Oana Lang

Eulerian calibration for stochastic models

Stochastic partial differential equations are widely used to model the evolution of uncertain dynamical systems in geophysical fluid dynamics. For a judicious modelling of the evolution of a fluid flow, the noise term needs to be properly calibrated. Lagrangian methods have been developed in this sense, where particle trajectories are simulated starting from each point on both the physical grid and its refined version, then the differences between the particle positions are used to calibrate the noise. This is computationally expensive and not fully justified from a theoretical perspective. We propose an Eulerian alternative which is tested on a stochastic rotating shallow water system, but it can be applied to a general class of stochastic models. This is joint work with Dan Crisan and Alex Lobbe and the results are being published in “Noise calibration for SPDEs: a case study for the rotating shallow water model” (Foundations of Data Science), arXiv:2305.03548.