Efficient Structural Optimization of Space Trusses Using Artificial Neural Network-Based Surrogate Models
Abstract
The Artificial Neural Network (ANN) has emerged as an essential element in the modern structural optimization due to its outstanding ability to approximate nonlinear structural behavior and drastically reduce computation cost involved in numerous finite element analyses. The traditional optimization algorithm for truss structures usually involves thousands of structural analyses in the process of searching solutions, which implies substantial computation cost and limited application to large-size engineering optimization tasks. Recent research results in machine learning, surrogate modeling, and data-driven optimization show the possibility of replacing numerically expensive structural analyses with neural network-based model without loss of the solution accuracy. The work studies the utilization of Backpropagation Neural Network (BPNN) and Counterpropagation Neural Network (CPNN) models as surrogate structural analyzers for the weight optimization of truss structures. The two types of neural networks are trained on the dataset of structural responses obtained in the process of finite element analysis and incorporated into the optimization process. The performance of BPNN and CPNN models is analyzed according to computation efficiency, convergence properties, and approximation accuracy on a benchmark 52-member space truss. Moreover, the review of modern developments in machine learning-assisted structural optimization is presented. Both of the neural network architectures have shown considerable improvements in computation times while sustaining adequate accuracy of predictions. While the CPNN shows greater speed of convergence, BPNN shows better accuracy of structural responses predictions during the optimization process. This approach proves that application of ANN models for surrogate modeling can be considered as an effective and robust method of solving challenging structural optimization problems.
Keywords:
Artificial neural networks, Structural optimization, Truss structures, Backpropagation neural network, Counterpropagation neural network, Surrogate modeling, Machine learningReferences
- [1] Haykin, S. S. (2009). Neural networks and learning machines. Pearson. https://books.google.com/books?id=KCwWOAAACAAJ
- [2] Rao, S. S. (2019). Engineering optimization: Theory and practice. John Wiley & Sons. https://onlinelibrary.wiley.com/doi/book/10.1002/9781119454816
- [3] Simpson, T. W., Poplinski, J. D., Koch, P. N., & Allen, J. K. (2001). Metamodels for computer-based engineering design: Survey and recommendations. Engineering with computers, 17(2), 129–150. https://doi.org/10.1007/PL00007198
- [4] Yu, Y., Hur, T., Jung, J., & Jang, I. G. (2019). Deep learning for determining a near-optimal topological design without any iteration. Structural and multidisciplinary optimization, 59(3), 787–799. https://doi.org/10.1007/s00158-018-2101-5
- [5] Banga, S., Gehani, H., Bhilare, S., Patel, S., & Kara, L. (2021). 3D topology optimization using convolutional neural networks. https://doi.org/10.48550/arXiv.1808.07440
- [6] Wang, J., Chen, K., Yang, H., & Zhang, L. (2024). Ensemble deep learning enabled multi-condition generative design of aerial building machine considering uncertainties. Automation in construction, 157, 105134. https://doi.org/10.1016/j.autcon.2023.105134
- [7] Faroughi, S. A., Pawar, N. M., Fernandes, C., Raissi, M., Das, S., Kalantari, N. K., & Kourosh Mahjour, S. (2024). Physics-guided, physics-informed, and physics-encoded neural networks and operators in scientific computing: Fluid and solid mechanics. Journal of computing and information science in engineering, 24(4), 40802. https://doi.org/10.1115/1.4064449
- [8] Kaveh, A., & Mahdavi, V. R. (2014). Colliding bodies optimization: A novel meta-heuristic method. Computers & structures, 139, 18–27. https://doi.org/10.1016/j.compstruc.2014.04.005
- [9] Sahin, T., Wolff, D., von Danwitz, M., & Popp, A. (2024). Towards a hybrid digital twin: physics-informed neural networks as surrogate model of a reinforced concrete beam. https://doi.org/10.48550/arXiv.2405.08406
- [10] Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning. MIT Press. https://books.google.com/books?id=-s2MEAAAQBAJ
- [11] Adeli, H., & Park, H. S. (1995). A neural dynamics model for structural optimization—Theory. Computers & structures, 57(3), 383–390. https://doi.org/10.1016/0045-7949(95)00048-L
- [12] Sunil, P., & Sills, R. B. (2026). FE-PINNs: Finite-element-based physics-informed neural networks for surrogate modeling. APL machine learning, 4(1). https://doi.org/10.1063/5.0299671
- [13] Đorđević, F., & Marinković, M. (2025). PINN surrogate model for nonlinear equilibrium path analysis of von Mises shallow truss. Journal of big data, 12(1), 103. https://doi.org/10.1186/s40537-025-01095-9
- [14] Zhang, C., & Yu, J. (2025). Fem-constrained neural network-based surrogate model (FCNN-SM) for rapid structural response prediction: Algorithm framework and reliability analysis applications. International journal of solids and structures, 321, 113556. https://doi.org/10.1016/j.ijsolstr.2025.113556
- [15] Martinez, Y., Rojas, L., Peña, A., Valenzuela, M., & Garcia, J. (2025). Physics-informed neural networks for the structural analysis and monitoring of railway bridges: A systematic review. Mathematics, 13(10), 1–40. https://doi.org/10.3390/math13101571
- [16] Yarmohammadian, R., Put, F., & Van Coile, R. (2025). Physics-informed surrogate modelling in fire safety engineering: A systematic review. Applied sciences, 15(15), 1–36. https://doi.org/10.3390/app15158740
- [17] Baniya, S., & Maity, D. (2025). A comprehensive review of theoretical concepts and advancements in physics-informed neural networks with applications in structural engineering. Artificial intelligence review, 59(2), 49. https://doi.org/10.1007/s10462-025-11444-y
- [18] Deb, K., & Sundar, J. (2006). Reference point based multi-objective optimization using evolutionary algorithms. Proceedings of the 8th annual conference on genetic and evolutionary computation (pp. 635–642). New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/1143997.1144112
- [19] Sahin, T., Wolff, D., von Danwitz, M., & Popp, A. (2024). Towards a hybrid digital twin: fusing sensor information and physics in surrogate modeling of a reinforced concrete beam. 2024 sensor data fusion: Trends, solutions, applications (SDF) (pp. 1–8). IEEE. https://doi.org/10.1109/SDF63218.2024.10773885
- [20] López-González, N., Rodríguez, E., & Greiner, D. (2025). A multi-objective evolutionary computation approach for improving neural network-based surrogate models in structural engineering. Algorithms, 18(12), 1–20. https://doi.org/10.3390/a18120754
- [21] Vanderplaats, G. N. (1988). Multidiscipline design optimization. Applied mechanics reviews, 41(6), 257–262. https://doi.org/10.1115/1.3151897