A structurally informed data assimilation approach for nonlinear partial differential equations

Tongtong Li, Anne Gelb, Yoonsang Lee

Abstract: Highlights•Development of a structurally informed prior that exploits statistical information from the state variable gradient.•New balancing of the data and model terms in the objective function accordingly.•Refinement of the local information regarding discontinuities in the solution.•Improved accuracy of state variable estimates with discontinuous profiles.