Physics Informed Model Error for Data Assimilation

Jules Guillot (1) , Emmanuel Frénod (1) , Pierre Ailliot (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

Data assimilation consists in combining a dynamical model with noisy observations to estimate the latent true state of a system. The dynamical model is generally misspecified and this generates a model error which is usually treated using a random noise. The aim of this paper is to suggest a new treatment for the model error that further takes into account the physics of the system: the physics informed model error. This model error treatment is a noisy stationary solution of the true dynamical model. It is embedded in the ensemble Kalman filter (EnKF), which is a usual method for data assimilation. The proposed strategy is then applied to study the heat di↵usion in a bar when the external heat source is unknown. It is compared to usual methods to quantify the model error. The numerical results show that our method is more accurate, in particular when the observations are available at a low temporal resolution.

Mots clés: Data Assimilation; EnKF; Heat Equation; Model Error; Uncertainty Quantification; data assimilation; heat equation; model error; uncertainty quantification

Domaines: Statistiques [math.ST]; Equations aux dérivées partielles [math.AP]

Jules Guillot, Emmanuel Frénod, Pierre Ailliot. Physics Informed Model Error for Data Assimilation. Discrete and Continuous Dynamical Systems - Series S, In press, ⟨10.3934/dcdss.2022059⟩. ⟨hal-03615129⟩