**Nonlinear data assimilation for ocean applications**

Peter Jan Van Leeuwen

Data assimilation (DA) combines information from observations with informations encoded in numerical models. Because the ocean flow field can be chaotic and observations are relatively sparse, the data-assimilation problem can be highly nonlinear. So-called particle filters are fully nonlinear DA methods, but cannot be used in standard form because they suffer from the curse of dimensionality. We explore so-called particle flows in which particles at observation times are subjected to a flow field that transports them from samples from the prior to samples from the posterior, thus solving the DA problem. Crucial for the methodology is the inclusion of techniques from machine learning, such as kernel embeddings and stochastic gradient descent methods. I will report on the methodology, applications to simplified systems, and plans for high-dimensional ocean applications.