2024/02/07 by Mairembam Kelvin Singh, Singh, Mairembam Kelvin, A. Surjalal Sharma +5
Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2403.06987
openalex publication_date 2024/02/07 · openalex created_date 2024/03/14 · openalex updated_date 2026/07/28
Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such systems where the volume of the phase space contracts with time. On the other hand, we employ dimensionality reduction techniques to study complicated and complex data, which are tough to analyse. The Principal Component Analysis (PCA) is a dimensionality reduction technique used as a means to study complex data. Through PCA, we studied the reduced dimensional features of the numerical data generated by a nonlinear partial differential equation called the Korteweg de Vries (KdV) equation, which is a nonlinear dispersive system, where solitary waves travel along a specific direction with finite amplitude. Dissipative nature, specific to that of the Lorenz system, were observed in the dimensionally reduced data, which implies a transition from a dispersive system to a dissipative system.