Data-driven state estimation of 1D partial differential equation for plasma applications

Data-driven state estimation in systems controlled by partial differential equations is a challenging yet crucial task in various scientific disciplines. We introduce an innovative method, combining the capabilities of Kalman Filters and precise handling of noises, to carry out data-driven state estimation of multi-dimensional partial differential equations. The efficacy of our method efficacy is thoroughly tested in 1D, exemplified estimating an effective diffusion coefficient within a stochastic reaction-diffusion system as well as tracing the space-time evolution of the reaction term in an advection-reaction system to study discharge oscillations in Hall effect thrusters (HETs). This multi-dimensional state estimation technique offers a practical and efficient model-data fusion framework with broad applicability in plasma as well as numerous fields.