Class of 1960s Speaker, Dr. Neranjaka Jayarathne, Clarkson University

Autoencoders with Time Delay Encoding in Data-Driven Science and Engineering for Reduced Order Modelling by Dr. Neranjaka Jayarathne, Research Associate, Clarkson University Center for Complex Systems Science, Mathematics Class of 1960s Speaker, Friday, April 21, 1 – 1:45 pm, North Science Building 015, Wachenheim.

Abstract:  In this talk, we present a novel approach to enhancing the effectiveness of Reduce Order Modeling (ROM) for representing higher-order dynamical systems.  The proposed approach utilizes Deep Autoencoders (DAE), an unsupervised learning technique capable of compressing large datasets and reducing their dimensionality.  By leveraging DAEs, we can transform data streams from dynamical systems, enabling manifold learning and non-linear transformations.  Our study shows that DAE-based ROM can effectively handle noisy data with a high degree of accuracy, reducing computational overhead significantly.  We demonstrate this by simulating the ROM of trajectories of the Van der Pol (VdP) oscillator, where we observe non-linear and tolerant-to-noise transformations produced by DAEs.  However, it is important to note that these transformations are arbitrary and not deterministic.  o further optimize the performance of the DAE, we suggest using time delay embeddings for individual trajectories, which enhances the loss function during training and increases the suitability of the ROM. Our findings suggest that DAE-based ROM is a promising approach for developing computationally efficient representations of higher-order dynamical systems, and we recommend further exploration of this approach in future research.