DeepONet for the Prediction of Failure Response of a Two-Dimensional Fibre-Reinforced Composite Plate

Georgios A. Drosopoulos; Georgios E. Stavroulakis

doi:10.53941/bci.2025.100005

Abstract

Applications in the field of data-driven mechanics are widely studied in the last years exploiting latest development of artificial intelligence. In this context, several machine learning techniques have been adopted to offer a fast and accurate prediction of the structural response of materials and complex structural systems. A relatively new machine learning concept relies on the use of Deep Operator Networks (DeepONets) that can approximate operators accurately and efficiently, from a relatively small dataset. The article, therefore, provides the methodology framework of applying a deep operator network (DeepONet) in structural mechanics applications. A dataset is developed using parametric non-linear finite element simulations for a two-dimensional fibre-reinforced composite structure. Then, a DeepONet is developed, aiming to predict the failure response of this structure. Comparison with results obtained from traditional Artificial Neural Networks (ANNs) is also presented. Results obtained from testing the trained DeepONet model on data not included in training indicate a proper performance. Testing the DeepONet model on unseen trunk input or branch input functions leads to satisfactory accuracy, while testing it on unseen trunk and branch input leads to a decent accuracy, that is improved compared with the one received from ANNs. Thus, the capacity of DeepONet to predict the response in the context of non-linear structural mechanics is evaluated.

References

1.
Asteris, P.G.; Drosopoulos, G.Α.; Cavaleri, L.; et al. Mapping and Revealing the Nature of Masonry Compressive Strength Using Computational Intelligence. Structures 2025, 78, 109189. https://doi.org/10.1016/j.istruc.2025.109189.
2.
Zhongbo, Y.; Hien, P.L. Pre-Trained Transformer Model as a Surrogate in Multiscale Computational Homogenization Framework for Elastoplastic Composite Materials Subjected to Generic Loading Paths. Comput. Methods Appl. Mech. Eng. 2024, 421, 116745. https://doi.org/10.1016/j.cma.2024.116745.
3.
Raissi, M.; Perdikaris, P.; Karniadakis, G.E. 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. https://doi.org/10.1016/j.jcp.2018.10.045.
4.
Milićević, B.; Ivanović, M.; Stojanović, B.; et al. Optimization of Physics-Informed Neural Networks for Efficient Surrogate Modeling of Huxley’s Muscle Model in Multi-Scale Finite Element Simulations. In Proceedings of the 2023 IEEE 23rd International Conference on Bioinformatics and Bioengineering (BIBE), Dayton, OH, USA, 4 December 2023; pp. 457–461.
5.
Sukhnandan, J.; Drosopoulos, G.A. A Machine Learning Approach Used to Predict the Peak Displacement, Base Shear and Fundamental Frequency of Multi-Storey Steel Structures under Seismic Excitation. Structures 2025, 73, 108367. https://doi.org/10.1016/j.istruc.2025.108367.
6.
Noureldin, M.; Ali, A.; Sim, S.; et al. A Machine Learning Procedure for Seismic Qualitative Assessment and Design of Structures Considering Safety and Serviceability. J. Build. Eng. 2022, 50, 104190. https://doi.org/10.1016/j.jobe.2022.104190.
7.
Asteris, P.G.; Lourenço, P.B.; Hajihassani, M.; et al. Soft Computing-Based Models for the Prediction of Masonry Compressive Strength. Eng. Struct. 2021, 248, 113276. https://doi.org/10.1016/j.engstruct.2021.113276.
8.
Asteris, P.G.; Skentou, A.D.; Bardhan, A.; et al. Soft Computing Techniques for the Prediction of Concrete Compressive Strength Using Non-Destructive Tests. Constr. Build. Mater. 2021, 303, 124450. https://doi.org/10.1016/j.conbuildmat.2021.124450.
9.
Asteris, P.G.; Skentou, A.D.; Bardhan, A.; et al. Predicting Concrete Compressive Strength Using Hybrid Ensembling of Surrogate Machine Learning Models. Cem. Concr. Res. 2021, 145, 106449. https://doi.org/10.1016/j.cemconres.2021.106449.
10.
Asteris, P.G.; Apostolopoulou, M.; Skentou, A.D.; et al. Application of Artificial Neural Networks for the Prediction of the Compressive Strength of Cement-Based Mortars. Comput. Concr. 2019, 24, 329–345. https://doi.org/10.12989/CAC.2019.24.4.329.
11.
Motsa, S.M.; Stavroulakis, G.Ε.; Drosopoulos, G.Α. A Data-Driven, Machine Learning Scheme Used to Predict the Structural Response of Masonry Arches. Eng. Struct. 2023, 296, 116912. https://doi.org/10.1016/j.engstruct.2023.116912.
12.
Fuhg, J.N.; Marino, M.; Bouklas, N. Local Approximate Gaussian Process Regression for Data-Driven Constitutive Models: Development and Comparison with Neural Networks. Comput. Methods Appl. Mech. Eng. 2022, 388, 114217. https://doi.org/10.1016/j.cma.2021.114217.
13.
Drosopoulos, G.A.; Stavroulakis, G.E. Nonlinear Mechanics for Composite Heterogeneous Structures; CRC Press: Boca Raton, FL, USA, 2022.
14.
Li, Z.; Kovachki, N.; Azizzadenesheli, K.; et al. Fourier Neural Operator for Parametric Partial Differential Equations. arXiv 2021, arXiv:2010.08895.
15.
Lu, L.; Jin, P.; Pang, G.; et al. Learning Nonlinear Operators via DeepONet Based on the Universal Approximation Theorem of Operators. Nat. Mach. Intell. 2021, 3, 218–229. https://doi.org/10.1038/s42256-021-00302-5.
16.
Lu, L.; Meng, X.; Mao, Z.; et al. DeepXDE: A Deep Learning Library for Solving Differential Equations. SIAM Rev. 2021, 63, 208–228. https://doi.org/10.1137/19m1274067.
17.
Yin, M.; Zhang, E.; Yu, Y.; et al. Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems. Comput. Methods Appl. Mech. Eng. 2022, 402, 115027. https://doi.org/10.1016/j.cma.2022.115027.
18.
He, J.; Kushwaha, S.; Park, J.; et al. Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-Field Solutions under Time-Dependent Loads. Eng. Appl. Artif. Intell. 2024, 127, 107258. https://doi.org/10.1016/j.engappai.2023.107258.
19.
Goswami, S.; Yin, M.; Yu, Y.; et al. A Physics-Informed Variational DeepONet for Predicting Crack Path in Quasi-Brittle Materials. Comput. Methods Appl. Mech. Eng. 2022, 391, 114587. https://doi.org/10.1016/j.cma.2022.114587.
20.
He, J.; Koric, S.; Kushwaha, S.; et al. Novel DeepONet Architecture to Predict Stresses in Elastoplastic Structures with Variable Complex Geometries and Loads. Comput. Methods Appl. Mech. Eng. 2023, 415, 116277. https://doi.org/10.1016/j.cma.2023.116277.
21.
Ahmed, B.; Qiu, Y.; Abueidda, D.W.; et al. Physics-Informed Deep Operator Networks with Stiffness-Based Loss Functions for Structural Response Prediction. Eng. Appl. Artif. Intell. 2025, 144, 110097. https://doi.org/10.1016/j.engappai.2025.110097.
22.
Abueidda, D.W.; Pantidis, P.; Mobasher, M.E. DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems. Comput. Methods Appl. Mech. Eng. 2025, 436, 117699. https://doi.org/10.1016/j.cma.2024.117699.
23.
Karniadakis, G.E.; Kevrekidis, I.G.; Lu, L.; et al. Physics-Informed Machine Learning. Nat Rev Phys 2021, 3, 422–440. https://doi.org/10.1038/s42254-021-00314-5.
24.
Chen, T.; Chen, H. Universal Approximation to Nonlinear Operators by Neural Networks with Arbitrary Activation Functions and Its Application to Dynamical Systems. IEEE Trans. Neural Netw. 1995, 6, 911–917. https://doi.org/10.1109/72.392253.
25.
Hornik, K.; Stinchcombe, M.; White, H. Multilayer Feedforward Networks Are Universal Approximators. Neural Netw. 1989, 2, 359–366. https://doi.org/10.1016/0893-6080(89)90020-8.
26.
Zhu, M.; Feng, S.; Lin, Y.; et al. Fourier-DeepONet: Fourier-Enhanced Deep Operator Networks for Full Waveform Inversion with Improved Accuracy, Generalizability, and Robustness. Comput. Methods Appl. Mech. Eng. 2023, 416, 116300. https://doi.org/10.1016/j.cma.2023.116300.
27.
Spathopoulos, S.C.; Stavroulakis, G.E. Springback Prediction in Sheet Metal Forming, Based on Finite Element Analysis and Artificial Neural Network Approach. Appl. Mech. 2020, 1, 97–110. https://doi.org/10.3390/applmech1020007.

Scilight Press

Author Information

Abstract

Keywords

References

About Scilight

Journals

Publishing Policies

Contact Us