Paper of Imran Nasim on dynamical systems and machine learning published in Mathematics

The paper “Dynamically Meaningful Latent Representations of Dynamical Systems“, co-authored by Imran Nasim (IBM, and Visiting Lecturer at Surrey) and Michael Henderson (IBM, New York), has been published in the MPDI journal “Mathematics” (open access link here). The paper presents a data-driven hybrid modeling approach to tackle the problem of reduction by combining numerically derived representations and latent representations obtained from an autoencoder. The latent representations are validated and they are shown to be dynamically interpretable. Furthermore, the paper probes the topological preservation of the latent representation with respect to the raw dynamical data using methods from persistent homology. Finally, the paper shows that the framework is generalizable, having been successfully applied to both integrable and non-integrable systems that capture a rich and diverse array of solution types. The methodology does not require any prior dynamical knowledge of the system and can be used to discover the intrinsic dynamical behavior in a purely data-driven way. The image below shows Figure 7 from the paper.