Development of a Conceptual Framework for Physics-Informed Neural Networks for Nonlinear Material Systems
Keywords:
Physics-informed neural networks, Nonlinear material systems, Conceptual framework, Scientific machine learningAbstract
This qualitative study aims to develop a conceptual framework for Physics-Informed Neural Networks (PINNs) in nonlinear material systems. The study addresses the growing need for physically consistent machine learning models that can explain complex material behavior under limited experimental data conditions. A qualitative conceptual case study approach was used because the research focused on understanding the methodological structure, assumptions, and interpretive logic behind PINN-based material modeling. Data were collected through semi-structured interviews with 8 to 12 experts in computational mechanics, material modeling, machine learning, or PINNs, supported by documentation of academic articles published between 2020 and 2025 and nonparticipant observation of model-building logic in selected studies. The data were analyzed using reflexive thematic analysis. The findings revealed five main themes: the central role of physical laws, the importance of limited but meaningful data, the need for constitutive assumptions, the challenge of loss function design and training stability, and the role of interpretability in nonlinear material modeling. These findings show that PINNs should not be viewed only as computational tools, but as hybrid conceptual frameworks that connect material mechanics, governing equations, empirical data, and neural network learning. The study contributes to the theoretical development of scientific machine learning and offers practical guidance for researchers who design PINN models for nonlinear materials. Future research should validate the proposed framework through simulation studies, experimental datasets, and comparative applications across different material systems.
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