory predictions has not been addressed. Toward this end, this paper introduces 1) a method to test the convergence of PIML IOD algorithms as a function of initial state error and 2) a batch estimation routine for the PIML algorithm that allows for the prediction of uncertainty in PIML trajectory estimates. We ultimately find that the PIML’s accuracy is sensitive to the initial trajectory estimate; this sensitivity is a function of both the initial state estimate as well as the pseudopotential region of the truth trajectory. We also find that the trajectory uncertainty derived using the batch estimation routine bounds the error in the trajectory solutions when the model converges on a solution with low line-of-sight error. We discuss how these results provide guidance on future algorithms that must be developed to improve explainability of and confidence in PIML algorithms for operational IOD.