Data Driven Reduced Order

Data-driven reduced-order modeling (ROM) aims to create computationally efficient surrogates for complex, high-dimensional systems, typically governed by partial differential equations, by leveraging machine learning to learn low-dimensional representations of the system's dynamics. Current research emphasizes non-intrusive methods, employing architectures like neural ordinary differential equations (NODEs), autoencoders (including variational and convolutional variants), and recurrent neural networks (RNNs, such as LSTMs), often combined with dimensionality reduction techniques such as proper orthogonal decomposition (POD). This approach significantly accelerates simulations and enables real-time predictions for applications ranging from fluid dynamics and process engineering to cardiovascular modeling and aerospace propulsion, impacting both scientific understanding and engineering design.