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

Benjin Wang; Peng Zhang; Yujie Xiang; Dalei Wang; Baijian Wu; Xianqiao Wang; Keke Tang; Airong Chen

doi:10.1016/j.eng.2025.10.003

Engineering ›› DOI: 10.1016/j.eng.2025.10.003

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

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Abstract

While machine learning (ML) shows significant potential for structural-failure analysis, purely data-driven approaches face critical limitations, including data scarcity, lack of physical consistency, and poor interpretability in safety–critical applications. Physics-informed ML (PIML) addresses these challenges by integrating physical principles with data-driven methods, thereby enabling accurate and interpretable predictions, while maintaining physical consistency. This study presents a systematic categorization of PIML implementation strategies in structural-failure analysis, classifying the approaches into four distinct categories: physics-guided data manipulation, physics-inspired architectural design, physics-constrained loss functions, and hybrid physics–ML models. We examined the applications across the complete failure lifecycle, from mechanism analysis and fatigue-life prediction to structural-health monitoring and post-failure analysis, to demonstrate how different PIML strategies address specific engineering challenges. Through a critical evaluation of representative studies, we identified the current limitations, including data-integration complexities, physics-formalization difficulties, and computational trade-offs between accuracy and efficiency. Future research directions emphasize multisource knowledge fusion, transferable PIML frameworks, and enhanced post-failure analysis capabilities. This systematic framework provides clear guidance for selecting appropriate PIML strategies based on application requirements and available resources, thereby advancing the reliability and safety of engineering structures.

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Machine learning / Physics-informed machine learning / Structural-failure analysis / Engineering applications

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Benjin Wang, Peng Zhang, Yujie Xiang, Dalei Wang, Baijian Wu, Xianqiao Wang, Keke Tang, Airong Chen. Advancing Structural Failure Analysis with Physics-Informed Machine Learning in Engineering Applications. Engineering DOI:10.1016/j.eng.2025.10.003

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References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Bergant MA, Yawny AA, Perez JE Ipiña.Structural integrity assessments of steam generator tubes using the FAD methodology.Nucl Eng Des 2015; 295:457-467.

[2]	Cicero S, Madrazo V, Carrascal IA, Cicero R.Assessment of notched structural components using failure assessment diagrams and the theory of critical distances.Eng Fract Mech 2011; 78(16):2809-2825.

[3]	Delatte N.Failure literacy in structural engineering.Eng Struct 2010; 32(7):1952-1954.

[4]	Zhu SP, Niu X, Keshtegar B, Luo C, Bagheri M.Machine learning-based probabilistic fatigue assessment of turbine bladed disks under multisource uncertainties.Int J Struct Integr 2023; 14(6):1000-1024.

[5]	Wang D, Wang L, Liu Y, Tan B, Liu Y.Failure mechanism investigation of bottom plate in concrete box girder bridges.Eng Fail Anal 2020; 116:104711.

[6]	Feng J, Wang E, Huang Q, Ding H, Zhang X.Experimental and numerical study of failure behavior and mechanism of coal under dynamic compressive loads.Int J Min Sci Technol 2020; 30(5):613-621.

[7]	Han W, Jiang Y, Luan H, Liu J, Wu X, Du Y.Fracture evolution and failure mechanism of rock-like materials containing cross-flaws under the shearing effect.Theor Appl Fract Mech 2020; 110:102815.

[8]	Wang B, He P, Ma Y, Wang D, Chen A.Fatigue failure criteria for OSDs considering penetrating cracks and effects on pavements.J Constr Steel Res 2024; 219:108774.

[9]	Chen Y, Li YY, Kang R, Ali M.Reliability analysis of PMS with failure mechanism accumulation rules and a hierarchical method.Reliab Eng Syst Saf 2020; 197:106774.

[10]	Ravindra GHR, Gronz O, Dost JB, Sigtryggsdóttir FG.Description of failure mechanism in placed riprap on steep slope with unsupported toe using smartstone probes.Eng Struct 2020; 221:111038.

[11]	Deng X, Hu Y, Yi Y, Kan Q, Kang G.Influence of build direction and loading rate on the cyclic deformation of laser additively manufactured Ti6Al4V alloy.Eng Fail Anal 2025; 171:109367.

[12]	Zhang J, Song Z, Wu Z, Huang X, Kan Q.Cyclic deformation behavior of medium-manganese transformation-induced plasticity steel at elevated temperatures: mechanical tests and microstructural characterization.Int J Fatigue 2025; 195:108866.

[13]	Sun X, Huang L, Xiao BG, Zhang Q, Li JQ, Ding YH, et al.X-ray computed tomography in metal additive manufacturing: a review on prevention, diagnostic, and prediction of failure.Thin-walled Struct 2025; 207:112736.

[14]	Deng X, Zhu SP, Wang L, Luo C, Fu S, Wang Q.Probabilistic framework for strain-based fatigue life prediction and uncertainty quantification using interpretable machine learning.Int J Fatigue 2025; 190:108647.

[15]	Zhang P, Tang K.A TCN-based feature fusion framework for multiaxial fatigue life prediction: bridging loading dynamics and material characteristics.Int J Fatigue 2025; 197:108915.

[16]	Srinivasan DV, Moradi M, Komninos P, Zarouchas D, Vassilopoulos AP.A generalized machine learning framework to estimate fatigue life across materials with minimal data.Mater Des 2024; 246:113355.

[17]	Wang D, Ning Y, Xiang C, Chen A.A two-stage network framework for topology optimization incorporating deep learning and physical information.Eng Appl Artif Intell 2024; 133:108185.

[18]	Wang D, Zhang Y, Pan Y, Peng B, Liu H, Ma R.An automated inspection method for the steel box girder bottom of long-span bridges based on deep learning.IEEE Access 2020; 8:94010-94023.

[19]	Cong J, Liu Z, Zhou S, Gao S, Zhu X.Predicting fatigue life and crack growth rate of TC4 titanium alloy based on PINN before and after ultrasonic impact treatment.Eng Fail Anal 2024; 166:108875.

[20]	Roy A, Chatterjee T, Adhikari S.A physics-informed neural network enhanced importance sampling (PINN-IS) for data-free reliability analysis.Probab Eng Mech 2024; 78:103701.

[21]	Wang H, Li B, Gong J, Xuan FZ.Machine learning-based fatigue life prediction of metal materials: perspectives of physics-informed and data-driven hybrid methods.Eng Fract Mech 2023; 284:109242.

[22]	Guo K, Ma J, Wu J, Xiong X.Adaptive feature fusion and disturbance correction for accurate remaining useful life prediction of rolling bearings.Eng Appl Artif Intell 2024; 138:109433.

[23]	Zhang G, Liu G, Lu Z, Yan C, Xu L, Gao Q, et al.Evaluation method for health state of highway tunnel structure based on adaptive comprehensive weighting.Eng Fail Anal 2024; 163:108597.

[24]	Caglio L, Sadeqi A, Stang H, Katsanos E.Joint input-state estimation of structures subjected to complex loads via augmented Kalman filter with physics informed latent force models.Mech Syst Signal Process 2025; 223:111852.

[25]	Hu Y, She Y, Wu S, Kan Q, Yu H, Kang G.Critical physics-informed fatigue life prediction of laser 3D printed AlSi10Mg alloys with mass internal defects.Int J Mech Sci 2024; 284:109730.

[26]	Di F Trapani, Oddo MC, Sberna AP, La L Mendola.Structural health monitoring of masonry structures using stress sensors: experimental induced damage tests and proposed approach for real-time monitoring.Constr Build Mater 2024; 449:138077.

[27]

Vorobel R, Student O, Ivasenko I, Maruschak P, Krechkovska H, Zvirko O, et al.Development of a method for computer processing of fractographic images to assess the cohesion of inclusions to the matrix in the weld metal after its operational degradation and hydrogenation.Materialia (Oxf) 2024; 34:102074.

[28]	Bastidas-Rodriguez MX, Polania L, Gruson A, Prieto-Ortiz F.Deep learning for fractographic classification in metallic materials.Eng Fail Anal 2020; 113:104532.

[29]	Zhu SP, Wang L, Luo C, Correia JAFO, De AMP Jesus, Berto F, et al.Physics-informed machine learning and its structural integrity applications: state of the art.Philos Trans A Math Phys Eng Sci 2023; 381(2260):20220406.

[30]	Hou J, Jiang H, Wan C, Yi L, Gao S, Ding Y, et al.Deep learning and data augmentation based data imputation for structural health monitoring system in multi-sensor damaged state.Measurement 2022; 196:111206.

[31]	Hayashi K, Shimabukuro M, Kishida R, Tsuchiya A, Ishikawa K.Structurally optimized honeycomb scaffolds with outstanding ability for vertical bone augmentation.J Adv Res 2022; 41:101-112.

[32]	Yadav D, Sekar K, Ramu P.Adaptive sampling based estimation of small probability of failure using interpretable self-organising map.Struct Saf 2024; 109:102470.

[33]	Xiao S, Bai J, Jeong H, Alzubaidi L, Gu YT.A meshless Runge-Kutta-based physics-informed neural network framework for structural vibration analysis.Eng Anal Bound Elem 2025; 170:106054.

[34]	Wu Y, Sicard B, Gadsden SA.Physics-informed machine learning: a comprehensive review on applications in anomaly detection and condition monitoring.Expert Syst Appl 2024; 255:124678.

[35]	Daneshvar MH, Gharighoran A, Zareei SA, Karamodin A.Structural health monitoring using high-dimensional features from time series modeling by innovative hybrid distance-based methods.J Civ Struct Health Monit 2021; 11(2):537-557.

[36]	Akrim A, Gogu C, Vingerhoeds R, Salaün M.Self-supervised learning for data scarcity in a fatigue damage prognostic problem.Eng Appl Artif Intell 2023; 120:105837.

[37]	Wang L, Zhu SP, Luo C, Liao D, Wang Q.Physics-guided machine learning frameworks for fatigue life prediction of AM materials.Int J Fatigue 2023; 172:107658.

[38]	Latrach A, Malki ML, Morales M, Mehana M, Rabiei M.A critical review of physics-informed machine learning applications in subsurface energy systems.Geoenergy Sci Eng 2024; 239:212938.

[39]	Alzubaidi L, Bai J, Al-Sabaawi A, Santamaría J, Albahri AS, Al-dabbagh BSN, et al.A survey on deep learning tools dealing with data scarcity: definitions, challenges, solutions, tips, and applications.J Big Data 2023; 10(1):46.

[40]	Deng W, Nguyen KTP, Gogu C, Morio J, Medjaher K.Physics-informed lightweight temporal convolution networks for fault prognostics associated to bearing stiffness degradation, The Prognostics and Health Management Society, Turin, Italy. Ottawa (2022), pp. 118-125

[41]	Karolczuk A, Kurek M.Fatigue life uncertainty prediction using the Monte Carlo and Latin hypercube sampling techniques under uniaxial and multiaxial cyclic loading.Int J Fatigue 2022; 160:106867.

[42]	Qian H, Huang Z, Xu Y, Zhou Q, Wang J, Shen J, et al.Very high cycle fatigue life prediction of Ti60 alloy based on machine learning with data enhancement.Eng Fract Mech 2023; 289:109431.

[43]	Luleci F, Necati F Catbas, Avci O.CycleGAN for undamaged-to-damaged domain translation for structural health monitoring and damage detection.Mech Syst Signal Process 2023; 197:110370.

[44]	Jin Z, Teng S, Zhang J, Chen G, Cui F.Structural damage recognition based on filtered feature selection and convolutional neural network.Int J Struct Stab Dyn 2022; 22(12):2250134.

[45]	Li Q, Fu N, Omee SS, Hu J.MD-HIT: machine learning for material property prediction with dataset redundancy control.Npj Comput Mater 2024; 10:245.

[46]	Dang HV, Tran-Ngoc H, Nguyen TV, Bui-Tien T, De G Roeck, Nguyen HX.Data-driven structural health monitoring using feature fusion and hybrid deep learning.IEEE Trans Autom Sci Eng 2020; 18(4):2087-2103.

[47]	He GY, Zhao YX, Yan CL.Multiaxial fatigue life prediction using physics-informed neural networks with sensitive features.Eng Fract Mech 2023; 289:109456.

[48]	Feng F, Zhu T, Yang B, Zhou S, Xiao S.A physics-informed neural network approach for predicting fatigue life of SLM 316L stainless steel based on defect features.Int J Fatigue 2024; 188:108486.

[49]	Wang H, Li B, Xuan FZ.Fatigue-life prediction of additively manufactured metals by continuous damage mechanics (CDM)-informed machine learning with sensitive features.Int J Fatigue 2022; 164:107147.

[50]	Swischuk R, Mainini L, Peherstorfer B, Willcox K.Projection-based model reduction: formulations for physics-based machine learning.Comput Fluids 2019; 179:704-717.

[51]	Zhang P, Tang K, Wang A, Wu H, Zhong Z.Neural network integrated with symbolic regression for multiaxial fatigue life prediction.Int J Fatigue 2024; 188:108535.

[52]	Chen Z, Liu Y, Sun H.Physics-informed learning of governing equations from scarce data.Nat Commun 2021; 12(1):6136.

[53]	Huang Z, Zhao W, Gao J, Hu Z, Luo X, Cao Y, et al.Physics-informed regularization for domain-agnostic dynamical system modeling., arXiv:2410.06366 (2024)

[54]	Sawant N, Kramer B, Peherstorfer B.Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference.Comput Methods Appl Mech Eng 2023; 404:115836.

[55]	Zhou T, Jiang S, Han T, Zhu SP, Cai Y.A physically consistent framework for fatigue life prediction using probabilistic physics-informed neural network.Int J Fatigue 2023; 166:107234.

[56]	Cuomo S, Di VS Cola, Giampaolo F, Rozza G, Raissi M, Piccialli F.Scientific machine learning through physics-informed neural networks: where we are and what’s next.J Sci Comput 2022; 92(3):88.

[57]	Chen J, Liu Y.Fatigue property prediction of additively manufactured Ti-6Al-4V using probabilistic physics-guided learning.Addit Manuf 2021; 39:101876.

[58]	Li H, Zhang Z, Li T, Si X.A review on physics-informed data-driven remaining useful life prediction: challenges and opportunities.Mech Syst Signal Process 2024; 209:111120.

[59]	Raissi M, Perdikaris P, Karniadakis G.Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.J Comput Phys 2019; 378:686-707.

[60]	Wu Z, Li Y.An adaptive physics-informed deep learning approach for structural nonlinear response prediction.J Supercomput 2025; 81(1):92.

[61]	Ryu I, Park G, Lee Y, Choi DH.Physics-informed neural network for engineers: a review from an implementation aspect.J Mech Sci Technol 2024; 38(7):3499-3519.

[62]	Worthington M, Chew H.Crack path predictions in heterogeneous media by machine learning.J Mech Phys Solids 2023; 172:105188.

[63]	Jia X, Willard J, Karpatne A, Read JS, Zwart JA, Steinbach M, et al.Physics-guided machine learning for scientific discovery: an application in simulating lake temperature profiles.ACM IMS Trans Data Sci 2021; 2(3):1-26.

[64]	Liang R, Liu W, Fu Y, Ma M.Physics-informed deep learning for structural dynamics under moving load.Int J Mech Sci 2024; 284:109766.

[65]	Chen D, Li Y, Liu K, Li Y.A physics-informed neural network approach to fatigue life prediction using small quantity of samples.Int J Fatigue 2023; 166:107270.

[66]	Lee R, Mulder E, Hopkins J.Mechanical neural networks: architected materials that learn behaviors. Sci Robot, 7(71):abq7278 (2022)

[67]	Zhang J, Ding C.Simple yet effective adaptive activation functions for physics-informed neural networks.Comput Phys Commun 2025; 307:109428.

[68]	Abbasi J, Andersen P.Physical activation functions (PAFs): an approach for more efficient induction of physics into physics-informed neural networks (PINNs).Neurocomputing 2024; 608:128352.

[69]	Jagtap A, Kawaguchi K, Karniadakis G.Adaptive activation functions accelerate convergence in deep and physics-informed neural networks.J Comput Phys 2020; 404:109136.

[70]	Chen J, Liu Y.Probabilistic physics-guided machine learning for fatigue data analysis.Expert Syst Appl 2021; 168:114316.

[71]	Li H, Zhao H, Shen Y, Zheng S, Zhang R.Structural health monitoring and failure analysis of large-scale hydro-steel structures, based on multi-sensor information fusion.Water 2024; 16(22):3167.

[72]	Shen W, Tian X, Zeng D, Zhang Y.Multi-scale image compression and reconstruction algorithm for structural health monitoring system.Eng Struct 2024; 315:118516.

[73]	Chen Z, Liu Q, Ding Z, Liu F.Automated structural resilience evaluation based on a multi-scale transformer network using field monitoring data.Mech Syst Signal Process 2025; 222:111813.

[74]	Mantawy IM, Mantawy MO.Convolutional neural network based structural health monitoring for rocking bridge system by encoding time‐series into images.Struct Contr Health Monit 2022; 29(3):e2897.

[75]	Goswami S, Anitescu C, Chakraborty S, Rabczuk T.Transfer learning enhanced physics informed neural network for phase-field modeling of fracture.Theor Appl Fract Mech 2020; 106:102447.

[76]	LeCun Y, Bengio Y, Hinton G.Deep learning.Nature 2015; 521(7553):436-444.

[77]	Rumelhart DE, Hinton GE, Williams RJ.Learning representations by back-propagating errors.Nature 1986; 323(6088):533-536.

[78]	Bai J, Rabczuk T, Gupta A, Alzubaidi L, Gu Y.A physics-informed neural network technique based on a modified loss function for computational 2D and 3D solid mechanics.Comput Mech 2023; 71(3):543-562.

[79]	Nicodemus J, Kneifl J, Fehr J, Unger B.Physics-informed neural networks-based model predictive control for multi-link manipulators.IFAC-PapersOnLine 2022; 55(20):331-336.

[80]	Cai S, Wang Z, Wang S, Perdikaris P, Karniadakis GE.Physics-informed neural networks for heat transfer problems.J Heat Transfer 2021; 143(6):060801.

[81]	Lu L, Pestourie R, Yao W, Wang Z, Verdugo F, Johnson SG.Physics-informed neural networks with hard constraints for inverse design.SIAM J Sci Comput 2021; 43(6):B1105-B1132.

[82]	Chen H, Flores GEC, Li C.Physics-informed neural networks with hard linear equality constraints.Comput Chem Eng 2024; 189:108764.

[83]	Ning L, Cai Z, Dong H, Liu Y, Wang W.Physics-informed neural network frameworks for crack simulation based on minimized peridynamic potential energy.Comput Methods Appl Mech Eng 2023; 417:116430.

[84]	Li X, Deng J, Wu J, Zhang S, Li W, Wang YG.Physical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansions.Comput Math Appl 2024; 159:60-75.

[85]	Wang L, Zhu SP, Luo C, Niu X, He JC.Defect driven physics-informed neural network framework for fatigue life prediction of additively manufactured materials.Philos Trans A Math Phys Eng Sci 2023; 381(2260):20220386.

[86]	Liao W, Long X, Jiang C.A physics-informed neural network method for identifying parameters and predicting remaining life of fatigue crack growth.Int J Fatigue 2025; 191:108678.

[87]	Xu X, Liu C.Physics-guided deep learning for damage detection in CFRP composite structures.Compos Struct 2024; 331:117889.

[88]	Zhou K, Sun H, Enos R, Zhang D, Tang J.Harnessing deep learning for physics-informed prediction of composite strength with microstructural uncertainties.Comput Mater Sci 2021; 197:110663.

[89]	Lu J, Tao T, Yan J, Liu Y.Pre-calculation of wind turbine blade fatigue damage by machine learning. In: Proceedings of the 10th Renewable Power Generation Conference (RPG 2021); 2021 Oct 14–15; Held virtually. New York City: IEEE; 2021. p. 1067–72.

[90]	Djeziri MA, Benmoussa S, Sanchez R.Hybrid method for remaining useful life prediction in wind turbine systems.Renew Energy 2018; 116:173-187.

[91]	Vu PA, Aldea E, Bouarroudj M, H SLégarat-Mascle..Probabilistic and physics-informed machine learning for predictive maintenance with time series data, IEEE, Graz, Austria. New York City (2023), pp. 1-8

[92]	Zhang W, Zhao M, Du X, Gao Z, Ni P.Probabilistic machine learning approach for structural reliability analysis.Probab Eng Mech 2023; 74:103502.

[93]	Linka K, Schäfer A, Meng X, Zou Z, Karniadakis GE, Kuhl E.Bayesian physics informed neural networks for real-world nonlinear dynamical systems.Comput Methods Appl Mech Eng 2022; 402:115346.

[94]	Wang T, Bahrami Z, Renaud G, Yang C, Liao M, Liu Z.A probabilistic model for fatigue crack growth prediction based on closed-form solution.Structures 2022; 44:1583-1596.

[95]	Lorenzoni F, Casarin F, Caldon M, Islami K, Modena C.Uncertainty quantification in structural health monitoring: applications on cultural heritage buildings.Mech Syst Signal Process, 66–67 2016; 268-281.

[96]	Sarmadi H, Yuen K.Structural health monitoring by a novel probabilistic machine learning method based on extreme value theory and mixture quantile modeling.Mech Syst Signal Process 2022; 173:109049.

[97]	Tu H, Moura S, Wang Y, Fang H.Integrating physics-based modeling with machine learning for lithium-ion batteries.Appl Energy 2023; 329:120289.

[98]	Abbasi A, Kambali P, Shahidi P, Nataraj C.Physics-informed machine learning for modeling multidimensional dynamics.Nonlinear Dyn 2024; 112(24):21565-21585.

[99]	Jiao S, Li W, Li Z, Gai J, Zou L, Su Y.Hybrid physics–machine learning models for predicting rate of penetration in the Halahatang oil field, Tarim Basin.Sci Rep 2024; 14(1):5957.

[100]

Xu Y, Kohtz S, Boakye J, Gardoni P, Wang P.Physics-informed machine learning for reliability and systems safety applications: state of the art and challenges.Reliab Eng Syst Saf 2023; 230:108900.

[101]

Gan L, Fan Z, Wu H, Zhong Z.Prediction of multiaxial fatigue life with a data-driven knowledge transfer model.Int J Fatigue 2025; 190:108636.

[102]

Go MS, Noh HK, Hyuk LJ.Real-time full-field inference of displacement and stress from sparse local measurements using physics-informed neural networks.Mech Syst Signal Process 2025; 224:112009.

[103]

Dourado AD, Viana F.Physics-informed neural networks for bias compensation in corrosion-fatigue, American Institute of Aeronautics and Astronautics, Orlando, FL, USA. Reston (2020), p. 1149

[104]

Zhang P, Tang K, Chen G, Li J, Li Y.Multimodal data fusion enhanced deep learning prediction of crack path segmentation in CFRP composites.Compos Sci Technol 2024; 257:110812.

[105]

Chen S, Kalanat N, Xie Y, Li S, Zwart JA, Sadler JM, et al.Physics-guided machine learning from simulated data with different physical parameters.Knowl Inf Syst 2023; 65(8):3223-3250.

[106]

Lei Y, Li J, Hao H.Physics-guided deep learning based on modal sensitivity for structural damage identification with unseen damage patterns.Eng Struct 2024; 316:118510.

[107]

Gan L, Wang A, Zhong Z, Wu H.Multiaxial fatigue life prediction based on modular neural network pretrained with uniaxial fatigue data. Eng Comput, 0852 (2024 May)

[108]

Gan L, Wu H, Zhong Z.Fatigue life prediction in presence of mean stresses using domain knowledge‐integrated ensemble of extreme learning machines.Fatigue Fract Eng Mater Struct 2022; 45(9):2748-2766.

[109]

Ma Y, Wang B, Chen A.Inspection data‐based prediction on fatigue crack of orthotropic steel deck using interpretable machine learning method.Fatigue Fract Eng Mater Struct 2024; 47(10):3874-3893.

[110]

Jiang L, Hu Y, Li H, Shao X, Zhang X, Kan Q, et al.A cGAN-based fatigue life prediction of 316 austenitic stainless steel in high-temperature and high-pressure water environments.Int J Fatigue 2025; 190:108633.

[111]

Gan L, Wu H, Zhong Z.Integration of symbolic regression and domain knowledge for interpretable modeling of remaining fatigue life under multistep loading.Int J Fatigue 2022; 161:106889.

[112]

Santecchia E, Hamouda AMS, Musharavati F, Zalnezhad E, Cabibbo M, El M Mehtedi, et al.A review on fatigue life prediction methods for metals.Adv Mater Sci Eng 2016; 2016:9573524.

[113]

He G, Zhao Y, Yan C.MFLP-PINN: a physics-informed neural network for multiaxial fatigue life prediction.Eur J Mech A, Solids 2023; 98:104889.

[114]

He G, Zhao Y, Yan C.A physics‐informed generative adversarial network framework for multiaxial fatigue life prediction.Fatigue Fract Eng Mater Struct 2023; 46(10):4036-4052.

[115]

Jiang L, Hu Y, Liu Y, Zhang X, Kang G, Kan Q.Physics-informed machine learning for low-cycle fatigue life prediction of 316 stainless steels.Int J Fatigue 2024; 182:108187.

[116]

Fan J, Zhu G, Zhu M, Xuan FZ.A data-physics integrated approach to life prediction in very high cycle fatigue regime.Int J Fatigue 2023; 176:107917.

[117]

Chen B, Zhang J, Zhou S, Zhang G, Xu F.Physics-informed transfer learning model for fatigue life prediction of IN718 alloy.J Mater Res Technol 2024; 32:2767-2779.

[118]

Liu H, Ding X, Liu J, Zhang Y, Zhang B, Li E, et al.A physics-informed neural network model for combined high and low cycle fatigue life prediction.Mech Mater 2025; 209:105429.

[119]

Abiria I, Wang C, Zhang Q, Liu C, Jin X.High-cycle and very-high-cycle fatigue life prediction in additive manufacturing using hybrid physics-informed neural networks.Eng Fract Mech 2025; 319:111026.

[120]

Zhou S, Henrich M, Wei Z, Feng F, Yang B, Münstermann S.A general physics-informed neural network framework for fatigue life prediction of metallic materials.Eng Fract Mech 2025; 322:111136.

[121]

Zhao S, Zhang Y, Wang S, Zhou B, Cheng C.A recurrent neural network approach for remaining useful life prediction utilizing a novel trend features construction method.Measurement 2019; 146:279-288.

[122]

Zheng S, Ristovski K, Farahat A, Gupta C.Long short-term memory network for remaining useful life estimation, IEEE, Dallas, TX, USA. New York City (2017), pp. 88-95

[123]

Li X, Zhang W, Ding Q.Deep learning-based remaining useful life estimation of bearings using multi-scale feature extraction.Reliab Eng Syst Saf 2019; 182:208-218.

[124]

Lu Z, Guo C, Liu M, Shi R.Remaining useful lifetime estimation for discrete power electronic devices using physics-informed neural network.Sci Rep 2023; 13(1):10167.

[125]

Liu Z, Zheng X, Xue A, Ge M.Multi-scale temporal-spatial feature-based hybrid deep neural network for remaining useful life prediction of aero-engine.ACS Omega 2024; 9(48):47410-47427.

[126]

Ma R, Zhang Z, Dong Y, Pan Y.Deep learning based vehicle detection and classification methodology using strain sensors under bridge deck.Sensors 2020; 20(18):5051.

[127]

Wang D, Dong Y, Pan Y, Ma R.Machine vision-based monitoring methodology for the fatigue cracks in U-rib-to-deck weld seams.IEEE Access 2020; 8:94204-94219.

[128]

Ge L, Sadhu A.Domain adaptation for structural health monitoring via physics-informed and self-attention-enhanced generative adversarial learning.Mech Syst Signal Process 2024; 211:111236.

[129]

Ye J, Do NC, Zeng W, Lambert M.Physics-informed neural networks for hydraulic transient analysis in pipeline systems.Water Res 2022; 221:118828.

[130]

Huang Z, Yin X, Liu Y.Physics-guided deep neural network for structural damage identification.Ocean Eng 2022; 260:112073.

[131]

Deng W, Nguyen KTP, Medjaher K, Gogu C, Morio J.Rotor dynamics informed deep learning for detection, identification, and localization of shaft crack and unbalance defects.Adv Eng Inform 2023; 58:102128.

[132]

Tang K, Zhang P, Zhao Y, Zhong Z.Deep learning-based semantic segmentation for morphological fractography.Eng Fract Mech 2024; 303:110149.

[133]

Tsopanidis S, Osovski S.Unsupervised machine learning in fractography: evaluation and interpretation.Mater Charact 2021; 182:111551.

[134]

Rosenberger J, Tlatlik J, Münstermann S.Deep learning based initial crack size measurements utilizing macroscale fracture surface segmentation.Eng Fract Mech 2023; 293:109686.

[135]

Schmies L, Hemmleb M, Bettge D.Relevant input data for crack feature segmentation with deep learning on SEM imagery and topography data.Eng Fail Anal 2024; 156:107814.

[136]

Wang F, Zhang P, Bu H, Chen W, Li B, Zhan X.Effect of clamping pressure on interfacial fusion morphology and fracture mechanism of CFRTP/Ti6Al4V laser bonding joint featuring blind hole surface microtextures.Opt Laser Technol 2022; 153:108192.

[137]

Hao X, Liang G, Huang Y, Zhao J, Cheng M, Yang S, et al.Effect of addition on microstructures and mechanical properties of cBN/Cu-Zn-Ti composites via the pulse electric current sintering.J Alloys Compd 2025; 1010:177455.

[138]

Wang S, Zhang P, Zhou S, Wei DB, Ding F, Li FK.A computer vision based machine learning approach for fatigue crack initiation sites recognition.Comput Mater Sci 2020; 171:109259.

[139]

Jones K, Musinski WD, Pilchak AL, John R, Shade PA, Rollett AD, et al.Predicting fatigue crack growth metrics from fractographs: towards fractography by computer vision.Int J Fatigue 2023; 177:107915.

[140]

Mototake Y, Ito K, Demura M.Quantitative prediction of fracture toughness (K_I_c) of polymer by fractography using deep neural networks.Sci Technol Adv Material Meth 2022; 2(1):310-321.

[141]

Chen N, Ma R, Chen A, Cui C.PC-PINNs: physics-informed neural networks for solving the phase-field model of pitting corrosion.J.S. Jensen, D.M. Frangopol, J.W. Schmidt (Eds.), Bridge maintenance, safety, management, digitalization and sustainability, CRC Press, Parkway 2024; 244-252.

[142]

Chen N, Lucarini S, Ma R, Chen A, Cui C.PF-PINNs: physics-informed neural networks for solving coupled Allen–Cahn and Cahn–Hilliard phase field equations.J Comput Phys 2025; 529:113843.

[143]

Yu H, Hu Y, Kang G, Peng X, Chen B, Wu S.High-cycle fatigue life prediction of L-PBF AlSi10Mg alloys: a domain knowledge-guided symbolic regression approach.Philos Trans A Math Phys Eng Sci 2024; 382(2264):20220383.