Governing Equation

Discovering governing equations from data is a burgeoning field aiming to automate the process of deriving mathematical models describing physical systems, bypassing traditional theoretical derivations. Current research heavily utilizes machine learning, employing architectures like Physics-Informed Neural Networks (PINNs), Sparse Identification of Nonlinear Dynamics (SINDy), and graph neural networks, often incorporating techniques like symbolic regression and Bayesian inference to enhance robustness and uncertainty quantification. This approach promises to accelerate scientific discovery across diverse disciplines by enabling the analysis of complex systems with limited theoretical understanding and facilitating the development of more accurate and reliable predictive models for engineering and scientific applications.