Applications of Physics-Informed Machine Learning in Engineering

Dear Colleagues,

The integration of physics-informed machine learning (PIML) into engineering disciplines marks a paradigm shift that bridges the gap between empirical data and fundamental physical laws. By embedding domain-specific constraints—such as conservation laws, constitutive relationships, and boundary conditions—directly into neural network architectures, PIML models achieve superior generalization and interpretability compared to purely data-driven approaches. This methodology is particularly transformative in fields where experimental data is scarce, noisy, or computationally expensive to obtain, such as turbulent flow simulations, nonlinear material behavior prediction, and multiscale biological systems. The hybrid nature of PIML not only mitigates overfitting risks but also ensures that model outputs remain physically plausible, a critical requirement for engineering applications where safety and reliability are paramount.

Beyond its technical advantages, PIML fosters a symbiotic relationship between machine learning and traditional computational methods. For instance, in fluid dynamics, DeepONet-based models can accelerate Navier–Stokes simulations by orders of magnitude while preserving the fine-grained physics of turbulence. Similarly, in materials science, PIML enables the prediction of crack propagation by incorporating fracture mechanics principles into deep learning frameworks, circumventing the need for exhaustive experimental datasets. These advancements are not merely incremental improvements but represent a redefinition of how engineering problems are approached—by treating physics not as a limiting factor but as an enabling framework for innovation.

The current Special Issue on application of PIML in engineering serves as a timely compendium of these developments, offering practical case studies that demonstrate the methodology's versatility. It builds upon existing literature by systematically addressing key challenges, such as the trade-off between model complexity and physical fidelity, as well as strategies for integrating disparate sources of prior knowledge. Moreover, this Special Issue highlights emerging applications in interdisciplinary domains—like biomechanics and renewable energy systems—where traditional modeling approaches struggle to capture the full complexity of coupled phenomena. By providing a unified platform for showcasing these innovations, the collection not only advances the field but also establishes PIML as an indispensable tool for next-generation engineering design and discovery.

Prof. Dr. Xiaoning Zheng
Dr. Jianfang Lu
Guest Editors

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• PIML
• flow simulation
• material prediction
• biomechanics and biological systems
• multi-physics coupling problems
• sparse or low-data engineering problems
• digital twin of complex systems