Data Driven Model Reduction

Data-driven model reduction aims to create simplified, computationally efficient representations of complex systems using data, enabling faster simulations and real-time control. Current research emphasizes leveraging machine learning techniques, such as Koopman theory, autoencoders, and graph convolutional networks, often combined with traditional methods like Proper Orthogonal Decomposition, to build accurate reduced-order models for diverse applications. These advancements are particularly impactful for high-dimensional systems in areas like robotics, process control, and fluid dynamics, offering significant improvements in computational speed and enabling real-time control of previously intractable systems. The focus is on developing robust and accurate models, often incorporating structural information from the underlying physics to improve generalization and predictive capabilities.