Identifying Governing ODEs in Irregular Physical Domain with Diffusion

Simulating the complex plasmas created in experiments performed on the Z-Machine at Sandia National Laboratories is challenging due to both the range of spatio-temporal scales and the poorly constrained physical models needed to describe the system. In addition, the transient nature of the pulsed power drive results in a lack of a physically meaningful average or steady state about which the physical system could be linearized. Overall, this means that applying existing reduced order models (ROMs) to these transient, multi-scale, multi-physics systems presents a severe challenge. Here we develop a ROM for simulation data of 1D magnetic diffusion through a slab of finite resistivity. This problem addresses challenges regarding sharp boundaries and transient dynamics within the domain of interest. Making use of proper orthogonal decomposition (POD) coupled with the Sparse Identification of Nonlinear Dynamics (SINDy) model discovery method, we recover ordinary differential equations describing system evolution with varying amounts of problem periodicity. Finally, we examine the effects of noise and physics constraints when recovering this behavior.