Developing Latent Space System Identification Techniques for Autoencoders

A Brief Synopsis

Numerically solving time-dependent partial differential equations (PDEs) can be challenging and computationally expensive. This has prompted the development of reduced order models (ROMs) for providing fast and accurate approximate solutions. During my time at Lawrence Livermore National Lab, I worked on GPLaSDI: a noval ROM architecture that uses machine learning for compression and system identification methods for modelling the dynamics. In this project, I explored different system identification methods - non-linear basis functions for SINDy (Sparse Identification of NonLinear Dynamics) and Dynamic Mode Decomposition (DMD). The tests for these methods are conducted on standardized PDEs like Burgers1D and Two stream plasma instability problem. The corresponding results can be found here.

Documentation

The github repository to GPLaSDI and my work can be found here