Physics-Informed Dynamic Mode Decomposition

Explore the integration of physical laws into dynamic mode decomposition (DMD) through this informative video lecture by Peter Baddoo from MIT. Delve into the concept of physics-informed DMD (piDMD), which addresses limitations of standard DMD by incorporating fundamental physical principles such as symmetries, invariances, and conservation laws. Learn how piDMD optimization can be formulated as a Procrustes problem, restricting models to respect the physical structure of systems. Discover the focus on five key physical principles: conservation, self-adjointness, localization, causality, and shift-invariance. Gain insights into closed-form solutions and efficient algorithms for piDMD optimizations. Understand the advantages of piDMD models, including reduced overfitting, lower data requirements, and improved computational efficiency. Examine applications of piDMD across various challenging problems in physical sciences, from energy-preserving fluid flow to three-dimensional transitional channel flow. Compare the performance of piDMD against standard DMD in areas such as spectral identification, state prediction, and estimation of optimal forcings and responses.