Physics guided neural networks for modelling of non-linear dynamics

Area of Science:

• Artificial Intelligence
• Nonlinear Dynamics
• Machine Learning

Background:

• Deep neural networks (DNNs) excel at pattern recognition in large datasets.
• Training DNNs on complex dynamical systems is challenging due to data inefficiency and sensitivity.
• Existing methods struggle with learning nonlinear system dynamics from data alone.

Purpose of the Study:

• To enhance the training of deep neural networks for complex dynamical systems.
• To improve model accuracy, reduce uncertainty, and accelerate convergence.
• To demonstrate the efficacy of physics-guided neural networks.

Main Methods:

• Injecting partially known information into an intermediate layer of a DNN.
• Utilizing physics-guided neural networks (PGNNs).
• Testing PGNNs on five well-known nonlinear dynamical systems.

Main Results:

• Improved model accuracy and reduced uncertainty in DNNs.
• Faster convergence during the training process.
• Successful learning of dynamics for Lotka-Volterra, Duffing, Van der Pol, Lorenz, and Henon-Heiles systems.

Conclusions:

• Physics-guided neural networks offer a robust approach to learning complex dynamical systems.
• Integrating domain knowledge significantly benefits deep learning models.
• PGNNs represent a promising advancement in AI for scientific modeling.