Physics Constrained Neural Networks for Engineering Modeling With Few Data Samples
DOI:
https://doi.org/10.66238/jaeee31Keywords:
physics-informed neural network, engineering modeling, PDE residual, physical constraint, fluid flow, heat conduction, model reliabilityAbstract
Data-driven neural networks are widely used in engineering modeling, but they may produce results that do not follow physical laws when training data are limited or boundary conditions change. This study proposes a physics-constrained neural-network method based on the PINN framework. PDE residuals, boundary conditions, and initial conditions are added to the training loss. Thus, the model can learn from both sampled data and physical equations. The method was tested on fluid-flow and heat-conduction cases. Navier–Stokes equations were used for flow modeling, and heat-conduction equations were used for temperature prediction. Compared with a traditional neural network, the proposed method reduced prediction error by about 32%. Under changed boundary conditions, the generalization error decreased by about 21%. The model also remained stable with limited training samples. These results show that physical constraints can improve prediction accuracy, physical consistency, and model reliability. The method provides a practical tool for flow prediction, thermal-field estimation, equipment monitoring, and fast engineering simulation
References
Gao, G., Ma, X., Lu, C., & Gao, R. (2026). Reliability Analysis and Application Research of SMS Communication Systems in Medical Notification Scenarios.
Padmaja, K., Kumar, B. R., Kumar, A. V., & Gorla, R. S. (2025). A comprehensive review of mathematical methods for fluid flow, heat and mass transfer problems: pros, cons and key findings: K. Padmaja et al. Journal of Thermal Analysis and Calorimetry, 150(16), 12075-12101.
Yan, B. (2026). A Comparative Study: Greedy versus GAN-Based Compressed Sensing for Fast MRI Reconstruction. International Journal of Advance in Applied Science Research, 5(3), 36-42.
Aldakheel, F., Elsayed, E. S., Heider, Y., & Weeger, O. (2025). Physics-based machine learning for computational fracture mechanics. Machine Learning for Computational Science and Engineering, 1(1), 18.
Wang, Y., Yin, X., Chen, J., & Wang, Y. (2026). Evidence-Based Study on Low-Burden Digital Phenotyping for Precision Screening of Oral Anti-Obesity Drug Efficacy.
Gamella, J. L., Peters, J., & Bühlmann, P. (2025). Causal chambers as a real-world physical testbed for AI methodology. Nature Machine Intelligence, 7(1), 107-118.
Jiao, Y., Wang, A., Zhao, B., & Shi, T. (2026). The Impact of Visual Language Strategies in Public Art Creation on Community Spatial Perception and Public Behavior.
Plankovskyy, S., Tsegelnyk, Y., Shyshko, N., Litvinchev, I., Romanova, T., & Velarde Cantú, J. M. (2025). Review of physics-informed neural networks: Challenges in loss function design and geometric integration. Mathematics, 13(20), 3289.
Liu, S., Liu, X., & Feng, H. (2025, November). Research on AI-Driven Visual Design and Immersive Interactive Experiences Based on Multimodal Cognition and User. In Proceedings of the 2025 International Conference on Digital Society and Intelligent Computing (pp. 734-740).
Mousa, J., Negny, S., & Ouaret, R. (2025). Hybrid neural networks for improved chemical process modeling: bridging data-driven insights with physical consistency. Digital Chemical Engineering, 100256.
Chen, F., Li, S., Liang, H., Xu, P., & Yue, L. (2025). Optimization Study of Thermal Management of Domestic SiC Power Semiconductor Based on Improved Genetic Algorithm.
Boza, A. B., Jiménez, J. J. M., & Vingerhoeds, R. (2026, January). A Multi-Metric Trade-Off Framework for AI Model Selection for Diagnosis and Prognosis in Predictive Maintenance. In 2026 International Workshop on Systems Engineering Research (pp. 1-8). IEEE.
Liang, R., Feifan, F. N. U., Liang, Y., & Ye, Z. (2025). Emotion-Aware Interface Adaptation in Mobile Applications Based on Color Psychology and Multimodal User State Recognition. Frontiers in Artificial Intelligence Research, 2(1), 51-57.
El Hassan, M., Mjalled, A., Miron, P., Mönnigmann, M., & Bukharin, N. (2025). Machine Learning in Fluid Dynamics—Physics-Informed Neural Networks (PINNs) Using Sparse Data: A Review. Fluids, 10(9).
Zhu, W., Yao, Y., & Yang, J. (2025). Optimizing Financial Risk Control for Multinational Projects: A Joint Framework Based on CVaR-Robust Optimization and Panel Quantile Regression.
Garcia-Ferreira, S., & Aguirre, G. (2025, June). Temperature Field Prediction and Convection Coefficient Estimation from Temperature Data Using PINNs. In International Conference on Thermal Issues in Machine Tools (pp. 573-587). Cham: Springer Nature Switzerland.
Feng, H. (2024, October). Design of Intelligent Charging System for Portable Electronic Devices Based on Internet of Things (IoT). In 2024 5th International Conference on Big Data, Artificial Intelligence and Internet of Things Engineering (ICBAIE) (pp. 568-571). IEEE.
Ghafoorian, F., Wang, Y., & Wan, H. (2025). Numerical analysis of thermal performance in triply periodic minimal surface structures with phase change material for passive thermal management. Journal of Energy Storage, 134, 118093.
Liu, S., & Yim, J. (2025). Research on Generative AI Creation Systems Based on Visual Language Modeling: Human-Machine Collaboration and Cognitive Feedback Mechanisms. Available at SSRN 6139770.
Totounferoush, A., Kotchourko, S., Mahoney, M. W., & Staab, S. (2025). Paving the way for scientific foundation models: enhancing generalization and robustness in PDEs with constraint-aware pre-training. arXiv preprint arXiv:2503.19081.
Chen, X., Xiao, H., Zeng, Z., Zhang, S., & Xiao, R. (2025). Fine-Grained Multivariate Time Series Anomaly Detection via Causal Inference. Knowledge-Based Systems, 114765.
El Hassan, M., Mjalled, A., Miron, P., Mönnigmann, M., & Bukharin, N. (2025). Machine Learning in Fluid Dynamics—Physics-Informed Neural Networks (PINNs) Using Sparse Data: A Review. Fluids, 10(9).
Gao, X., & Lan, Y. (2025, December). Data-Driven Identification Method for Low-Voltage Distribution Station-User Relationships Based on Voltage Sequence Correlation. In 2025 7th International Academic Exchange Conference on Science and Technology Innovation (IAECST) (pp. 508-512). IEEE.
Nooraiepour, M. (2025). Traditional and machine learning approaches to partial differential equations: A critical review of methods, trade-offs, and integration. Preprints (Sept. 2025). Doi, 10, 20944.
Gao, X., Chen, J., & Huang, M. (2026, January). Research on Risk Dependency Structures and Resource Allocation Optimization in New Energy Technology Collaboration within Enterprise Distributed Innovation. In 2026 International Conference on Electrical Engineering, Intelligent Control and Artificial Intelligence (EEICAI) (pp. 43-47). IEEE.
Utkarsh, U., Cai, P., Edelman, A., Gomez-Bombarelli, R., & Rackauckas, C. (2026). Physics-constrained flow matching: Sampling generative models with hard constraints. Advances in Neural Information Processing Systems, 38, 160217-160252.
Xu, S., Ma, Q., Liu, H., & Yue, L. (2026). Continuous Reorganization and Performance Preservation of Agent Memory Structure Under Distributed Change Environments.
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Copyright (c) 2026 Hannah Wong, Matthew Chan, Natalie Leung
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