Response estimation and system identification of dynamical systems via physics-informed neural networks

Area of Science:

• Engineering
• Computational Science
• Machine Learning

Background:

• Accurate modeling of structural dynamics is vital for engineering applications like Structural Health Monitoring (SHM).
• Physics-based models often struggle with nonlinearities and uncertainties, especially with sparse sensor data.
• Existing methods face challenges in precise system identification and parameter estimation.

Purpose of the Study:

• To explore the application of Physics-Informed Neural Networks (PINNs) for identifying and estimating dynamical systems.
• To investigate PINNs for state estimation with sparse sensing and joint state-parameter estimation.
• To evaluate PINNs for parameter estimation from full-field data within a Bayesian framework.

Main Methods:

• Utilizing Physics-Informed Neural Networks (PINNs), a physics-enhanced machine learning (PEML) technique.
• Embedding physical laws directly into the neural network's loss function.
• Applying PINNs to state estimation, joint state-parameter estimation, and parameter estimation with uncertainty quantification.

Main Results:

• PINNs demonstrated efficiency across all investigated tasks, including systems with modeling errors.
• PINNs effectively handle complex phenomena and uncertainties in dynamical system modeling.
• Parameter estimation proved more sensitive to modeling errors compared to state estimation.

Conclusions:

• PINNs offer a promising and robust tool for dynamical system modeling and identification.
• The integration of physical laws enhances machine learning models' ability to handle real-world engineering challenges.
• PINNs provide a valuable approach for improving accuracy and reliability in structural dynamics applications.