🧩Physics-informed machine learning uses optimization and machine learning techniques to incorporate and discover physics in complex systems.

🌌Parsimonious modeling involves learning differential equations from measurement data using machine learning algorithms.

🧠Physics-informed neural networks leverage known physics to improve the training and generalization of neural network models.

🧪Operator methods focus on learning solution operators of differential equations to model complex systems.

🌐Digital twins integrate physics-based models with real-world measurements to optimize and design complex engineering systems.