Using physics-informed neural networks (PINNs) to predict dynamic behaviors in complex systems

Predicting dynamic behaviors in complex systems such as chaotic flows, turbulent fluids, and nonlinear vibrations remains a major challenge. Classical numerical methods struggle with high dimensionality, unknown parameters, noisy data, and sensitivity to initial conditions. Physics‑Informed Neural Networks (PINNs) offer a transformative alternative by embedding physical laws directly into the loss function of deep neural networks, enabling accurate predictions from sparse measurements. This review synthesizes recent advances (۲۰۲۴–۲۰۲۶) in PINN‑based dynamic prediction based on ۴۱ peer‑reviewed sources. We present a taxonomy of advanced architectures: causal PINNs with ResNet blocks for chaotic systems, neural operators (DeepONet, FNO, PINO) for parameter‑to‑solution mapping, Hamiltonian PINNs for energy conservation, domain decomposition (XPINN, NeuroSEM) for multiscale problems, and meta‑learning adaptive frameworks. Key applications span fluid dynamics, structural vibrations, quantum mechanics, geophysics, biomedical engineering, and industrial systems. Major challenges include convergence difficulties, loss imbalance, uncertainty, computational cost, and interpretability. Future directions point to trustworthy PINNs, foundation models, and real‑time deployment.

کلیدواژه ها:

: Physics‑Informed Neural Networks ، Dynamic Behavior Prediction ، Complex Systems ، Chaotic Dynamics ، Neural Operators